#CEJ ,,BC
           ,,ON ,,! ,,H1V5S
               0,>I/OTLE
      TRANSLAT$ BY ;,J4 ,L4 ,/OCKS
    ,TRANSLAT$ 6,GRADE ,,II ,BRL 0,MIKE
    ,KEI?LEY
                ,BOOK ,I
                   #A
  ,! SCI;E : HAS 6D ) NATURE CLE>LY
3C]NS XF =! MO/ "P ) BODIES & MAGNITUDES
& _! PROP]TIES & MOVE;TS1 B AL )!
PR9CIPLES ( ? SORT ( SUB/.E1 Z _M Z !Y
MAY BE4 ,=( ?+S 3/ITUT$ 0NATURE "S >E
BODIES & MAGNITUDES1 "S POSSESS BODY &
MAGNITUDE1 & "S >E PR9CIPLES ( ?+S :
POSSESS ^!4 ,N[ A 3T9UUM IS T : IS
DIVISI# 96"PS ALW CAPA# ( SUBDIVI.N1 &A
BODY IS T : IS E WAY DIVISI#4 ,A
MAGNITUDE IF DIVISI# "O WAY IS A L9E1 IF
TWO WAYS A SURFACE1 & IF ?REE A BODY4
,2Y ^! "! IS NO O!R MAGNITUDE1 2C ! ?REE
DIM5.NS >E ALL T "! >E1 & T : IS DIVISI#
9 ?REE DIREC;NS IS DIVISI# 9 ALL4 ,=1 Z
! ,PY?AGOR1NS SAY1 ! _W & ALL T IS 9 X
IS DET]M9$ 0! NUMB] ?REE1 S9CE 2G9N+ &
MI4LE & 5D GIVE ! NUMB] ( AN ,8ALL0'1 &!
NUMB] !Y GIVE IS ! TRIAD4 ,& S1 HAV+
TAK5 ^! ?REE F NATURE Z 7S 6SP1K7 LAWS (
X1 WE MAKE FUR!R USE (! NUMB] ?REE 9 !
WOR%IP (! ,GODS4 ,FUR!R1 WE USE ! T]MS 9
PRACTICE 9 ? WAY4 ,( TWO ?+S1 OR M51 WE
SAY ,8BO?0'1 B N ,8ALL0'3 ?REE IS ! F/
NUMB] 6: ! T]M ,8ALL0' HAS BE5
APPROPRIAT$4 ,& 9 ?1 Z WE H SD1 WE D B
FOLL[ ! L1D : NATURE GIVES4 ,"!=E1 S9CE
,8E0' & ,8ALL0' & ,8-PLETE0' D N DI6] F
"O ANO!R 9 RESPECT ( =M1 B ONLY1 IF AT
ALL1 9 _! MATT] & 9 T 6: !Y >E APPLI$1
BODY AL"O AM;G MAGNITUDES C 2 -PLETE4 ,=
X AL"O IS DET]M9$ 0! ?REE DIM5.NS1 T IS1
IS AN ,8ALL0'4 ,B IF X IS DIVISI# 9 ?REE
DIM5.NS X IS E WAY DIVISI#1 :ILE ! O!R
MAGNITUDES >E DIVISI# 9 "O DIM5.N OR 9
TWO AL"O3 =! DIVISIBIL;Y & 3T9U;Y (
MAGNITUDES DEP5D ^U ! NUMB] (! DIM5.NS1
"O SORT 2+ 3T9U\S 9 "O DIREC;N1 ANO!R 9
TWO1 ANO!R 9 ALL4 ,ALL MAGNITUDES1 !N1 :
>E DIVISI# >E AL 3T9U\S4 ,:E!R WE C AL
SAY T :AT"E IS 3T9U\S IS DIVISI# DOES N
YET1 ON \R PRES5T GR.DS1 APPE>4 ,"O ?+1
H["E1 IS CLE>4 ,WE _C PASS 2Y BODY 6A
FUR!R K9D1 Z WE PASS$ F L5G? 6SURFACE1 &
F SURFACE 6BODY4 ,= IF WE CD1 X WD C1SE
6BE TRUE T BODY IS -PLETE MAGNITUDE4 ,WE
CD PASS 2Y X ONLY 9 VIRTUE (A DEFECT 9
X2 & T : IS -PLETE _C 2 DEFECTIVE1 S9CE
X HAS 2+ 9 E RESPECT4 ,N[ BODIES : >E
CLASS$ Z "PS (! :OLE >E EA* -PLETE AC
6\R =MULA1 S9CE EA* POSSESSES E DIM5.N4
,B EA* IS DET]M9$ RELATIVELY 6T "P : IS
NEXT 6X 03TACT1 = : R1SON EA* ( !M IS 9
A S5SE _M BODIES4 ,B ! :OLE ( : !Y >E
"PS M/ NECESS>ILY 2 -PLETE1 & ?US1 9
A3ORD.E )! M1N+ (! ^W1 H 2+1 N 9 "S
RESPECT ONLY1 B 9 E RESPECT4
                   #B
  ,! "Q Z 6! NATURE (! :OLE1 :E!R X IS
9F9ITE 9 SIZE OR LIMIT$ 9 XS TOTAL MASS1
IS A MATT] = SUBSEQU5T 9QUIRY4 ,WE W N[
SP1K ( ^? "PS (! :OLE : >E SPECIFIC,Y
4T9CT4 ,LET U TAKE ? Z \R />T+-PO9T4
,ALL NATURAL BODIES & MAGNITUDES WE HOLD
6BE1 Z S*1 CAPA# ( LOCOMO;N2 = NATURE1
WE SAY1 IS _! PR9CIPLE ( MOVE;T4 ,B ALL
MOVE;T T IS 9 PLACE1 ALL LOCOMO;N1 Z WE
T]M X1 IS EI /RAI<T OR CIRCUL> OR A
-B9,N ( ^! TWO1 : >E ! ONLY SIMPLE
MOVE;TS4 ,&! R1SON ( ? IS T ^! TWO1 !
/RAI<T &! CIRCUL> L9E1 >E ! ONLY SIMPLE
MAGNITUDES4 ,N[ REVOLU;N AB ! C5TRE IS
CIRCUL> MO;N1 :ILE ! UPW>D & D[NW>D
MOVE;TS >E 9 A /RAI<T L9E1 ,8UPW>D0'
M1N+ MO;N AWAY F ! C5TRE1 & ,8D[NW>D0'
MO;N T[>DS X4 ,ALL SIMPLE MO;N1 !N1 M/ 2
MO;N EI AWAY F OR T[>DS OR AB ! C5TRE4
,? SEEMS 6BE 9 EXACT A3ORD ) :AT WE SD
ABV3 Z BODY F.D XS -PLE;N 9 ?REE
DIM5.NS1 S XS MOVE;T -PLETES XF 9 ?REE
=MS4
  ,BODIES >E EI SIMPLE OR -P.D$ ( S*2 &
0SIMPLE BODIES ,I M1N ^? : POSSESS A
PR9CIPLE ( MOVE;T 9 _! [N NATURE1 S* Z
FIRE & E>? ) _! K9DS1 & :AT"E IS AK9
6!M4 ,NECESS>ILY1 !N1 MOVE;TS AL W 2 EI
SIMPLE OR 9 "S SORT -P.D-SIMPLE 9 ! CASE
(! SIMPLE BODIES1 -P.D 9 T (! -POSITE-&
9 ! LATT] CASE ! MO;N W 2 T (! SIMPLE
BODY : PREVAILS 9 ! -POSI;N4 ,SUPPOS+1
!N1 T "! IS S* A ?+ Z SIMPLE MOVE;T1 & T
CIRCUL> MOVE;T IS AN 9/.E ( X1 & T BO?
MOVE;T (A SIMPLE BODY IS SIMPLE & SIMPLE
MOVE;T IS (A SIMPLE BODY 7= IF X IS
MOVE;T (A -P.D X W 2 9 VIRTUE (A
PREVAIL+ SIMPLE ELE;T71 !N "! M/
NECESS>ILY 2 "S SIMPLE BODY : REVOLVES
NATUR,Y & 9 VIRTUE ( XS [N NATURE )A
CIRCUL> MOVE;T4 ,03/RA9T1 ( C\RSE1 X MAY
2 BR"\ 6MOVE )! MO;N ( "S?+ ELSE DI6]5T
F XF1 B X _C S MOVE NATUR,Y1 S9CE "! IS
"O SORT ( MOVE;T NATURAL 6EA* (! SIMPLE
BODIES4 ,AG1 IF ! UNNATURAL MOVE;T IS !
3TR>Y (! NATURAL &A ?+ C H NO M ?AN "O
3TR>Y1 X W FOLL[ T CIRCUL> MOVE;T1 2+ A
SIMPLE MO;N1 M/ 2 UNNATURAL1 IF X IS N
NATURAL1 6! BODY MOV$4 ,IF !N 7#A7 !
BODY1 ^: MOVE;T IS CIRCUL>1 IS FIRE OR
"S O!R ELE;T1 XS NATURAL MO;N M/ 2 !
3TR>Y (! CIRCUL> MO;N4 ,B A S+LE ?+ HAS
A S+LE 3TR>Y2 & UPW>D & D[NW>D MO;N >E !
3TR>IES ( "O ANO!R4 ,IF1 ON ! O!R H&1
7#B7 ! BODY MOV+ ) ? CIRCUL> MO;N : IS
UNNATURAL 6X IS "S?+ DI6]5T F ! ELE;TS1
"! W 2 "S O!R MO;N : IS NATURAL 6X4 ,B ?
_C BE4 ,= IF ! NATURAL MO;N IS UPW>D1 X
W 2 FIRE OR AIR1 & IF D[NW>D1 WAT] OR
E>?4 ,FUR!R1 ? CIRCUL> MO;N IS
NECESS>ILY PRIM>Y4 ,=! P]FECT IS NATUR,Y
PRIOR 6! IMP]FECT1 &! CIRCLE IS A P]FECT
?+4 ,? _C 2 SD ( ANY /RAI<T L9E3-N ( AN
9F9ITE L9E2 =1 IF X 7 P]FECT1 X WD H A
LIMIT & AN 5D3 NOR ( ANY F9ITE L9E2 = 9
E CASE "! IS "S?+ 2Y X1 S9CE ANY F9ITE
L9E C 2 EXT5D$4 ,& S1 S9CE ! PRIOR
MOVE;T 2L;GS 6! BODY : NATUR,Y PRIOR1 &
CIRCUL> MOVE;T IS PRIOR 6/RAI<T1 &
MOVE;T 9 A /RAI<T L9E 2L;GS 6SIMPLE
BODIES-FIRE MOV+ /RAI<T UPW>D & E>?Y
BODIES /RAI<T D[NW>D T[>DS ! C5TRE-S9CE
? IS S1 X FOLL[S T CIRCUL> MOVE;T AL M/
2 ! MOVE;T ( "S SIMPLE BODY4 ,=! MOVE;T
( -POSITE BODIES IS1 Z WE SD1 DET]M9$ 0T
SIMPLE BODY : PREPOND]ATES 9 ! -POSI;N4
,^! PREMISES CLE>LY GIVE ! 3CLU.N T "!
IS 9 NATURE "S BODILY SUB/.E O!R ?AN !
=M,NS WE "K1 PRIOR 6!M ALL & M DIV9E ?AN
!Y4 ,B X MAY AL 2 PROV$ Z FOLL[S4 ,WE
MAY TAKE X T ALL MOVE;T IS EI NATURAL OR
UNNATURAL1 & T ! MOVE;T : IS UNNATURAL
6"O BODY IS NATURAL 6ANO!R-Z1 = 9/.E1 IS
! CASE )! UPW>D & D[NW>D MOVE;TS1 : >E
NATURAL & UNNATURAL 6FIRE & E>?
RESPECTIVELY4 ,X NECESS>ILY FOLL[S T
CIRCUL> MOVE;T1 2+ UNNATURAL 6^! BODIES1
IS ! NATURAL MOVE;T ( "S O!R4 ,FUR!R1
IF1 ON ! "O H&1 CIRCUL> MOVE;T IS
NATURAL 6"S?+1 X M/ SURELY 2 "S SIMPLE &
PRIM>Y BODY : IS ORDA9$ 6MOVE )A NATURAL
CIRCUL> MO;N1 Z FIRE IS ORDA9$ 6FLY UP &
E>? D[N4 ,IF1 ON ! O!R H&1 ! MOVE;T (!
ROTAT+ BODIES AB ! C5TRE IS UNNATURAL1 X
WD 2 REM>KA# & 9DE$ Q 9CONCEIVA# T ?
MOVE;T AL"O %D 2 3T9U\S & ET]NAL1 2+
N"E!.S 3TR>Y 6NATURE4 ,AT ANY RATE !
EVID;E ( ALL O!R CASES GOES 6%[ T X IS !
UNNATURAL : QKE/ PASSES AWAY4 ,& S1 IF1
Z "S SAY1 ! BODY S MOV$ IS FIRE1 ?
MOVE;T IS J Z UNNATURAL 6X Z D[NW>D
MOVE;T2 = ANY "O C SEE T FIRE MOVES 9 A
/RAI<T L9E AWAY F ! C5TRE4 ,ON ALL ^!
GR.DS1 "!=E1 WE MAY 9F] ) 3FID;E T "! IS
"S?+ 2Y ! BODIES T >E AB U ON ? E>?1
DI6]5T & SEP>ATE F !M2 & T ! SUP]IOR
GLORY ( XS NATURE IS PROPOR;NATE 6XS
4T.E F ? _W ( \RS4
                   #C
  ,9 3SEQU;E ( :AT HAS BE5 SD1 9 "P 0WAY
( ASSUMP;N & 9 "P 0WAY ( PRO(1 X IS CLE>
T N E BODY EI POSSESSES LI<T;S OR
H1VI;S4 ,Z A PRELIM9>Y WE M/ EXPLA9 9
:AT S5SE WE >E US+ ! ^WS ,8H1VY0' &
,8LI<T0'1 SU6ICI5TLY1 AT L1/1 = \R
PRES5T PURPOSE3 WE C EXAM9E ! T]MS M
CLOSELY LAT]1 :5 WE -E 63SID] _!
ESS5TIAL NATURE4 ,LET U !N APPLY ! T]M
,8H1VY0' 6T : NATUR,Y MOVES T[>DS !
C5TRE1 & ,8LI<T0' 6T : MOVES NATUR,Y
AWAY F ! C5TRE4 ,! H1VIE/ ?+ W 2 T :
S9KS 6! BOTTOM ( ALL ?+S T MOVE D[NW>D1
&! LI<TE/ T : RISES 6! SURFACE ( "EY?+ T
MOVES UPW>D4 ,N[1 NECESS>ILY1 "EY?+ :
MOVES EI UP OR D[N POSSESSES LI<T;S OR
H1VI;S OR BO?-B N BO? RELATIVELY 6! SAME
?+3 = ?+S >E H1VY & LI<T RELATIVELY 6"O
ANO!R2 AIR1 = 9/.E1 IS LI<T RELATIVELY
6WAT]1 & WAT] LI<T RELATIVELY 6E>?4 ,!
BODY1 !N1 : MOVES 9 A CIRCLE _C POSSIBLY
POSSESS EI H1VI;S OR LI<T;S4 ,= NEI
NATUR,Y NOR UNNATUR,Y C X MOVE EI T[>DS
OR AWAY F ! C5TRE4 ,MOVE;T 9 A /RAI<T
L9E C]TA9LY DOES N 2L;G 6X NATUR,Y1 S9CE
"O SORT ( MOVE;T IS1 Z WE SAW1
APPROPRIATE 6EA* SIMPLE BODY1 & S WE %D
2 -PELL$ 6ID5TIFY X ) "O (! BODIES :
MOVE 9 ? WAY4 ,SUPPOSE1 !N1 T ! MOVE;T
IS UNNATURAL4 ,9 T CASE1 IF X IS !
D[NW>D MOVE;T : IS UNNATURAL1 ! UPW>D
MOVE;T W 2 NATURAL2 & IF X IS ! UPW>D :
IS UNNATURAL1 ! D[NW>D W 2 NATURAL4 ,=
WE DECID$ T ( 3TR>Y MOVE;TS1 IF ! "O IS
UNNATURAL 6ANY?+1 ! O!R W 2 NATURAL 6X4
,B S9CE ! NATURAL MOVE;T (! :OLE &( XS
"P ( E>?1 = 9/.E1 Z A :OLE &(A SMALL
CLOD-H "O &! SAME DIREC;N1 X RESULTS1 9
! F/ PLACE1 T ? BODY C POSSESS NO LI<T;S
OR H1VI;S AT ALL 7= T WD M1N T X CD MOVE
0XS [N NATURE EI F OR T[>DS ! C5TRE1 :1
Z WE "K1 IS IMPOSSI#72 &1 SECONDLY1 T X
_C POSSIBLY MOVE 9 ! WAY ( LOCOMO;N 02+
=C$ VIOL5TLY ASIDE 9 AN UPW>D OR D[NW>D
DIREC;N4 ,= NEI NATUR,Y NOR UNNATUR,Y C
X MOVE ) ANY O!R MO;N B XS [N1 EI XF OR
ANY "P ( X1 S9CE ! R1SON+ : APPLIES 6!
:OLE APPLIES AL 6! "P4
  ,X IS EQU,Y R1SONA# 6ASSUME T ? BODY W
2 UNG5]AT$ & 9DE/RUCTI# & EXEMPT F
9CR1SE & ALT],N1 S9CE "EY?+ T -ES 6BE
-ES 962+ F XS 3TR>Y & 9 "S SUB/RATE1 &
PASSES AWAY LIKEWISE 9 A SUB/RATE 0!
AC;N (! 3TR>Y 96! 3TR>Y1 Z WE EXPLA9$ 9
\R OP5+ 4CUS.NS4 ,N[ ! MO;NS ( 3TR>IES
>E 3TR>Y4 ,IF !N ? BODY C H NO 3TR>Y1 2C
"! C 2 NO 3TR>Y MO;N 6! CIRCUL>1 NATURE
SEEMS JU/LY 6H EXEMPT$ F 3TR>IES ! BODY
: 0 6BE UNG5]AT$ & 9DE/RUCTI#4 ,= X IS 9
3TR>IES T G5],N & DECAY SUBSI/4 ,AG1 T :
IS SUBJECT 69CR1SE 9CR1SES ^U 3TACT )A
K9DR$ BODY1 : IS RESOLV$ 96XS MATT]4 ,B
"! IS NO?+ \ ( : ? BODY C H BE5 G5]AT$4
,& IF X IS EXEMPT F 9CR1SE & DIM9U;N1 !
SAME R1SON+ L1DS U 6SUPPOSE T X IS AL
UNALT]A#4 ,= ALT],N IS MOVE;T 9 RESPECT
( QUAL;Y2 & QUALITATIVE /ATES &
4POSI;NS1 S* Z H1L? & 41SE1 D N -E 962+
)\T *ANGES ( PROP]TIES4 ,B ALL NATURAL
BODIES : *ANGE _! PROP]TIES WE SEE 6BE
SUBJECT )\T EXCEP;N 69CR1SE & DIM9U;N4
,? IS ! CASE1 = 9/.E1 )! BODIES (
ANIMALS & _! "PS &) VEGETA# BODIES1 &
SIMIL>LY AL ) ^? (! ELE;TS4 ,& S1 IF !
BODY : MOVES )A CIRCUL> MO;N _C ADMIT (
9CR1SE OR DIM9U;N1 X IS R1SONA# 6SUPPOSE
T X IS AL UNALT]A#4
  ,! R1SONS :Y ! PRIM>Y BODY IS ET]NAL &
N SUBJECT 69CR1SE OR DIM9U;N1 B UNAG+ &
UNALT]A# & UNMODIFI$1 W 2 CLE> F :AT HAS
BE5 SD 6ANY "O :O 2LIEVES 9 \R
ASSUMP;NS4 ,\R !ORY SEEMS 63FIRM EXP]I;E
& 6BE 3FIRM$ 0X4 ,= ALL M5 H "S 3CEP;N (
! NATURE (! GODS1 & ALL :O 2LIEVE 9 !
EXI/;E ( GODS AT ALL1 :E!R B>B>IAN OR
,GREEK1 AGREE 9 ALLOTT+ ! HI<E/ PLACE 6!
DE;Y1 SURELY 2C !Y SUPPOSE T IMMORTAL IS
L9K$ ) IMMORTAL & REG>D ANY O!R
SUPPOSI;N Z 9CONCEIVA#4 ,IF !N "! IS1 Z
"! C]TA9LY IS1 ANY?+ DIV9E1 :AT WE H J
SD AB ! PRIM>Y BODILY SUB/.E 0 WELL SD4
,! M]E EVID;E (! S5SES IS 5 63V9CE U (
?1 AT L1/ ) HUMAN C]TA9TY4 ,= 9 ! :OLE
RANGE ( "T PA/1 S F> Z \R 9H]IT$ RECORDS
R1*1 NO *ANGE APPE>S 6H TAK5 PLACE EI 9
! :OLE S*EME (! \T]MO/ H1V5 OR 9 ANY (
XS PROP] "PS4 ,! -MON "N1 TOO1 : HAS BE5
H&$ D[N F \R 4TANT ANCE/ORS EV5 6\R [N
"D1 SEEMS 6%[ T !Y 3CVD ( X 9 ! FA%ION :
WE H BE5 EXPRESS+4 ,! SAME ID1S1 "O M/
2LIEVE1 RECUR 9 M5'S M9DS N ONCE OR
TWICE B AG & AG4 ,& S1 IMPLY+ T ! PRIM>Y
BODY IS "S?+ ELSE 2Y E>?1 FIRE1 AIR1 &
WAT]1 !Y GAVE ! HI<E/ PLACE A "N ( XS
[N1 AI!R1 DERIV$ F ! FACT T X ,8RUNS
ALW0' = AN ET]N;Y ( "T4 ,ANAXAGORAS1
H["E1 SC&AL\SLY MISUSES ? "N1 TAK+ AI!R
Z EQUIVAL5T 6FIRE4
  ,X IS AL CLE> F :AT HAS BE5 SD :Y !
NUMB] ( :AT WE CALL SIMPLE BODIES _C 2
GRT] ?AN X IS4 ,! MO;N (A SIMPLE BODY M/
XF 2 SIMPLE1 & WE ASS]T T "! >E ONLY ^!
TWO SIMPLE MO;NS1 ! CIRCUL> &! /RAI<T1 !
LATT] 2+ SUBDIVID$ 96MO;N AWAY F & MO;N
T[>DS ! C5TRE4

                   #D
  ,T "! IS NO O!R =M ( MO;N OPPOS$ Z
3TR>Y 6! CIRCUL> MAY 2 PROV$ 9 V>I\S
WAYS4 ,9 ! F/ PLACE1 "! IS AN OBVI\S
T5D5CY 6OPPOSE ! /RAI<T L9E 6! CIRCUL>4
,= 3CAVE & 3VEX >E A N ONLY REG>D$ Z
OPPOS$ 6"O ANO!R1 B !Y >E AL C\PL$ TGR &
TR1T$ Z A UN;Y 9 OPPOSI;N 6! /RAI<T4 ,&
S1 IF "! IS A 3TR>Y 6CIRCUL> MO;N1 MO;N
9 A /RAI<T L9E M/ 2 RECOGNIZ$ Z HAV+ !
BE/ CLAIM 6T "N4 ,B ! TWO =MS (
RECTIL9E> MO;N >E OPPOS$ 6"O ANO!R
0R1SON ( _! PLACES2 = UP & D[N IS A
DI6];E &A 3TR>Y OPPOSI;N 9 PLACE4
,SECONDLY1 X MAY 2 ?"\ T ! SAME R1SON+ :
HOLDS GD (! RECTIL9E> PA? APPLIES AL !
CIRCUL>1 MOVE;T F ,A TO ;,B 2+ OPPOS$ Z
3TR>Y 6MOVE;T F ;,B TO ;,A4 ,B :AT IS
M1NT IS / RECTIL9E> MO;N4 ,= T IS LIMIT$
6A S+LE PA?1 :ILE ! CIRCUL> PA?S : PASS
"? ! SAME TWO PO9TS >E 9F9ITE 9 NUMB]4
,EV5 IF WE >E 3F9$ 6! S+LE SEMICIRCLE &!
OPPOSI;N IS 2T MOVE;T F ;,C TO ;,D & F
;,D TO ;,C AL;G T SEMICIRCLE1 ! CASE IS
NO BETT]4 ,=! MO;N IS ! SAME Z T AL;G !
DIAMET]1 S9CE WE 9V>IABLY REG>D ! 4T.E
2T TWO PO9TS Z ! L5G? (! /RAI<T L9E :
JO9S !M4 ,X IS NO M SATISFACTORY 63/RUCT
A CIRCLE & TR1T MO;N ,8AL;G "O
SEMICIRCLE Z 3TR>Y 6MO;N AL;G ! O!R4 ,=
EXAMPLE1 TAK+ A -PLETE CIRCLE1 MO;N F
;,E TO ;,F ON ! SEMICIRCLE ;,G MAY 2
OPPOS$ 6MO;N F ;,F TO ;,E ON !
SEMICIRCLE ,H4 ,B EV5 SUPPOS+ ^! >E
3TR>IES1 X 9 NO WAY FOLL[S T ! REV]SE
MO;NS ON ! -PLETE CIRCUMF];E 3TR>IES4
,NOR AG C MO;N AL;G ! CIRCLE F ,A TO ;,B
2 REG>D$ Z ! 3TR>Y ( MO;N F ,A TO ;,C3 =
! MO;N GOES F ! SAME PO9T T[>DS ! SAME
PO9T1 & 3TR>Y MO;N 0 4T+UI%$ Z MO;N F A
3TR>Y 6XS 3TR>Y4 ,& EV5 IF ! MO;N R.D A
CIRCLE IS ! 3TR>Y (! REV]SE MO;N1 "O (!
TWO WD 2 9E6ECTIVE3 = BO? MOVE 6! SAME
PO9T1 2C T : MOVES 9 A CIRCLE1 AT :AT"E
PO9T X 2G9S1 M/ NECESS>ILY PASS "? ALL !
3TR>Y PLACES ALIKE4 7,03TR>IETIES (
PLACE ,I M1N UP & D[N1 BACK & FRONT1 &
"R & LEFT2 &! 3TR>Y OPPOSI;NS ( MOVE;TS
>E DET]M9$ 0^? ( PLACES47 ,"O (! MO;NS1
!N1 WD 2 9E6ECTIVE1 = IF ! TWO MO;NS 7 (
EQUAL /R5G?1 "! WD 2 NO MOVE;T EI WAY1 &
IF "O (! TWO 7 PREPOND]ANT1 ! O!R WD 2
9OP]ATIVE4 ,S T IF BO? BODIES 7 "!1 "O (
!M1 9ASM* Z X WD N 2 MOV+ ) XS [N
MOVE;T1 WD 2 USE.S1 9 ! S5SE 9 : A %OE
IS USE.S :5 X IS N WORN4 ,B ,GOD &
NATURE CR1TE NO?+ T HAS N XS USE4
                   #E
  ,? 2+ CLE>1 WE M/ G ON 63SID] ! "QS :
REMA94 ,F/1 IS "! AN 9F9ITE BODY1 Z !
MAJOR;Y (! ANCI5T PHILOSOPH]S ?"\1 OR IS
? AN IMPOSSIBIL;Y8 ,! DECI.N ( ? "Q1 EI
WAY1 IS N UNIMPORTANT1 B R ALL-
IMPORTANT1 6\R SE>* =! TRU?4 ,X IS ?
PRO#M : HAS PRACTIC,Y ALW BE5 ! S\RCE (!
DI6];ES ( ^? :O H WRITT5 AB NATURE Z A
:OLE4 ,S X HAS BE5 & S X M/ BE2 S9CE !
L1/ 9ITIAL DEVI,N F ! TRU? IS MULTIPLI$
LAT] A ?\S&FOLD4 ,ADMIT1 = 9/.E1 !
EXI/;E (A M9IMUM MAGNITUDE1 & Y W F9D T
! M9IMUM : Y H 9TRODUC$1 SMALL Z X IS1
CAUSES ! GRTE/ TRU?S ( MA!MATICS 6TOTT]4
,! R1SON IS T A PR9CIPLE IS GRT R 9 P[]
?AN 9 EXT5T2 H;E T : 0 SMALL AT ! />T
TURNS \ A GIANT AT ! 5D4 ,N[ ! 3CEP;N (!
9F9ITE POSSESSES ? P[] ( PR9CIPLES1 &
9DE$ 9 ! SPH]E ( QUANT;Y POSSESSES X 9 A
HI<] DEGREE ?AN ANY O!R 3CEP;N2 S T X IS
9 NO WAY ABSURD OR UNR1SONA# T !
ASSUMP;N T AN 9F9ITE BODY EXI/S %D 2 (
PECULI> MO;T 6\R 9QUIRY4 ,! 9F9ITE1 !N1
WE M/ N[ 4CUSS1 OP5+ ! :OLE MATT] F !
2G9N+4
  ,E BODY IS NECESS>ILY 6BE CLASS$ EI Z
SIMPLE OR Z -POSITE2 ! 9F9ITE BODY1
"!=E1 W 2 EI SIMPLE OR -POSITE4
  ,B X IS CLE>1 FUR!R1 T IF ! SIMPLE
BODIES >E F9ITE1 ! -POSITE M/ AL 2
F9ITE1 S9CE T : IS -POS$ ( BODIES F9ITE
BO? 9 NUMB] & 9 MAGNITUDE IS XF F9ITE 9
RESPECT ( NUMB] & MAGNITUDE3 XS QUANT;Y
IS 9 FACT ! SAME Z T (! BODIES : -POSE
X4 ,:AT REMA9S = U 63SID]1 !N1 IS :E!R
ANY (! SIMPLE BODIES C 2 9F9ITE 9
MAGNITUDE1 OR :E!R ? IS IMPOSSI#4 ,LET U
TRY ! PRIM>Y BODY F/1 & !N G ON 63SID] !
O!RS4
  ,! BODY : MOVES 9 A CIRCLE M/
NECESS>ILY 2 F9ITE 9 E RESPECT1 =!
FOLL[+ R1SONS4 7#A7 ,IF ! BODY S MOV+ IS
9F9ITE1 ! RADII DRAWN F ! C5TRE W 2
9F9ITE4 ,B ! SPACE 2T 9F9ITE RADII IS
9F9ITE3 & 0! SPACE 2T ! RADII ,I M1N !
>EA \TSIDE : NO MAGNITUDE : IS 9 3TACT )
! TWO L9ES C 2 3CVD Z FALL+4 ,?1 ,I SAY1
W 2 9F9ITE3 F/1 2C 9 ! CASE ( F9ITE
RADII X IS ALW F9ITE2 & SECONDLY1 2C 9 X
"O C ALW G ON 6A WID? GRT] ?AN ANY GIV5
WID?2 ?US ! R1SON+ : =CES U 62LIEVE 9
9F9ITE NUMB]1 2C "! IS NO MAXIMUM1
APPLIES AL 6! SPACE 2T ! RADII4 ,N[ !
9F9ITE _C 2 TRAV]S$1 & IF ! BODY IS
9F9ITE ! 9T]VAL 2T ! RADII IS NECESS>ILY
9F9ITE3 CIRCUL> MO;N "!=E IS AN
IMPOSSIBIL;Y4 ,YET \R EYES TELL U T !
H1V5S REVOLVE 9 A CIRCLE1 & 0>GU;T AL WE
H DET]M9$ T "! IS "S?+ 6: CIRCUL> MOVE;T
2L;GS4
  7#B7 ,AG1 IF F A F9ITE "T A F9ITE "T 2
SUBTRACT$1 :AT REMA9S M/ 2 F9ITE & H A
2G9N+4 ,& IF ! "T (A J\RNEY HAS A 2G9N+1
"! M/ 2 A 2G9N+ AL (! MOVE;T1 &
3SEQU5TLY AL (! 4T.E TRAV]S$4 ,? APPLIES
UNIV]S,Y4 ,TAKE A L9E1 ,,ACE1 9F9ITE 9
"O DIREC;N1 ;,E1 & ANO!R L9E1 ,,BB1
9F9ITE 9 BO? DIREC;NS4 ,LET ,,ACE
DESCRIBE A CIRCLE1 REVOLV+ ^U ;,C Z
C5TRE4 ,9 XS MOVE;T X W CUT ,,BB
3T9U\SLY =A C]TA9 "T4 ,? W 2 A F9ITE "T1
S9CE ! TOTAL "T IS F9ITE 9 : ! H1V5S
-PLETE _! CIRCUL> ORBIT1 & 3SEQU5TLY !
"T SUBTRACT$ F X1 DUR+ : ! "O L9E 9 XS
MO;N CUTS ! O!R1 IS AL F9ITE4 ,"!=E "! W
2 A PO9T AT : ,,ACE 2GAN =! F/ "T 6CUT
,,BB4 ,?1 H["E1 IS IMPOSSI#4 ,! 9F9ITE1
!N1 _C REVOLVE 9 A CIRCLE2 NOR CD ! _W1
IF X 7 9F9ITE4
  7#C7 ,T ! 9F9ITE _C MOVE MAY AL 2 %[N
Z FOLL[S4 ,LET ,A 2 A F9ITE L9E MOV+ PA/
! F9ITE L9E1 ,B4 ,( NECESS;Y ,A W PASS
CLE> ( ;,B & ;,B ( ,A AT ! SAME MO;T2 =
EA* OV]LAPS ! O!R 6PRECISELY ! SAME
EXT5T4 ,N[ IF ! TWO 7 BO? MOV+1 & MOV+ 9
3TR>Y DIREC;NS1 !Y WD PASS CLE> ( "O
ANO!R M RAPIDLY2 IF "O 7 / &! O!R MOV+
PA/ X1 LESS RAPIDLY2 PROVID$ T ! SPE$ (!
LATT] 7 ! SAME 9 BO? CASES4 ,?1 H["E1 IS
CLE>3 T X IS IMPOSSI# 6TRAV]SE AN 9F9ITE
L9E 9 A F9ITE "T4 ,9F9ITE "T1 !N1 WD 2
REQUIR$4 7,? WE DEMON/RAT$ ABV 9 !
4CUS.N ( MOVE;T47 ,& X MAKES NO DI6];E
:E!R A F9ITE IS PASS+ 0AN 9F9ITE OR AN
9F9ITE 0A F9ITE4 ,= :5 ,A IS PASS+ ;,B1
!N ;,B OV]LAPS ;,A & X MAKES NO DI6];E
:E!R ;,B IS MOV$ OR UNMOV$1 EXCEPT T1 IF
BO? MOVE1 !Y PASS CLE> ( "O ANO!R M
QKLY4 ,X IS1 H["E1 Q POSSI# T A MOV+ L9E
%D 9 C]TA9 CASES PASS "O : IS /,N>Y QK]
?AN X PASSES "O MOV+ 9 AN OPPOSITE
DIREC;N4 ,"O HAS ONLY 6IMAG9E ! MOVE;T
6BE SL[ ": BO? MOVE & M* FA/] ": "O IS
/,N>Y4 ,6SUPPOSE "O L9E /,N>Y1 !N1 MAKES
NO DI6ICULTY = \R >GU;T1 S9CE X IS Q
POSSI# = ,A 6PASS ;,B AT A SL[] RATE :5
BO? >E MOV+ ?AN :5 ONLY "O IS4 ,IF1
"!=E1 ! "T : ! F9ITE MOV+ L9E TAKES
6PASS ! O!R IS 9F9ITE1 !N NECESS>ILY !
"T O3UPI$ 0! MO;N (! 9F9ITE PA/ ! F9ITE
IS AL 9F9ITE4 ,=! 9F9ITE 6MOVE AT ALL IS
?US ABSOLUTELY IMPOSSI#2 S9CE ! V
SMALLE/ MOVE;T 3CEIVA# M/ TAKE AN 9F9;Y
( "T4 ,MOREOV] ! H1V5S C]TA9LY REVOLVE1
& !Y -PLETE _! CIRCUL> ORBIT 9 A F9ITE
"T2 S T !Y PASS R.D ! :OLE EXT5T ( ANY
L9E )9 _! ORBIT1 S* Z ! F9ITE L9E ;,,AB4
,! REVOLV+ BODY1 "!=E1 _C 2 9F9ITE4
  7#D7 ,AG1 Z A L9E : HAS A LIMIT _C 2
9F9ITE1 OR1 IF X IS 9F9ITE1 IS S ONLY 9
L5G?1 S A SURFACE _C 2 9F9ITE 9 T
RESPECT 9 : X HAS A LIMIT2 OR1 9DE$1 IF
X IS -PLETELY DET]M9ATE1 9 ANY RESPECT
:AT"E4 ,:E!R X 2 A SQU>E OR A CIRCLE OR
A SPH]E1 X _C 2 9F9ITE1 ANY M ?AN A
FOOT-RULE C4 ,"! IS !N NO S* ?+ Z AN
9F9ITE SPH]E OR SQU>E OR CIRCLE1 & ": "!
IS NO CIRCLE "! C 2 NO CIRCUL> MOVE;T1 &
SIMIL>LY ": "! IS NO 9F9ITE AT ALL "! C
2 NO 9F9ITE MOVE;T2 & F ? X FOLL[S T1 AN
9F9ITE CIRCLE 2+ XF AN IMPOSSIBIL;Y1 "!
C 2 NO CIRCUL> MO;N ( AN 9F9ITE BODY4
  7#E7 ,AG1 TAKE A C5TRE ;,C1 AN 9F9ITE
L9E1 ;,,AB1 ANO!R 9F9ITE L9E AT "R
ANGLES 6X1 ;,E1 &A MOV+ RADIUS1 ;,,CD4
;,,CD W N"E C1SE 3TACT ) ;,E1 B ! POSI;N
W ALW 2 "S?+ L ,,CE1 ;,,CD CUTT+ ;,E AT
,F4 ,! 9F9ITE L9E1 "!=E1 REFUSES 6-PLETE
! CIRCLE4
  7#F7 ,AG1 IF ! H1V5 IS 9F9ITE & MOVES
9 A CIRCLE1 WE % H 6ADMIT T 9 A F9ITE "T
X HAS TRAV]S$ ! 9F9ITE4 ,= SUPPOSE !
FIX$ H1V5 9F9ITE1 & T : MOVES )9 X EQUAL
6X4 ,X RESULTS T :5 ! 9F9ITE BODY HAS
-PLET$ XS REVOLU;N1 X HAS TRAV]S$ AN
9F9ITE EQUAL 6XF 9 A F9ITE "T4 ,B T WE
"K 6BE IMPOSSI#4
  7#G7 ,X C AL 2 %[N1 3V]SELY1 T IF ! "T
( REVOLU;N IS F9ITE1 ! >EA TRAV]S$ M/ AL
2 F9ITE2 B ! >EA TRAV]S$ 0 EQUAL 6XF2
"!=E1 X IS XF F9ITE4
  ,WE H N[ %[N T ! BODY : MOVES 9 A
CIRCLE IS N 5D.S OR 9F9ITE1 B HAS XS
LIMIT4
                   #F
  ,FUR!R1 NEI T : MOVES T[>DS NOR T :
MOVES AWAY F ! C5TRE C 2 9F9ITE4 ,=!
UPW>D & D[NW>D MO;NS >E 3TR>IES & >E
"!=E MO;NS T[>DS 3TR>Y PLACES4 ,B IF "O
(A PAIR ( 3TR>IES IS DET]M9ATE1 ! O!R M/
2 DET]M9ATE AL4 ,N[ ! C5TRE IS DET]M9$2
=1 F :AT"E PO9T ! BODY : S9KS 6! BOTTOM
/>TS XS D[NW>D MO;N1 X _C G F>!R ?AN !
C5TRE4 ,! C5TRE1 "!=E1 2+ DET]M9ATE1 !
UPP] PLACE M/ AL 2 DET]M9ATE4 ,B IF ^!
TWO PLACES >E DET]M9$ & F9ITE1 !
CORRESPOND+ BODIES M/ AL 2 F9ITE4
,FUR!R1 IF UP & D[N >E DET]M9ATE1 !
9T]M$IATE PLACE IS AL NECESS>ILY
DET]M9ATE4 ,=1 IF X IS 9DET]M9ATE1 !
MOVE;T )9 X W 2 9F9ITE2 & T WE H ALR %[N
6BE AN IMPOSSIBIL;Y4 ,! MI4LE REGION !N
IS DET]M9ATE1 & 3SEQU5TLY ANY BODY : EI
IS 9 X1 OR MI<T 2 9 X1 IS DET]M9ATE4 ,B
! BODIES : MOVE UP & D[N MAY 2 9 X1 S9CE
! "O MOVES NATUR,Y AWAY F ! C5TRE &! O!R
T[>DS X4
  ,F ? AL"O X IS CLE> T AN 9F9ITE BODY
IS AN IMPOSSIBIL;Y2 B "! IS A FUR!R
PO9T4 ,IF "! IS NO S* ?+ Z 9F9ITE WEI<T1
!N X FOLL[S T N"O ( ^! BODIES C 2
9F9ITE4 ,=! SUPPOS$ 9F9ITE BODY WD H 6BE
9F9ITE 9 WEI<T4 7,! SAME >GU;T APPLIES
6LI<T;S3 = Z ! "O SUPPOSI;N 9VOLVES
9F9ITE WEI<T1 S ! 9F9;Y (! BODY : RISES
6! SURFACE 9VOLVES 9F9ITE LI<T;S47 ,? IS
PROV$ Z FOLL[S4 ,ASSUME ! WEI<T 6BE
F9ITE1 & TAKE AN 9F9ITE BODY1 ;,,AB1 (!
WEI<T ,C4 ,SUBTRACT F ! 9F9ITE BODY A
F9ITE MASS1 ,,BD1 ! WEI<T ( : % 2 ,E4
;,E !N IS LESS ?AN ;,C1 S9CE X IS !
WEI<T (A LESS] MASS4 ,SUPPOSE !N T !
SMALL] GOES 96! GRT] A C]TA9 NUMB] (
"TS1 & TAKE ,,BF BE>+ ! SAME PROPOR;N
6,,BD : ! GRT] WEI<T BE>S 6! SMALL]4 ,=
Y MAY SUBTRACT Z M* Z Y PL1SE F AN
9F9ITE4 ,IF N[ ! MASSES >E PROPOR;NATE
6! WEI<TS1 &! LESS] WEI<T IS T (! LESS]
MASS1 ! GRT] M/ 2 T (! GRT]4 ,! WEI<TS1
"!=E1 (! F9ITE &(! 9F9ITE BODY >E EQUAL4
,AG1 IF ! WEI<T (A GRT] BODY IS GRT] ?AN
T (A LESS1 ! WEI<T ( ,,GB W 2 GRT] ?AN T
( ,,FB2 & ?US ! WEI<T (! F9ITE BODY IS
GRT] ?AN T (! 9F9ITE4 ,&1 FUR!R1 ! WEI<T
( UNEQUAL MASSES W 2 ! SAME1 S9CE !
9F9ITE &! F9ITE _C 2 EQUAL4 ,X DOES N
MATT] :E!R ! WEI<TS >E -M5SURA# OR N4
,IF 7A7 !Y >E 9COMM5SURA# ! SAME R1SON+
HOLDS4 ,= 9/.E1 SUPPOSE ;,E MULTIPLI$
0?REE IS R M ?AN ;,C3 ! WEI<T ( ?REE
MASSES (! FULL SIZE ( ,,BD W 2 GRT] ?AN
,C4 ,WE ?US >RIVE AT ! SAME IMPOSSIBIL;Y
Z 2F4 ,AG 7B7 WE MAY ASSUME WEI<TS : >E
-M5SURATE2 = X MAKES NO DI6];E :E!R WE
2G9 )! WEI<T OR )! MASS4 ,= EXAMPLE1
ASSUME ! WEI<T ;,E 6BE -M5SURATE ) ;,C1
& TAKE F ! 9F9ITE MASS A "P ,,BD ( WEI<T
,E4 ,!N LET A MASS ,,BF 2 TAK5 HAV+ !
SAME PROPOR;N 6,,BD : ! TWO WEI<TS H 6"O
ANO!R4 7,=! MASS 2+ 9F9ITE Y MAY
SUBTRACT F X Z M* Z Y PL1SE47 ,^! ASSUM$
BODIES W 2 -M5SURATE 9 MASS & 9 WEI<T
ALIKE4 ,NOR AG DOES X MAKE ANY DI6];E
6\R DEMON/R,N :E!R ! TOTAL MASS HAS XS
WEI<T EQU,Y OR UNEQU,Y 4TRIBUT$4 ,= X M/
ALW 2 ,POSSI# 6TAKE F ! 9F9ITE MASS A
BODY ( EQUAL WEI<T 6,,BD 0DIM9I%+ OR
9CR1S+ ! SIZE (! SEC;N 6! NEC EXT5T4
  ,F :AT WE H SD1 !N1 X IS CLE> T !
WEI<T (! 9F9ITE BODY _C 2 F9ITE4 ,X M/
!N 2 9F9ITE4 ,WE H "!=E ONLY 6%[ ? 6BE
IMPOSSI# 9 ORD] 6PROVE AN 9F9ITE BODY
IMPOSSI#4 ,B ! IMPOSSIBIL;Y ( 9F9ITE
WEI<T C 2 %[N 9 ! FOLL[+ WAY4 ,A GIV5
WEI<T MOVES A GIV5 4T.E 9 A GIV5 "T2 A
WEI<T : IS Z GRT & M MOVES ! SAME 4T.E 9
A LESS "T1 ! "TS 2+ 9 9V]SE PROPOR;N 6!
WEI<TS4 ,= 9/.E1 IF "O WEI<T IS TWICE
ANO!R1 X W TAKE HALF Z L;G OV] A GIV5
MOVE;T4 ,FUR!R1 A F9ITE WEI<T TRAV]SES
ANY F9ITE 4T.E 9 A F9ITE "T4 ,X
NECESS>ILY FOLL[S F ? T 9F9ITE WEI<T1 IF
"! IS S* A ?+1 2+1 ON ! "O H&1 Z GRT & M
?AN Z GRT Z ! F9ITE1 W MOVE ACLY1 B 2+1
ON ! O!R H&1 -PELL$ 6MOVE 9 A "T 9V]SELY
PROPOR;NATE 6XS GRT;S1 _C MOVE AT ALL4
,! "T %D 2 LESS 9 PROPOR;N Z ! WEI<T IS
GRT]4 ,B "! IS NO PROPOR;N 2T ! 9F9ITE &
! F9ITE3 PROPOR;N C ONLY HOLD 2T A LESS
&A GRT] F9ITE "T4 ,& ?\< Y MAY SAY T !
"T (! MOVE;T C 2 3T9U,Y DIM9I%$1 YET "!
IS NO M9IMUM4 ,NOR1 IF "! W]E1 WD X HELP
U4 ,= "S F9ITE BODY CD H BE5 F.D GRT]
?AN ! GIV5 F9ITE 9 ! SAME PROPOR;N : IS
SUPPOS$ 6HOLD 2T ! 9F9ITE &! GIV5 F9ITE2
S T AN 9F9ITE &A F9ITE WEI<T M/ H
TRAV]S$ AN EQUAL 4T.E 9 EQUAL "T4 ,B T
IS IMPOSSI#4 ,AG1 :AT"E ! "T1 S L;G Z X
IS F9ITE1 9 : ! 9F9ITE P]=MS ! MO;N1 A
F9ITE WEI<T M/ NECESS>ILY MOVE A C]TA9
F9ITE 4T.E 9 T SAME "T4 ,9F9ITE WEI<T IS
"!=E IMPOSSI#1 &! SAME R1SON+ APPLIES AL
69F9ITE LI<T;S4 ,BODIES !N ( 9F9ITE
WEI<T &( 9F9ITE LI<T;S >E EQU,Y
IMPOSSI#4
  ,T "! IS NO 9F9ITE BODY MAY 2 %[N1 Z
WE H %[N X1 0A DETAIL$ 3SID],N (! V>I\S
CASES4 ,B X MAY AL 2 %[N UNIV]S,Y1 N
ONLY 0S* R1SON+ Z WE ADV.ED 9 \R 4CUS.N
( PR9CIPLES 7?\< 9 T PASSAGE WE H ALR
DET]M9$ UNIV]S,Y ! S5SE 9 : ! EXI/;E (
AN 9F9ITE IS 6BE ASS]T$ OR D5I$71 B AL
SUITABLY 6\R PRES5T PURPOSE 9 ! FOLL[+
WAY4 ,T W L1D U 6A FUR!R "Q4 ,EV5 IF !
TOTAL MASS IS N 9F9ITE1 X MAY YET 2 GRT
5 6ADMIT A PLURAL;Y ( UNIV]SES4 ,! "Q
MI<T POSSIBLY 2 RAIS$ :E!R "! IS ANY
OB/ACLE 6\R 2LIEV+ T "! >E O!R UNIV]SES
-POS$ ON ! PATT]N ( \R [N1 M ?AN "O1 ?\<
/OPP+ %ORT ( 9F9;Y4 ,F/1 H["E1 LET U
TR1T (! 9F9ITE UNIV]S,Y4
                   #G
  ,E BODY M/ NECESS>ILY 2 EI F9ITE OR
9F9ITE1 & IF 9F9ITE1 EI ( SIMIL> OR (
4SIMIL> "PS4 ,IF XS "PS >E 4SIMIL>1 !Y
M/ REPRES5T EI A F9ITE OR AN 9F9ITE
NUMB] ( K9DS4 ,T ! K9DS _C 2 9F9ITE IS
EVID5T1 IF \R ORIG9AL PRESUPPOSI;NS
REMA9 UN*ALL5G$4 ,=! PRIM>Y MOVE;TS 2+
F9ITE 9 NUMB]1 ! K9DS ( SIMPLE BODY >E
NECESS>ILY AL F9ITE1 S9CE ! MOVE;T (A
SIMPLE BODY IS SIMPLE1 &! SIMPLE MOVE;TS
>E F9ITE1 & E NATURAL BODY M/ ALW H XS
PROP] MO;N4 ,N[ IF ! 9F9ITE BODY IS 6BE
-POS$ (A F9ITE NUMB] ( K9DS1 !N EA* ( XS
"PS M/ NECESS>ILY 2 9F9ITE 9 QUANT;Y1 T
IS 6SAY1 ! WAT]1 FIRE1 &C41 : -POSE X4
,B ? IS IMPOSSI#1 2C1 Z WE H ALR %[N1
9F9ITE WEI<T & LI<T;S D N EXI/4 ,MOREOV]
X WD 2 NEC AL T _! PLACES %D 2 9F9ITE 9
EXT5T1 S T ! MOVE;TS TOO ( ALL ^! BODIES
WD 2 9F9ITE4 ,B ? IS N POSSI#1 IF WE >E
6HOLD 6! TRU? ( \R ORIG9AL PRESUPPOSI;NS
& 6! VIEW T NEI T : MOVES D[NW>D1 NOR1
0! SAME R1SON+1 T : MOVES UPW>D1 C
PROL;G XS MOVE;T 69F9;Y4 ,= X IS TRUE 9
REG>D 6QUAL;Y1 QUANT;Y1 & PLACE ALIKE T
ANY PROCESS ( *ANGE IS IMPOSSI# : C H NO
5D4 ,I M1N T IF X IS IMPOSSI# =A ?+ 6H
-E 6BE :ITE1 OR A CUBIT L;G1 OR 9
,EGYPT1 X IS AL IMPOSSI# = X 6BE 9
PROCESS ( -+ 6BE ANY ( ^!4 ,X IS ?US
IMPOSSI# =A ?+ 6BE MOV+ 6A PLACE AT : 9
XS MO;N X C N"E 0ANY POSSIBIL;Y >RIVE4
,AG1 SUPPOSE ! BODY 6EXI/ 9 4P].N1 X MAY
2 MA9TA9$ N"O ! LESS T ! TOTAL ( ALL ^!
SCATT]$ "PICLES1 SAY1 ( FIRE1 IS 9F9ITE4
,B BODY WE SAW 6BE T : HAS EXT5.N E WAY4
,H[ C "! 2 S"EAL 4SIMIL> ELE;TS1 EA*
9F9ITE8 ,EA* WD H 6BE 9F9ITELY EXT5D$ E
WAY4
  ,X IS NO M 3CEIVA#1 AG1 T ! 9F9ITE %D
EXI/ Z A :OLE ( SIMIL> "PS4 ,=1 9 ! F/
PLACE1 "! IS NO O!R 7/RAI<T7 MOVE;T 2Y
^? M5;N$3 WE M/ "!=E GIVE X "O ( !M4 ,&
IF S1 WE % H 6ADMIT EI 9F9ITE WEI<T OR
9F9ITE LI<T;S4 ,NOR1 SECONDLY1 CD ! BODY
^: MOVE;T IS CIRCUL> 2 9F9ITE1 S9CE X IS
IMPOSSI# =! 9F9ITE 6MOVE 9 A CIRCLE4 ,?1
9DE$1 WD 2 Z GD Z SAY+ T ! H1V5S >E
9F9ITE1 : WE H %[N 6BE IMPOSSI#4
  ,MOREOV]1 9 G5]AL1 X IS IMPOSSI# T !
9F9ITE %D MOVE AT ALL4 ,IF X DID1 X WD
MOVE EI NATUR,Y OR 03/RA9T3 & IF
03/RA9T1 X POSSESSES AL A NATURAL MO;N1
T IS 6SAY1 "! IS ANO!R PLACE1 9F9ITE L
XF1 6: X W MOVE4 ,B T IS IMPOSSI#4
  ,T 9 G5]AL X IS IMPOSSI# =! 9F9ITE 6BE
ACT$ ^U 0! F9ITE OR 6ACT ^U X MAY 2 %[N
Z FOLL[S4
  7#A4 ,! 9F9ITE _C 2 ACT$ ^U 0! F9ITE47
,LET ,A 2 AN 9F9ITE1 ;,B A F9ITE1 ;,C !
"T (A GIV5 MOVE;T PRODUC$ 0"O 9 ! O!R4
,SUPPOSE1 !N1 T ,A 0 H1T$1 OR IMPELL$1
OR MODIFI$ 9 ANY WAY1 OR CAUS$ 6"UGO ANY
SORT ( MOVE;T :AT"E1 0IN ! "T ,C4 ,LET
;,D 2 LESS ?AN ;,B2 &1 ASSUM+ T A LESS]
AG5T MOVES A LESS] PATI5T 9 AN EQUAL "T1
CALL ! QUANT;Y ?US MODIFI$ BY ;,D1 ,E4
,!N1 Z ;,D IS TO ;,B1 S IS ;,E 6"S F9ITE
QUANTUM4 ,WE ASSUME T ! ALT],N ( EQUAL
0EQUAL TAKES EQUAL "T1 &! ALT],N ( LESS
0LESS OR ( GRT] 0GRT] TAKES ! SAME "T1
IF ! QUANT;Y (! PATI5T IS S* Z 6KEEP !
PROPOR;N : OBTA9S 2T ! AG5TS1 GRT] &
LESS4 ,IF S1 NO MOVE;T C 2 CAUS$ 9 !
9F9ITE 0ANY F9ITE AG5T 9 ANY "T :AT"E4
,=A LESS AG5T W PRODUCE T MOVE;T 9 A
LESS PATI5T 9 AN EQUAL "T1 &!
PROPOR;NATE EQUIVAL5T ( T PATI5T W 2 A
F9ITE QUANT;Y1 S9CE NO PROPOR;N HOLDS 2T
F9ITE & 9F9ITE4
  7#B4 ,! 9F9ITE _C ACT ^U ! F9ITE47
,NOR1 AG1 C ! 9F9ITE PRODUCE A MOVE;T 9
! F9ITE 9 ANY "T :AT"E4 ,LET ,A 2 AN
9F9ITE1 ;,B A F9ITE1 ;,C ! "T ( AC;N4 ,9
! "T ;,C1 ;,D W PRODUCE T MO;N 9 A
PATI5T LESS ?AN ;,B1 SAY ,F4 ,!N TAKE
;,E1 BE>+ ! SAME PROPOR;N TO ;,D Z !
:OLE ,,BF BE>S TO ;,F4 ;,E W PRODUCE !
MO;N 9 ,,BF 9 ! "T ,C4 ,?US ! F9ITE &
9F9ITE E6ECT ! SAME ALT],N 9 EQUAL "TS4
,B ? IS IMPOSSI#2 =! ASSUMP;N IS T !
GRT] E6ECTS X 9 A %ORT] "T4 ,X W 2 !
SAME ) ANY "T T C 2 TAK51 S T "! W NO "T
9 : ! 9F9ITE C E6ECT ? MOVE;T4 ,&1 Z
69F9ITE "T1 9 T NO?+ C MOVE ANO!R OR 2
MOV$ 0X4 ,= S* "T HAS NO LIMIT1 :ILE !
AC;N & REAC;N H4
  7#C4 ,"! IS NO 9T]AC;N 2T 9F9ITES47
,NOR C 9F9ITE 2 ACT$ ^U 9 ANY WAY
09F9ITE4 ,LET ;,A & ;,B 2 9F9ITES1 ;,,CD
2+ ! "T (! AC;N ;,A ( ^U ,B4 ,N[ ! :OLE
;,B 0 MODIFI$ 9 A C]TA9 "T1 &! "P ( ?
9F9ITE1 ;,E1 _C 2 S MODIFI$ 9 ! SAME "T1
S9CE WE ASSUME T A LESS QUANT;Y MAKES !
MOVE;T 9 A LESS "T4 ,LET ;,E !N1 :5 ACT$
^U BY ;,A1 -PLETE ! MOVE;T 9 ! "T ,D4
,!N1 Z ;,D IS 6;,,CD1 S IS ;,E 6"S F9ITE
"P ( ,B4 ,? "P W NECESS>ILY 2 MOV$ BY
;,A 9 ! "T ;,,CD4 ,= WE SUPPOSE T ! SAME
AG5T PRODUCES A GIV5 E6ECT ON A GRT] &A
SMALL] MASS 9 L;G] & %ORT] "TS1 ! "TS &
MASSES V>Y+ PROPOR;NATELY4 ,"! IS ?US NO
F9ITE "T 9 : 9F9ITES C MOVE "O ANO!R4
,IS _! "T !N 9F9ITE8 ,NO1 = 9F9ITE "T
HAS NO 5D1 B ! MOVE;T -MUNICAT$ HAS4
  ,IF "!=E E P]CEPTI# BODY POSSESSES !
P[] ( ACT+ OR ( 2+ ACT$ ^U1 OR BO? ( ^!1
X IS IMPOSSI# T AN 9F9ITE BODY %D 2
P]CEPTI#4 ,ALL BODIES1 H["E1 T O3UPY
PLACE >E P]CEPTI#4 ,"! IS "!=E NO 9F9ITE
BODY 2Y ! H1V54 ,NOR AG IS "! ANY?+ (
LIMIT$ EXT5T 2Y X4 ,& S 2Y ! H1V5 "! IS
NO BODY AT ALL4 ,= IF Y SUPPOSE X AN
OBJECT ( 9TELLIG;E1 X W 2 9 A PLACE-S9CE
PLACE IS :AT ,8)9' & ,82Y0' DENOTE-&
"!=E AN OBJECT ( P]CEP;N4 ,B NO?+ T IS N
9 A PLACE IS P]CEPTI#4
  ,! "Q MAY AL 2 EXAM9$ 9 ! LI<T ( M
G5]AL 3SID],NS Z FOLL[S4 ,! 9F9ITE1
3SID]$ Z A :OLE ( SIMIL> "PS1 _C1 ON !
"O H&1 MOVE 9 A CIRCLE4 ,= "! IS NO
C5TRE (! 9F9ITE1 & T : MOVES 9 A CIRCLE
MOVES AB ! C5TRE4 ,NOR AG C ! 9F9ITE
MOVE 9 A /RAI<T L9E4 ,= "! WD H 6BE
ANO!R PLACE 9F9ITE L XF 6BE ! GOAL ( XS
NATURAL MOVE;T & ANO!R1 EQU,Y GRT1 =!
GOAL ( XS UNNATURAL MOVE;T4 ,MOREOV]1
:E!R XS RECTIL9E> MOVE;T IS NATURAL OR
3/RA9$1 9 EI CASE ! =CE : CAUSES XS MO;N
W H 6BE 9F9ITE4 ,= 9F9ITE =CE IS =CE (
AN 9F9ITE BODY1 &( AN 9F9ITE BODY ! =CE
IS 9F9ITE4 ,S ! MOTIVE BODY AL W 2
9F9ITE4 7,! PRO( ( ? IS GIV5 9 \R 4CUS.N
( MOVE;T1 ": X IS %[N T NO F9ITE ?+
POSSESSES 9F9ITE P[]1 & NO 9F9ITE ?+
F9ITE P[]47 ,IF !N T : MOVES NATUR,Y C
AL MOVE UNNATUR,Y1 "! W 2 TWO 9F9ITES1
"O : CAUSES1 & ANO!R : EXHIBITS ! LATT]
MO;N4 ,AG1 :AT IS X T MOVES ! 9F9ITE8
,IF X MOVES XF1 X M/ 2 ANIMATE4 ,B H[ C
X POSSIBLY 2 3CVD Z AN 9F9ITE ANIMAL8 ,&
IF "! IS "S?+ ELSE T MOVES X1 "! W 2 TWO
9F9ITES1 T : MOVES & T : IS MOV$1 DI6]+
9 _! =M & P[]4
  ,IF ! :OLE IS N 3T9U\S1 B EXI/S1 Z
,DEMOCRITUS & ,LEUCIPPUS ?9K1 9 ! =M (
"PS SEP>AT$ 0VOID1 "! M/ NECESS>ILY 2 "O
MOVE;T ( ALL ! MULTITUDE4 ,!Y >E
4T+UI%$1 WE >E TOLD1 F "O ANO!R 0_!
FIGURES2 B _! NATURE IS "O1 L _M PIECES
( GOLD SEP>AT$ F "O ANO!R4 ,B EA* PIECE
M/1 Z WE ASS]T1 H ! SAME MO;N4 ,=A S+LE
CLOD MOVES 6! SAME PLACE Z ! :OLE MASS (
E>?1 &A SP>K 6! SAME PLACE Z ! :OLE MASS
( FIRE4 ,S T IF X 2 WEI<T T ALL POSSESS1
NO BODY IS1 /RICTLY SP1K+1 LI<T3 & IF
LI<T;S 2 UNIV]SAL1 N"O IS H1VY4
,MOREOV]1 :AT"E POSSESSES WEI<T OR
LI<T;S W H XS PLACE EI AT "O (! EXTREMES
OR 9 ! MI4LE REGION4 ,B ? IS IMPOSSI#
:ILE ! _W IS 3CVD Z 9F9ITE4 ,&1 G5],Y1 T
: HAS NO C5TRE OR EXTREME LIMIT1 NO UP
OR D[N1 GIVES ! BODIES NO PLACE = _!
MO;N2 & )\T T MOVE;T IS IMPOSSI#4 ,A ?+
M/ MOVE EI NATUR,Y OR UNNATUR,Y1 &! TWO
MOVE;TS >E DET]M9$ 0! PROP] & ALI5
PLACES4 ,AG1 A PLACE 9 : A ?+ RE/S OR 6:
X MOVES UNNATUR,Y1 M/ 2 ! NATURAL PLACE
= "S O!R BODY1 Z EXP]I;E %[S4
,NECESS>ILY1 "!=E1 N "EY?+ POSSESSES
WEI<T OR LI<T;S1 B "S ?+S D & "S D N4 ,F
^! >GU;TS !N X IS CLE> T ! BODY (!
UNIV]SE IS N 9F9ITE4
                   #H
  ,WE M/ N[ PROCE$ 6EXPLA9 :Y "! _C 2 M
?AN "O H1V5-! FUR!R "Q M5;N$ ABV4 ,= X
MAY 2 ?"\ T WE H N PROV$ UNIV]SAL (
BODIES T N"O :AT"E C EXI/ \TSIDE \R
UNIV]SE1 & T \R >GU;T APPLI$ ONLY 6^? (
9DET]M9ATE EXT5T4
  ,N[ ALL ?+S RE/ & MOVE NATUR,Y &
03/RA9T4 ,A ?+ MOVES NATUR,Y 6A PLACE 9
: X RE/S )\T 3/RA9T1 & RE/S NATUR,Y 9 A
PLACE 6: X MOVES )\T 3/RA9T4 ,ON ! O!R
H&1 A ?+ MOVES 03/RA9T 6A PLACE 9 : X
RE/S 03/RA9T1 & RE/S 03/RA9T 9 A PLACE
6: X MOVES 03/RA9T4 ,FUR!R1 IF A GIV5
MOVE;T IS DUE 63/RA9T1 XS 3TR>Y IS
NATURAL4 ,IF1 !N1 X IS 03/RA9T T E>?
MOVES F A C]TA9 PLACE 6! C5TRE "H1 XS
MOVE;T F "H 6"! W 2 NATURAL1 & IF E>? F
"! RE/S "H )\T 3/RA9T1 XS MOVE;T HI!R W
2 NATURAL4 ,&! NATURAL MOVE;T 9 EA* CASE
IS "O4 ,FUR!R1 ^! _WS1 2+ SIMIL> 9
NATURE 6\RS1 M/ ALL 2 -POS$ (! SAME
BODIES Z X4 ,MOREOV] EA* (! BODIES1
FIRE1 ,I M1N1 & E>? & _! 9T]M$IATES1 M/
H ! SAME P[] Z 9 \R _W4 ,= IF ^! "NS >E
US$ EQUIVOC,Y1 IF ! ID5T;Y ( "N DOES N
RE/ ^U AN ID5T;Y ( =M 9 ^! ELE;TS & \RS1
!N ! :OLE 6: !Y 2L;G C ONLY 2 CALL$ A _W
0EQUIVOC,N4 ,CLE>LY1 !N1 "O (! BODIES W
MOVE NATUR,Y AWAY F ! C5TRE & ANO!R
T[>DS ! C5TRE1 S9CE FIRE M/ 2 ID5TICAL )
FIRE1 E>? ) E>?1 & S ON1 Z ! FRAG;TS (
EA* >E ID5TICAL 9 ? _W4 ,T ? M/ 2 ! CASE
IS EVID5T F ! PR9CIPLES LAID D[N 9 \R
4CUS.N (! MOVE;TS1 = ^! >E LIMIT$ 9
NUMB]1 &! 4T9C;N (! ELE;TS DEP5DS ^U !
4T9C;N (! MOVE;TS4 ,"!=E1 S9CE ! MOVE;TS
>E ! SAME1 ! ELE;TS M/ AL 2 ! SAME
"EY":4 ,! "PICLES ( E>?1 !N1 9 ANO!R _W
MOVE NATUR,Y AL 6\R C5TRE & XS FIRE 6\R
CIRCUMF];E4 ,?1 H["E1 IS IMPOSSI#1 S9CE1
IF X 7 TRUE1 E>? M/1 9 XS [N _W1 MOVE
UPW>DS1 & FIRE 6! C5TRE2 9 ! SAME WAY !
E>? ( \R _W M/ MOVE NATUR,Y AWAY F !
C5TRE :5 X MOVES T[>DS ! C5TRE ( ANO!R
UNIV]SE4 ,? FOLL[S F ! SUPPOS$
JUXTAPOSI;N (! _WS4 ,= EI WE M/ REFUSE
6ADMIT ! ID5TICAL NATURE (! SIMPLE
BODIES 9 ! V>I\S UNIV]SES1 OR1 ADMITT+
?1 WE M/ MAKE ! C5TRE &! EXTREM;Y "O Z
SU7E/$4 ,? 2+ S1 X FOLL[S T "! _C 2 M
_WS ?AN "O4
  ,6PO/ULATE A DI6];E ( NATURE 9 !
SIMPLE BODIES AC Z !Y >E M OR LESS 4TANT
F _! PROP] PLACES IS UNR1SONA#4 ,= :AT
DI6];E C X MAKE :E!R WE SAY T A ?+ IS ?
4T.E AWAY OR T8 ,"O WD H 6SUPPOSE A
DI6];E PROPOR;NATE 6! 4T.E & 9CR1S+ ) X1
B ! =M IS 9 FACT ! SAME4 ,MOREOV]1 !
BODIES M/ H "S MOVE;T1 S9CE ! FACT T !Y
MOVE IS Q EVID5T4 ,>E WE 6SAY !N T ALL
_! MOVE;TS1 EV5 ^? : >E MUTU,Y 3TR>Y1 >E
DUE 63/RA9T8 ,NO1 =A BODY : HAS NO
NATURAL MOVE;T AT ALL _C 2 MOV$ 03/RA9T4
,IF !N ! BODIES H A NATURAL MOVE;T1 !
MOVE;T (! "PICUL> 9/.ES ( EA* =M M/
NECESS>ILY H = GOAL A PLACE NUM]IC,Y "O1
I4E4 A "PICUL> C5TRE OR A "PICUL>
EXTREM;Y4 ,IF X 2 SU7E/$ T ! GOAL 9 EA*
CASE IS "O 9 =M B NUM]IC,Y M ?AN "O1 ON
! ANALOGY ( "PICUL>S : >E _M ?\< EA*
UNDI6]5TIAT$ 9 =M1 WE REPLY T ! V>IETY (
GOAL _C 2 LIMIT$ 6? POR;N OR T B M/
EXT5D 6ALL ALIKE4 ,= ALL >E EQU,Y
UNDI6]5TIAT$ 9 =M1 B ANY "O IS DI6]5T
NUM]IC,Y F ANY O!R4 ,:AT ,I M1N IS ?3 IF
! POR;NS 9 ? _W 2HAVE SIMIL>LY BO? 6"O
ANO!R & 6^? 9 ANO!R _W1 !N ! POR;N : IS
TAK5 H;E W N 2HAVE DI6]5TLY EI F !
POR;NS 9 ANO!R _W OR F ^? 9 ! SAME _W1 B
SIMIL>LY 6!M1 S9CE 9 =M NO POR;N DI6]S F
ANO!R4 ,! RESULT IS T WE M/ EI AB&ON \R
PRES5T ASSUMP;N OR ASS]T T ! C5TRE &!
EXTREM;Y >E EA* NUM]IC,Y "O4 ,B ? 2+ S1
! H1V51 0! SAME EVID;E &! SAME NEC
9F];ES1 M/ 2 "O ONLY & NO M4
  ,A 3SID],N (! O!R K9DS ( MOVE;T AL
MAKES X PLA9 T "! IS "S PO9T 6: E>? &
FIRE MOVE NATUR,Y4 ,= 9 G5]AL T : IS
MOV$ *ANGES F "S?+ 96"S?+1 ! />T+-PO9T &
! GOAL 2+ DI6]5T 9 =M1 & ALW X IS A
F9ITE *ANGE4 ,= 9/.E1 6RECOV] H1L? IS
6*ANGE F 41SE 6H1L?1 69CR1SE IS 6*ANGE F
SMALL;S 6GRT;S4 ,LOCOMO;N M/ 2 SIMIL>3 =
X AL HAS XS GOAL & />T+-PO9T--& "!=E !
/>T+-PO9T &! GOAL (! NATURAL MOVE;T M/
DI6] 9 =M-J Z ! MOVE;T ( -+ 6H1L? DOES N
TAKE ANY DIREC;N : *.E OR ! WI%ES (!
MOV] MAY SELECT4 ,?US1 TOO1 FIRE & E>?
MOVE N 69F9;Y B 6OPPOSITE PO9TS2 & S9CE
! OPPOSI;N 9 PLACE IS 2T ABV & 2L1 ^! W
2 ! LIMITS ( _! MOVE;T4 7,EV5 9 CIRCUL>
MOVE;T "! IS A SORT ( OPPOSI;N 2T ! 5DS
(! DIAMET]1 ?\< ! MOVE;T Z A :OLE HAS NO
3TR>Y3 S T "H TOO ! MOVE;T HAS 9 A S5SE
AN OPPOS$ & F9ITE GOAL47 ,"! M/ "!=E 2
"S 5D 6LOCOMO;N3 X _C 3T9UE 69F9;Y4
  ,? 3CLU.N T LOCAL MOVE;T IS N 3T9U$
69F9;Y IS CORROBORAT$ 0! FACT T E>?
MOVES M QKLY ! NE>] X IS 6! C5TRE1 &
FIRE ! NE>] X IS 6! UPP] PLACE4 ,B IF
MOVE;T 7 9F9ITE SPE$ WD 2 9F9ITE AL2 &
IF SPE$ !N WEI<T & LI<T;S4 ,= Z SUP]IOR
SPE$ 9 D[NW>D MOVE;T IMPLIES SUP]IOR
WEI<T1 S 9F9ITE 9CR1SE ( WEI<T
NECESSITATES 9F9ITE 9CR1SE ( SPE$4
  ,FUR!R1 X IS N ! AC;N ( ANO!R BODY T
MAKES "O ( ^! BODIES MOVE UP &! O!R D[N2
NOR IS X 3/RA9T1 L ! ,8EXTRU.N0' ( "S
WRIT]S4 ,= 9 T CASE ! L>G] ! MASS ( FIRE
OR E>? ! SL[] WD 2 ! UPW>D OR D[NW>D
MOVE;T2 B ! FACT IS ! REV]SE3 ! GRT] !
MASS ( FIRE OR E>? ! QK] ALW IS XS
MOVE;T T[>DS XS [N PLACE4 ,AG1 ! SPE$ (!
MOVE;T WD N 9CR1SE T[>DS ! 5D IF X 7 DUE
63/RA9T OR EXTRU.N2 =A 3/RA9$ MOVE;T ALW
DIM9I%ES 9 SPE$ Z ! S\RCE ( 3/RA9T
2COMES M 4TANT1 &A BODY MOVES )\T 3/RA9T
6! PLACE :;E X 0 MOV$ 03/RA9T4
  ,A 3SID],N ( ^! PO9TS1 !N1 GIVES
ADEQUATE ASSUR.E (! TRU? ( \R 3T5;NS4 ,!
SAME CD AL 2 %[N )! AID (! 4CUS.NS :
FALL "U ,F/ ,PHILOSOPHY1 Z WELL Z F !
NATURE (! CIRCUL> MOVE;T1 : M/ 2 ET]NAL
BO? "H & 9 ! O!R _WS4 ,X IS PLA91 TOO1 F
! FOLL[+ 3SID],NS T ! UNIV]SE M/ 2 "O4
  ,! BODILY ELE;TS >E ?REE1 & "!=E !
PLACES (! ELE;TS W 2 ?REE AL2 ! PLACE1
F/1 (! BODY : S9KS 6! BOTTOM1 "NLY !
REGION AB ! C5TRE2 ! PLACE1 SECONDLY1 (!
REVOLV+ BODY1 "NLY ! \T]MO/ PLACE1 &
?IRDLY1 ! 9T]M$IATE PLACE1 2L;G+ 6!
9T]M$IATE BODY4 ,"H 9 ? ?IRD PLACE W 2 !
BODY : RISES 6! SURFACE2 S9CE1 IF N "H1
X W 2 ELSE":1 & X _C 2 ELSE":3 = WE H
TWO BODIES1 "O WEI<T.S1 "O 5D[$ ) WEI<T1
& 2L IS PLACE (! BODY 5D[$ ) WEI<T1 S9CE
! REGION AB ! C5TRE HAS BE5 GIV5 6! H1VY
BODY4 ,& XS POSI;N _C 2 UNNATURAL 6X1 =
X WD H 6BE NATURAL 6"S?+ ELSE1 & "! IS
NO?+ ELSE4 ,X M/ !N O3UPY ! 9T]M$IATE
PLACE4 ,:AT 4T9C;NS "! >E )9 ! 9T]M$IATE
XF WE W EXPLA9 LAT] ON4
  ,WE H N[ SD 5 6MAKE PLA9 ! "* & NUMB]
(! BODILY ELE;TS1 ! PLACE ( EA*1 &
FUR!R1 9 G5]AL1 H[ _M 9 NUMB] ! V>I\S
PLACES >E4
                   #I
  ,WE M/ %[ N ONLY T ! H1V5 IS "O1 B AL
T M ?AN "O H1V5 IS &1 FUR!R1 T1 Z EXEMPT
F DECAY & G5],N1 ! H1V5 IS ET]NAL4 ,WE
MAY 2G9 0RAIS+ A DI6ICULTY4 ,F "O PO9T (
VIEW X MI<T SEEM IMPOSSI# T ! H1V5 %D 2
"O & UNIQUE1 S9CE 9 ALL =M,NS & PRODUCTS
:E!R ( NATURE OR ( >T WE C 4T+UI% ! %APE
9 XF &! %APE 9 -B9,N ) MATT]4 ,= 9/.E !
=M (! SPH]E IS "O ?+ &! GOLD OR BRONZE
SPH]E ANO!R2 ! %APE (! CIRCLE AG IS "O
?+1 ! BRONZE OR WOOD5 CIRCLE ANO!R4 ,=
:5 WE /ATE ! ESS5TIAL NATURE (! SPH]E OR
CIRCLE WE D N 9CLUDE 9 ! =MULA GOLD OR
BRONZE1 2C !Y D N 2L;G 6! ESS;E1 B IF WE
>E SP1K+ (! COPP] OR GOLD SPH]E WE D
9CLUDE !M4 ,WE / MAKE ! 4T9C;N EV5 IF WE
_C 3CV OR APPREH5D ANY O!R EXAMPLE 2S !
"PICUL> ?+4 ,? MAY1 ( C\RSE1 "S"TS 2 !
CASE3 X MI<T BE1 = 9/.E1 T ONLY "O
CIRCLE CD 2 F.D2 YET N"O ! LESS ! DI6];E
W REMA9 2T ! 2+ ( CIRCLE &( ? "PICUL>
CIRCLE1 ! "O 2+ =M1 ! O!R =M 9 MATT]1
I4E4 A "PICUL> ?+4 ,N[ S9CE ! UNIV]SE IS
P]CEPTI# X M/ 2 REG>D$ Z A "PICUL>2 =
"EY?+ T IS P]CEPTI# SUBSI/S1 Z WE "K1 9
MATT]4 ,B IF X IS A "PICUL>1 "! W 2 A
4T9C;N 2T ! 2+ ( ,8? UNIV]SE0' &(
,8UNIV]SE0' UNQUALIFI$4 ,"! IS A DI6];E1
!N1 2T ,8? UNIV]SE0' & SIMPLE
,8UNIV]SE0'2 ! SECOND IS =M & %APE1 ! F/
=M 9 -B9,N ) MATT]2 & ANY %APE OR =M
HAS1 OR MAY H1 M ?AN "O "PICUL> 9/.E4
  ,ON ! SUPPOSI;N ( ,=MS S* Z "S ASS]T1
? M/ 2 ! CASE1 & EQU,Y ON ! VIEW T NO S*
5T;Y HAS A SEP>ATE EXI/;E4 ,= 9 E CASE 9
: ! ESS;E IS 9 MATT] X IS A FACT (
OBS]V,N T ! "PICUL>S ( L =M >E S"EAL OR
9F9ITE 9 NUMB]4 ,H;E "! EI >E1 OR MAY
BE1 M H1V5S ?AN "O4 ,ON ^! GR.DS1 !N1 X
MI<T 2 9F]R$ EI T "! >E OR T "! MI<T 2
S"EAL H1V5S4 ,WE M/1 H["E1 RETURN & ASK
H[ M* ( ? >GU;T IS CORRECT & H[ M* N4
  ,N[ X IS Q "R 6SAY T ! =MULA (! %APE
A"P F ! MATT] M/ 2 DI6]5T F T (! %APE 9
! MATT]1 & WE MAY ALL[ ? 6BE TRUE4 ,WE
>E N1 H["E1 "!=E -PELL$ 6ASS]T A
PLURAL;Y ( _WS4 ,S* A PLURAL;Y IS 9 FACT
IMPOSSI# IF ? _W 3TA9S ! 5TIRETY (
MATT]1 Z 9 FACT X DOES4 ,B P]H \R 3T5;N
C 2 MADE CLE>] 9 ? WAY4 ,SUPPOSE
,8AQUIL9;Y0' 6BE CURVATURE 9 ! NOSE OR
FLE%1 & FLE% 6BE ! MATT] ( AQUIL9;Y4
,SUPPOSE FUR!R1 T ALL FLE% CAME TGR 96A
S+LE :OLE ( FLE% 5D[$ ) ? AQUIL9E
QUAL;Y4 ,!N NEI WD "! BE1 NOR CD "!
>ISE1 ANY O!R ?+ T 0 AQUIL9E4 ,SIMIL>LY1
SUPPOSE FLE% & B"OS 6BE ! MATT] ( MAN1 &
SUPPOSE A MAN 6BE CR1T$ ( ALL FLE% & ALL
B"OS 9 9DISSOLU# UNION4 ,! POSSIBIL;Y (
ANO!R MAN WD 2 REMOV$4 ,:AT"E CASE Y
TOOK X WD 2 ! SAME4 ,! G5]AL RULE IS ?3
A ?+ ^: ESS;E RESIDES 9 A SUB/RATUM (
MATT] C N"E -E 962+ 9 ! ABS;E ( ALL
MATT]4 ,N[ ! UNIV]SE IS C]TA9LY A
"PICUL> &A MAT]IAL ?+3 IF H["E1 X IS
-POS$ N (A "P B (! :OLE ( MATT]1 !N ?\<
! 2+ ( ,8UNIV]SE0' &( ,8? UNIV]SE0' >E /
4T9CT1 YET "! IS NO O!R UNIV]SE1 & NO
POSSIBIL;Y ( O!RS 2+ MADE1 2C ALL !
MATT] IS ALR 9CLUD$ 9 ?4 ,X REMA9S1 !N1
ONLY 6PROVE T X IS -POS$ ( ALL NATURAL
P]CEPTI# BODY4
  ,F/1 H["E1 WE M/ EXPLA9 :AT WE M1N BY
,8H1V50' & 9 H[ _M S5SES WE USE ! ^W1 9
ORD] 6MAKE CLE>] ! OBJECT ( \R 9QUIRY4
7A7 ,9 "O S5SE1 !N1 WE CALL ,8H1V50' !
SUB/.E (! EXTREME CIRCUMF];E (! :OLE1 OR
T NATURAL BODY ^: PLACE IS AT ! EXTREME
CIRCUMF];E4 ,WE RECOGNIZE HABITU,Y A
SPECIAL "R 6! "N ,8H1V50' 9 ! EXTREM;Y
OR UPP] REGION1 : WE TAKE 6BE ! S1T (
ALL T IS DIV9E4 7B7 ,9 ANO!R S5SE1 WE
USE ? "N =! BODY 3T9U\S )! EXTREME
CIRCUMF];E : 3TA9S ! MOON1 ! SUN1 & "S (
! />S2 ^! WE SAY >E ,8IN ! H1V50'4 7C7
,9 YET ANO!R S5SE WE GIVE ! "N 6ALL BODY
9CLUD$ )9 EXTREME CIRCUMF];E1 S9CE WE
HABITU,Y CALL ! :OLE OR TOTAL;Y ,8!
H1V50'4 ,! ^W1 !N1 IS US$ 9 ?REE S5SES4
  ,N[ ! :OLE 9CLUD$ )9 ! EXTREME
CIRCUMF];E M/ 2 -POS$ ( ALL PHYSICAL &
S5SI# BODY1 2C "! NEI IS1 NOR C -E 962+1
ANY BODY \TSIDE ! H1V54 ,= IF "! IS A
NATURAL BODY \TSIDE ! EXTREME CIRCUMF];E
X M/ 2 EI A SIMPLE OR A -POSITE BODY1 &
XS POSI;N M/ 2 EI NATURAL OR UNNATURAL4
,B X _C 2 ANY (! SIMPLE BODIES4 ,=1 F/1
X HAS BE5 %[N T T : MOVES 9 A CIRCLE _C
*ANGE XS PLACE4 ,&1 SECONDLY1 X _C 2 T :
MOVES F ! C5TRE OR T : LIES L[E/4
,NATUR,Y !Y CD N 2 "!1 S9CE _! PROP]
PLACES >E ELSE":2 & IF ^! >E "!
UNNATUR,Y1 ! EXT]IOR PLACE W 2 NATURAL
6"S O!R BODY1 S9CE A PLACE : IS
UNNATURAL 6"O BODY M/ 2 NATURAL 6ANO!R3
B WE SAW T "! IS NO O!R BODY 2SS ^!4 ,!N
X IS N POSSI# T ANY SIMPLE BODY %D 2
\TSIDE ! H1V54 ,B1 IF NO SIMPLE BODY1
NEI C ANY MIX$ BODY 2 "!3 =! PRES;E (!
SIMPLE BODY IS 9VOLV$ 9 ! PRES;E (!
MIXTURE4 ,FUR!R NEI C ANY BODY -E 96T
PLACE3 = X W D S EI NATUR,Y OR
UNNATUR,Y1 & W 2 EI SIMPLE OR -POSITE2 S
T ! SAME >GU;T W APPLY1 S9CE X MAKES NO
DI6];E :E!R ! "Q IS ,8DOES ,A EXI/80' OR
,8CD ,A -E 6EXI/80' ,F \R >GU;TS !N X IS
EVID5T N ONLY T "! IS N1 B AL T "! CD
N"E -E 6BE1 ANY BODILY MASS :AT"E \TSIDE
! CIRCUMF];E4 ,! _W Z A :OLE1 "!=E1
9CLUDES ALL XS APPROPRIATE MATT]1 : IS1
Z WE SAW1 NATURAL P]CEPTI# BODY4 ,S T
NEI >E "! N[1 NOR H "! "E BE51 NOR C "!
"E 2 =M$ M H1V5S ?AN "O1 B ? H1V5 ( \RS
IS "O & UNIQUE & -PLETE4
  ,X IS "!=E EVID5T T "! IS AL NO PLACE
OR VOID OR "T \TSIDE ! H1V54 ,= 9 E
PLACE BODY C 2 PRES5T2 & VOID IS SD 6BE
T 9 : ! PRES;E ( BODY1 ?\< N ACTUAL1 IS
POSSI#2 & "T IS ! NUMB] ( MOVE;T4 ,B 9 !
ABS;E ( NATURAL BODY "! IS NO MOVE;T1 &
\TSIDE ! H1V51 Z WE H %[N1 BODY NEI
EXI/S NOR C -E 6EXI/4 ,X IS CLE> !N T "!
IS NEI PLACE1 NOR VOID1 NOR "T1 \TSIDE !
H1V54 ,H;E :AT"E IS "!1 IS ( S* A NATURE
Z N 6O3UPY ANY PLACE1 NOR DOES "T AGE X2
NOR IS "! ANY *ANGE 9 ANY (! ?+S : LIE
2Y ! \T]MO/ MO;N2 !Y 3T9UE "? _! 5TIRE
DUR,N UNALT]A# & UNMODIFI$1 LIV+ ! BE/ &
MO/ SELFSU6ICI5T ( LIVES4 ,Z A MATT] (
FACT1 ? ^W ,8DUR,N0' POSSESS$ A DIV9E
SIGNIFIC.E =! ANCI5TS1 =! FULFIL;T :
9CLUDES ! P]IOD ( LIFE ( ANY CR1TURE1
\TSIDE ( : NO NATURAL DEVELOP;T C FALL1
HAS BE5 CALL$ XS DUR,N4 ,ON ! SAME
PR9CIPLE ! FULFIL;T (! :OLE H1V51 !
FULFIL;T : 9CLUDES ALL "T & 9F9;Y1 IS
,8DUR,N'-A "N BAS$ ^U ! FACT T X IS ALW-
DUR,N IMMORTAL & DIV9E4 ,F X DERIVE ! 2+
& LIFE : O!R ?+S1 "S M OR LESS
>TICULATELY B O!RS FEEBLY1 5JOY4 ,S1
TOO1 9 XS 4CUS.NS 3C]N+ ! DIV9E1 POPUL>
PHILOSOPHY (T5 PROP.DS ! VIEW T :AT"E IS
DIV9E1 :AT"E IS PRIM>Y & SUPREME1 IS
NECESS>ILY UN*ANGEA#4 ,? FACT 3FIRMS :AT
WE H SD4 ,= "! IS NO?+ ELSE /R;G] ?AN X
6MOVE X-S9CE T WD M1N M DIV9E-& X HAS NO
DEFECT & LACKS N"O ( XS PROP] EXCELL;ES4
,XS UNC1S+ MOVE;T1 !N1 IS AL R1SONA#1
S9CE "EY?+ C1SES 6MOVE :5 X -ES 6XS
PROP] PLACE1 B ! BODY ^: PA? IS ! CIRCLE
HAS "O &! SAME PLACE = />T+-PO9T & GOAL4
                  #AJ
  ,HAV+ E/ABLI%$ ^! 4T9C;NS1 WE MAY N[
PROCE$ 6! "Q :E!R ! H1V5 IS UNG5]AT$ OR
G5]AT$1 9DE/RUCTI# OR DE/RUCTI#4 ,LET U
/>T )A REVIEW (! !ORIES ( O!R ?9K]S2 =!
PRO(S (A !ORY >E DI6ICULTIES =! 3TR>Y
!ORY4 ,2SS1 ^? :O H F/ HE>D ! PL1S ( \R
ADV]S>IES W 2 M LIKELY 6CR$IT ! ASS];NS
: WE >E GO+ 6MAKE4 ,WE % 2 LESS OP5 6!
*>GE ( PROCUR+ JUDGE;T 0DEFAULT4 ,6GIVE
A SATISFACTORY DECI.N Z 6! TRU? X IS NEC
6BE R AN >BITRATOR ?AN A "PY 6! 4PUTE4
  ,T ! _W 0 G5]AT$ ALL >E AGRE$1 B1
G5],N OV]1 "S SAY T X IS ET]NAL1 O!RS
SAY T X IS DE/RUCTI# L ANY O!R NATURAL
=M,N4 ,O!RS AG1 ) ,EMP$LIOCLES (
,ACRAGAS & ,H]ACLITUS ( ,EPHESUS1 2LIEVE
T "! IS ALT]N,N 9 ! DE/RUCTIVE PROCESS1
: TAKES N[ ? DIREC;N1 N[ T1 & 3T9UES )\T
5D4
  ,N[ 6ASS]T T X 0 G5]AT$ & YET IS
ET]NAL IS 6ASS]T ! IMPOSSI#2 = WE _C
R1SONABLY ATTRIBUTE 6ANY?+ ANY "*I/ICS B
^? : OBS]V,N DETECTS 9 _M OR ALL 9/.ES4
,B 9 ? CASE ! FACTS PO9T ! O!R WAY3
G5]AT$ ?+S >E SE5 ALW 6BE DE/ROY$4
,FUR!R1 A ?+ ^: PRES5T /ATE _H NO 2G9N+
& : CD N H BE5 O!R ?AN X 0 AT ANY
PREVI\S MO;T "?\T XS 5TIRE DUR,N1 _C
POSSIBLY 2 *ANG$4 ,= "! W H 6BE "S CAUSE
( *ANGE1 & IF ? _H BE5 PRES5T E>LI] X WD
H MADE POSSI# ANO!R 3DI;N ( T 6: ANY O!R
3DI;N 0 IMPOSSI#4 ,SUPPOSE T ! _W 0 =M$
\ ( ELE;TS : 7 =M]LY O!RWISE 3DI;N$ ?AN
Z !Y >E N[4 ,!N 7#A7 IF _! 3DI;N 0 ALW S
& CD N H BE5 O!RWISE1 ! _W CD N"E H -E
962+4 ,& 7#B7 IF ! _W DID -E 962+1 !N1
CLE>LY1 _! 3DI;N M/ H BE5 CAPA# ( *ANGE
& N ET]NAL3 AF -B9,N "!=E !Y W 2 4P]S$1
J Z 9 ! PA/ AF 4P].N !Y CAME 96-B9,N1 &
? PROCESS EI HAS BE51 OR CD H BE51
9DEF9ITELY REP1T$4 ,B IF ? IS S1 ! _W _C
2 9DE/RUCTI#1 & X DOES N MATT] :E!R !
*ANGE ( 3DI;N HAS ACTU,Y O3URR$ OR
REMA9S A POSSIBIL;Y4
  ,"S ( ^? :O HOLD T ! _W1 ?\<
9DE/RUCTI#1 0 YET G5]AT$1 TRY 6SUPPORT
_! CASE 0A P>ALLEL : IS ILLUSORY4 ,!Y
SAY T 9 _! /ATE;TS AB XS G5],N !Y >E DO+
:AT GEOMETRICIANS D :5 !Y 3/RUCT _!
FIGURES1 N IMPLY+ T ! UNIV]SE RE,Y _H A
2G9N+1 B = DIDACTIC R1SONS FACILITAT+
"U/&+ 0EXHIBIT+ ! OBJECT1 L ! FIGURE1 Z
9 C\RSE ( =M,N4 ,! TWO CASES1 Z WE SD1
>E N P>ALLEL2 =1 9 ! 3/RUC;N (! FIGURE1
:5 ! V>I\S /EPS >E -PLET$ ! REQUIR$
FIGURE =?) RESULTS2 B 9 ^! O!R
DEMON/R,NS :AT RESULTS IS N T : 0
REQUIR$4 ,9DE$ X _C 2 S2 = ANTEC$5T &
3SEQU5T1 Z ASSUM$1 >E 9 3TRADIC;N4 ,!
ORD]$1 X IS SD1 >OSE \ (! UNORD]$2 &!
SAME ?+ _C 2 AT ! SAME "T BO? ORD]$ &
UNORD]$2 "! M/ 2 A PROCESS &A LAPSE ( "T
SEP>AT+ ! TWO /ATES4 ,9 ! FIGURE1 ON !
O!R H&1 "! IS NO TEMPORAL SEP>,N4 ,X IS
CLE> !N T ! UNIV]SE _C 2 AT ONCE ET]NAL
& G5]AT$4
  ,6SAY T ! UNIV]SE ALT]NATELY -B9ES &
4SOLVES IS NO M P>ADOXICAL ?AN 6MAKE X
ET]NAL B V>Y+ 9 %APE4 ,X IS Z IF "O 7
6?9K T "! 0 N[ DE/RUC;N & N[ EXI/;E :5 F
A * A MAN IS G5]AT$1 & F A MAN A *4 ,= X
IS CLE> T :5 ! ELE;TS -E TGR ! RESULT IS
N A *.E SY/EM & -B9,N1 B ! V SAME Z 2F-
ESPECI,Y ON ! VIEW ( ^? :O HOLD ? !ORY1
S9CE !Y SAY T ! 3TR>Y IS ! CAUSE ( EA*
/ATE4 ,S T IF ! TOTAL;Y ( BODY1 : IS A
3T9UUM1 IS N[ 9 ? ORD] OR 4POSI;N & N[ 9
T1 & IF ! -B9,N (! :OLE IS A _W OR H1V51
!N X W N 2 ! _W T -ES 962+ & IS DE/ROY$1
B ONLY XS 4POSI;NS4
  ,IF ! _W IS 2LIEV$ 6BE "O1 X IS
IMPOSSI# 6SUPPOSE T X %D BE1 Z A :OLE1
F/ G5]AT$ & !N DE/ROY$1 N"E 6REAPPE>2
S9CE 2F X CAME 962+ "! 0 ALW PRES5T !
-B9,N PRIOR 6X1 & T1 WE HOLD1 CD N"E
*ANGE IF X 0 N"E G5]AT$4 ,IF1 ON ! O!R
H&1 ! _WS >E 9F9ITE 9 NUMB] ! VIEW IS M
PLAUSI#4 ,B :E!R ? IS1 OR IS N1 IMPOSSI#
W 2 CLE> F :AT FOLL[S4 ,= "! >E "S :O
?9K X POSSI# BO? =! UNG5]AT$ 6BE DE/ROY$
&=! G5]AT$ 6P]SI/ UNDE/ROY$4 7,? IS HELD
9 ! ,TIMAEUS1 ": ,PLATO SAYS T ! H1V51
?\< X 0 G5]AT$1 W N"O ! LESS EXI/
6ET]N;Y47 ,S F> Z ! H1V5 IS 3C]N$ WE H
ANSW]$ ? VIEW ) >GU;TS APPROPRIATE 6!
NATURE (! H1V53 ON ! G5]AL "Q WE % ATTA9
CLE>;S :5 WE EXAM9E ! MATT] UNIV]S,Y4
                  #AA
  ,WE M/ F/ 4T+UI% ! S5SES 9 : WE USE !
^WS ,8UNG5]AT$0' & ,8G5]AT$0'1
,8DE/RUCTI#0' & ,89DE/RUCTI#0'4 ,^! H _M
M1N+S1 & ?\< X MAY MAKE NO DI6];E 6!
>GU;T1 YET "S 3FU.N ( M9D M/ RESULT F
TR1T+ Z UNI=M 9 XS USE A ^W : HAS S"EAL
4T9CT APPLIC,NS4 ,! "* : IS ! GR.D (!
PR$IC,N W ALW REMA9 OBSCURE4
  ,! ^W ,8UNG5]AT$0' !N IS US$ 7A7 9 "O
S5SE :5"E "S?+ N[ IS : =M]LY 0 N1 NO
PROCESS ( 2COM+ OR *ANGE 2+ 9VOLV$4 ,S*
IS ! CASE1 AC 6"S1 ) 3TACT & MO;N1 S9CE
"! IS NO PROCESS ( -+ 6BE 9 3TACT OR 9
MO;N4 7B7 ,X IS US$ 9 ANO!R S5SE1 :5
"S?+ : IS CAPA# ( -+ 6BE1 ) OR )\T
PROCESS1 DOES N EXI/2 S* A ?+ IS
UNG5]AT$ 9 ! S5SE T XS G5],N IS N A FACT
B A POSSIBIL;Y4 7C7 ,X IS AL APPLI$ ":
"! IS G5]AL IMPOSSIBIL;Y ( ANY G5],N S*
T ! ?+ N[ IS : !N 0 N4 ,&
,8IMPOSSIBIL;Y0' HAS TWO USES3 F/1 ": X
IS UNTRUE 6SAY T ! ?+ C "E -E 962+1 &
SECONDLY1 ": X _C D S EASILY1 QKLY1 OR
WELL4 ,9 ! SAME WAY ! ^W ,8G5]AT$0' IS
US$1 7A7 F/1 ": :AT =M]LY 0 N AFWS IS1
:E!R A PROCESS ( 2COM+ 0 OR 0 N 9VOLV$1
S L;G Z T : !N 0 N1 N[ IS2 7B7 SECONDLY1
( ANY?+ CAPA# ( EXI/+1 ,8CAPA#0' 2+
DEF9$ ) REF];E EI 6TRU? OR 6FACIL;Y2 7C7
?IRDLY1 ( ANY?+ 6: ! PASSAGE F N 2+ 62+
2L;GS1 :E!R ALR ACTUAL1 IF XS EXI/;E IS
DUE 6A PA/ PROCESS ( 2COM+1 OR N YET
ACTUAL B ONLY POSSI#4 ,! USES (! ^WS
,8DE/RUCTI#0' & ,89DE/RUCTI#0' >E
SIMIL>4 ,8,DE/RUCTI#0' IS APPLI$ 7A7 6T
: =M]LY 0 & AFWS EI IS N OR MI<T N BE1
:E!R A P]IOD ( 2+ DE/ROY$ & *ANG$
9T]V5ES OR N2 & 7B7 "S"TS WE APPLY ! ^W
6T : A PROCESS ( DE/RUC;N MAY CAUSE N
6BE2 & AL 7C7 9 A ?IRD S5SE1 6T : IS
EASILY DE/RUCTI#1 6! ,8EASILY DE/ROY$0'1
S 6SP1K4 ,(! 9DE/RUCTI# ! SAME A3.T
HOLDS GD4 ,X IS EI 7A7 T : N[ IS & N[ IS
N1 )\T ANY PROCESS ( DE/RUC;N1 L 3TACT1
: )\T 2+ DE/ROY$ AFWS IS N1 ?\< =M]LY X
WAS2 OR 7B7 T : IS B MI<T N BE1 OR : W
AT "S "T N BE1 ?\< X N[ IS4 ,= Y EXI/ N[
& S DOES ! 3TACT2 YET BO? >E DE/RUCTI#1
2C A "T W -E :5 X W N 2 TRUE ( Y T Y
EXI/1 NOR ( ^! ?+S T !Y >E 9 3TACT4
,?IRDLY 7C7 9 XS MO/ PROP] USE1 X IS T :
IS1 B IS 9CAPA# ( ANY DE/RUC;N S* T ! ?+
: N[ IS LAT] C1SES 6BE OR MI<T C1SE 6BE2
OR AG1 T : HAS N YET BE5 DE/ROY$1 B 9 !
FUTURE MAY C1SE 6BE4 ,= 9DE/RUCTI# IS AL
US$ ( T : IS DE/ROY$ ) DI6ICULTY4
  ,? 2+ S1 WE M/ ASK :AT WE M1N BY
,8POSSI#0' & ,8IMPOSSI#0'4 ,= 9 XS MO/
PROP] USE ! PR$ICATE ,89DE/RUCTI#0' IS
GIV5 2C X IS IMPOSSI# T ! ?+ %D 2
DE/ROY$1 I4E4 EXI/ AT "O "T & N AT
ANO!R4 ,& ,8UNG5]AT$0' AL 9VOLVES
IMPOSSIBIL;Y :5 US$ = T : _C 2 G5]AT$1 9
S* FA%ION T1 :ILE =M]LY X 0 N1 LAT] X
IS4 ,AN 9/.E IS A -M5SURA# DIAGONAL4 ,N[
:5 WE SP1K (A P[] 6MOVE OR 6LIFT WEI<TS1
WE REF] ALW 6! MAXIMUM4 ,WE SP1K1 =
9/.E1 (A P[] 6LIFT A HUNDR$ TAL5TS OR
WALK A HUNDR$ /ADES-?\< A P[] 6E6ECT !
MAXIMUM IS AL A P[] 6E6ECT ANY "P (!
MAXIMUM-S9CE WE FEEL OBLIG$ 9 DEF9+ !
P[] 6GIVE ! LIMIT OR MAXIMUM4 ,A ?+1 !N1
: IS )9 X4 ,IF1 = EXAMPLE1 A MAN C LIFT
A HUNDR$ TAL5TS1 HE C AL LIFT TWO1 & IF
HE C WALK A HUNDR$ /ADES1 HE C AL WALK
TWO4 ,B ! P[] IS (! MAXIMUM1 &A ?+ SD1 )
REF];E 6XS MAXIMUM1 6BE 9CAPA# ( S M* IS
AL 9CAPA# ( ANY GRT] AM.T4 ,X IS1 =
9/.E1 CLE> T A P]SON :O _C WALK A ?\S&
/ADES W AL 2 UNA# 6WALK A ?\S& & "O4 ,?
PO9T NE$ N TR\# U1 = WE MAY TAKE X Z
SETTL$ T :AT IS1 9 ! /RICT S5SE1 POSSI#
IS DET]M9$ 0A LIMIT+ MAXIMUM4 ,N[ P]H !
OBJEC;N MI<T 2 RAIS$ T "! IS NO NECESS;Y
9 ?1 S9CE HE :O SEES A /ADE NE$ N SEE !
SMALL] M1SURES 3TA9$ 9 X1 :ILE1 ON !
3TR>Y1 HE :O C SEE A DOT OR HE> A SMALL
S.D W P]CV :AT IS GRT]4 ,?1 H["E1 DOES N
T\* \R >GU;T4 ,! MAXIMUM MAY 2 DET]M9$
EI 9 ! P[] OR 9 XS OBJECT4 ,! APPLIC,N (
? IS PLA94 ,SUP]IOR SI<T IS SI<T (!
SMALL] BODY1 B SUP]IOR SPE$ IS T (! GRT]
BODY4

                  #AB
  ,HAV+ E/ABLI%$ ^! 4T9C;NS WE C> N[
PROCE$ 6! SEQUEL4 ,IF "! >E ?+6 CAPA#
BO? ( 2+ &( N 2+1 "! M/ 2 "S DEF9ITE
MAXIMUM "T ( _! 2+ & N 2+2 A "T1 ,I M1N1
DUR+ : 3T9U$ EXI/;E IS POSSI# 6!M &A "T
DUR+ : 3T9U$ NONEXI/;E IS POSSI#4 ,& ?
IS TRUE 9 E CATEGORY1 :E!R ! ?+ IS1 =
EXAMPLE1 ,8MAN0'1 OR ,8:ITE0'1 OR ,8?REE
CUBITS L;G0'1 OR :AT"E X MAY BE4 ,= IF !
"T IS N DEF9ITE 9 QUANT;Y1 B L;G] ?AN
ANY T C 2 SU7E/$ & %ORT] ?AN N"O1 !N X W
2 POSSI# = "O &! SAME ?+ 6EXI/ = 9F9ITE
"T & N 6EXI/ = ANO!R 9F9;Y4 ,?1 H["E1 IS
IMPOSSI#4
  ,LET U TAKE \R />T F ? PO9T4 ,!
IMPOSSI# &! FALSE H N ! SAME SIGNIFIC.E4
,"O USE ( ,8IMPOSSI#0' & ,8POSSI#0'1 &
,8FALSE0' & ,8TRUE0'1 IS HYPO!TICAL4 ,X
IS IMPOSSI#1 = 9/.E1 ON A C]TA9 HYPO!SIS
T ! TRIANGLE %D H XS ANGLES EQUAL 6TWO
"R ANGLES1 & ON ANO!R ! DIAGONAL IS
-M5SURA#4 ,B "! >E AL ?+S POSSI# &
IMPOSSI#1 FALSE & TRUE1 ABSOLUTELY4 ,N[
X IS "O ?+ 6BE ABSOLUTELY FALSE1 & ANO!R
?+ 6BE ABSOLUTELY IMPOSSI#4 ,6SAY T Y >E
/&+ :5 Y >E N /&+ IS 6ASS]T A FALSEHOOD1
B N AN IMPOSSIBIL;Y4 ,SIMIL>LY 6SAY T A
MAN :O IS PLAY+ ! H>P1 B N S++1 IS S++1
IS 6SAY :AT IS FALSE B N IMPOSSI#4
,6SAY1 H["E1 T Y >E AT ONCE /&+ & SITT+1
OR T ! DIAGONAL IS -M5SURA#1 IS 6SAY :AT
IS N ONLY FALSE B AL IMPOSSI#4 ,?US X IS
N ! SAME ?+ 6MAKE A FALSE & 6MAKE AN
IMPOSSI# HYPO!SIS1 & F ! IMPOSSI#
HYPO!SIS IMPOSSI# RESULTS FOLL[4 ,A MAN
HAS1 X IS TRUE1 ! CAPAC;Y AT ONCE (
SITT+ &( /&+1 2C :5 HE POSSESSES ! "O HE
AL POSSESSES ! O!R2 B X DOES N FOLL[ T
HE C AT ONCE SIT & /&1 ONLY T AT ANO!R
"T HE C D ! O!R AL4 ,B IF A ?+ HAS =
9F9ITE "T M ?AN "O CAPAC;Y1 ANO!R "T IS
IMPOSSI# &! "TS M/ CO9CIDE4 ,?US IF A ?+
: EXI/S = 9F9ITE "T IS DE/RUCTI#1 X W H
! CAPAC;Y ( N 2+4 ,N[ IF X EXI/S =
9F9ITE "T LET ? CAPAC;Y 2 ACTUALIZ$2 & X
W 2 9 ACTUAL;Y AT ONCE EXI/5T & NON-
EXI/5T4 ,?US A FALSE 3CLU.N WD FOLL[ 2C
A FALSE ASSUMP;N 0 MADE1 B IF :AT 0
ASSUM$ _H N BE5 IMPOSSI# XS 3SEQU;E WD N
H BE5 IMPOSSI#4
  ,ANY?+ !N : ALW EXI/S IS ABSOLUTELY
IMP]I%A#4 ,X IS AL UNG5]AT$1 S9CE IF X 0
G5]AT$ X W H ! P[] = "S "T ( N 2+4 ,= Z
T : =M]LY WAS1 B N[ IS N1 OR IS CAPA# AT
"S FUTURE "T ( N 2+1 IS DE/RUCTI#1 S T :
IS CAPA# ( =M]LY N HAV+ BE5 IS G5]AT$4
,B 9 ! CASE ( T : ALW IS1 "! IS NO "T =
S* A CAPAC;Y ( N 2+1 :E!R ! SUPPOS$ "T
IS F9ITE OR 9F9ITE2 = XS CAPAC;Y ( 2+ M/
9CLUDE ! F9ITE "T S9CE X COV]S 9F9ITE
"T4
  ,X IS "!=E IMPOSSI# T "O &! SAME ?+ %D
2 CAPA# ( ALW EXI/+ &( ALW N-EXI/+4 ,&
,8N ALW EXI/+0'1 ! 3TRADICTORY1 IS AL
EXCLUD$4 ,?US X IS IMPOSSI# =A ?+ ALW
6EXI/ & YET 6BE DE/RUCTI#4 ,NOR1
SIMIL>LY1 C X 2 G5]AT$4 ,=( TWO
ATTRIBUTES IF ;,B _C 2 PRES5T )\T ;,A1 !
IMPOSSIBIL;Y ;,A ( PROVES ! IMPOSSIBIL;Y
( ,B4 ,:AT ALW IS1 !N1 S9CE X IS 9CAPA#
( "E N 2+1 _C POSSIBLY 2 G5]AT$4 ,B S9CE
! 3TRADICTORY ( ,8T : IS ALW CAPA# (
2+0' ,8T : IS N ALW CAPA# ( 2+0'2 :ILE
,8T : IS ALW CAPA# ( N 2+0' IS ! 3TR>Y1
^: 3TRADICTORY 9 TURN IS ,8T : IS N ALW
CAPA# ( N 2+0'1 X IS NEC T !
3TRADICTORIES ( BO? T]MS %D 2 PR$ICA# (
"O &! SAME ?+1 & ?US T1 9T]M$IATE 2T :AT
ALW IS & :AT ALW IS N1 "! %D 2 T 6: 2+ &
N-2+ >E BO? POSSI#2 =! 3TRADICTORY ( EA*
W AT "TS 2 TRUE ( X UN.S X ALW EXI/S4
,H;E T : N ALW IS N W "S"TS 2 & "S"TS N
BE2 & X IS CLE> T ? IS TRUE AL ( T : _C
ALW 2 B "S"TS IS & "!=E "S"TS IS N4 ,"O
?+1 !N1 W H ! P[] ( 2+1 & W ?US 2
9T]M$IATE 2T ! O!R TWO4
  ,EXPRES$ UNIV]S,Y \R >GU;T IS Z
FOLL[S4 ,LET "! 2 TWO ATTRIBUTES1 ;,A &
;,B1 N CAPA# ( 2+ PRES5T 9 ANY "O ?+
TGR1 :ILE EI ,A OR ;,C & EI ;,B OR ;,D
>E CAPA# ( 2+ PRES5T 9 "EY?+4 ,!N ;,C &
;,D M/ 2 PR$ICAT$ ( "EY?+ ( : NEI ,A NOR
;,B IS PR$ICAT$4 ,LET ;,E LIE 2T ;,A &
;,B2 = T : IS NEI ( TWO 3TR>IES IS A M1N
2T !M4 ,9 ;,E BO? ;,C & ;,D M/ 2 PRES5T1
= EI ,A OR ;,C IS PRES5T "EY": & "!=E 9
,E4 ,S9CE !N ,A IS IMPOSSI#1 ;,C M/ 2
PRES5T1 &! SAME >GU;T HOLDS ( ,D4
  ,NEI T : ALW IS1 "!=E1 NOR T : ALW IS
N IS EI G5]AT$ OR DE/RUCTI#4 ,& CLE>LY
:AT"E IS G5]AT$ OR DE/RUCTI# IS N
ET]NAL4 ,IF X W]E1 X WD 2 AT ONCE CAPA#
( ALW 2+ & CAPA# ( N ALW 2+1 B X HAS ALR
BE5 %[N T ? IS IMPOSSI#4 ,SURELY !N
:AT"E IS UNG5]AT$ & 9 2+ M/ 2 ET]NAL1 &
:AT"E IS 9DE/RUCTI# & 9 2+ M/ EQU,Y 2 S4
7,I USE ! ^WS ,8UNG5]AT$0' &
,89DE/RUCTI#0' 9 _! PROP] S5SE1
,8UNG5]AT$0' = T : N[ IS & CD N AT ANY
PREVI\S "T H BE5 TRULY SD N 6BE2
,89DE/RUCTI#0' = T : N[ IS & _C AT ANY
FUTURE "T 2 TRULY SD N 6BE47 ,IF1 AG1 !
TWO T]MS >E CO9CID5T1 IF ! UNG5]AT$ IS
9DE/RUCTI#1 &! 9DE/RUCTI# UNG5E>T$1 !N
EA* ( !M IS CO9CID5T ) ,8ET]NAL0'2 ANY?+
UNG5]AT$ IS ET]NAL & ANY?+ 9DE/RUCTI# IS
ET]NAL4 ,? IS CLE> TOO F ! DEF9I;N (!
T]MS1 ,:AT"E IS DE/RUCTI# M/ 2 G5]AT$2 =
X IS EI UNG5]AT$1 OR G5]AT$1 B1 IF
UNG5]AT$1 X IS 0HYPO!SIS 9DE/RUCTI#4
,:AT"E1 FUR!R1 IS G5]AT$ M/ 2 DE/RUCTI#4
,= X IS EI DE/RUCTI# OR 9DE/RUCTI#1 B1
IF 9DE/RUCTI#1 X IS 0HYPO!SIS UNG5]AT$4
  ,IF1 H["E1 ,89DE/RUCTI#0' &
,8UNG5]AT$0' >E N CO9CID5T1 "! IS NO
NECESS;Y T EI ! UNG5]AT$ OR ! 9DE/RUCTI#
%D 2 ET]NAL4 ,B !Y M/ 2 CO9CID5T1 =!
FOLL[+ R1SONS4 ,! T]MS ,8G5]AT$0' &
,8DE/RUCTI#0' >E CO9CID5T2 ? IS OBVI\S F
\R =M] REM>KS1 S9CE 2T :AT ALW IS & :AT
ALW IS N "! IS AN 9T]M$IATE : IS NEI1 &
T 9T]M$IATE IS ! G5]AT$ & DE/RUCTI#4 ,=
:AT"E IS EI ( ^! IS CAPA# BO? ( 2+ &( N
2+ =A DEF9ITE "T3 9 EI CASE1 ,I M1N1 "!
IS A C]TA9 P]IOD ( "T DUR+ : ! ?+ IS &
ANO!R DUR+ : X IS N4 ,ANY?+ "!=E : IS
G5]AT$ OR DE/RUCTI# M/ 2 9T]M$IATE4 ,N[
LET ,A 2 T : ALW IS & ;,B T : ALW IS N1
;,C ! G5]AT$1 & ;,D ! DE/RUCTI#4 ,!N ;,C
M/ 2 9T]M$IATE 2T ;,A & ,B4 ,= 9 _! CASE
"! IS NO "T 9 ! DIREC;N ( EI LIMIT1 9 :
EI ,A IS N OR ;,B IS4 ,B =! G5]AT$ "! M/
2 S* A "T EI ACTU,Y OR POT5TI,Y1 ?\< N =
;,A & ;,B 9 EI WAY4 ;,C !N W BE1 & AL N
BE1 =A LIMIT$ L5G? ( "T1 & ? IS TRUE AL
( ;,D1 ! DE/RUCTI#4 ,"!=E EA* IS BO?
G5]AT$ & DE/RUCTI#4 ,"!=E ,8G5]AT$0' &
,8DE/RUCTI#0' >E CO9CID5T4 ,N[ LET ;,E
/& =! UNG5]AT$1 ;,F =! G5]AT$1 ;,G =!
9DE/RUCTI#1 & ;,H =! DE/RUCTI#4 ,Z = ;,F
& ;,H1 X HAS BE5 %[N T !Y >E CO9CID5T4
,B :5 T]MS /& 6"O ANO!R Z ^! D1 ;,F &
;,H CO9CID5T1 ;,E & ;,F N"E PR$ICAT$ (!
SAME ?+ B "O OR O!R ( "EY?+1 & ;,G & ;,H
LIKEWISE1 !N ;,E & ;,G M/ NE$S 2
CO9CID5T4 ,= SUPPOSE T ;,E IS N CO9CID5T
) ;,G1 !N ;,F W BE1 S9CE EI ;,E OR ;,F
IS PREDICTA# ( "EY?+4 ,B ( T ( : ;,F IS
PR$ICAT$ ;,H W 2 PR$ICA# AL4 ;,H W !N 2
CO9CID5T ) ;,G1 B ? WE SAW 6BE IMPOSSI#4
,&! SAME >GU;T %[S T ;,G IS CO9CID5T )
,E4
  ,N[ ! REL,N (! UNG5]AT$ 7,E7 6! G5]AT$
7,F7 IS ! SAME Z T (! 9DE/RUCTI# 7,G7 6!
DE/RUCTI# 7,H74 ,6SAY !N T "! IS NO
R1SON :Y ANY?+ %D N 2 G5]AT$ & YET
9DE/RUCTI# OR UNG5]AT$ & YET DE/ROY$1
6IMAG9E T 9 ! "O CASE G5],N & 9 ! O!R
CASE DE/RUC;N O3URS ONCE = ALL1 IS
6DE/ROY "P (! DATA4 ,= 7#A7 "EY?+ IS
CAPA# ( ACT+ OR 2+ ACT$ ^U1 ( 2+ OR N
2+1 EI = AN 9F9ITE1 OR =A DEF9ITELY
LIMIT$ SPACE ( "T2 &! 9F9ITE "T IS ONLY
A POSSI# ALT]NATIVE 2C X IS AF A FA%ION
DEF9$1 Z A L5G? ( "T : _C 2 EXCE$$4 ,B
9F9;Y 9 "O DIREC;N IS NEI 9F9ITE OR
F9ITE4 7#B7 ,FUR!R1 :Y1 AF ALW EXI/+1 0
! ?+ DE/ROY$1 :Y1 AF AN 9F9;Y ( N 2+1 0
X G5]AT$1 AT "O MO;T R ?AN ANO!R8 ,IF E
MO;T IS ALIKE &! MO;TS >E 9F9ITE 9
NUMB]1 X IS CLE> T A G5]AT$ OR DE/RUCTI#
?+ EXI/$ = AN 9F9ITE "T4 ,X HAS "!=E =
AN 9F9ITE "T ! CAPAC;Y ( N 2+ 7S9CE !
CAPAC;Y ( 2+ &! CAPAC;Y ( N 2+ W 2
PRES5T TGR71 IF DE/RUCTI#1 9 ! "T 2F
DE/RUC;N1 IF G5]AT$1 9 ! "T AF G5],N4
,IF !N WE ASSUME ! TWO CAPACITIES 6BE
ACTUALIZ$1 OPPOSITES W 2 PRES5T TGR4
7#C7 ,FUR!R1 ? SECOND CAPAC;Y W 2 PRES5T
L ! F/ AT E MO;T1 S T ! ?+ W H = AN
9F9ITE "T ! CAPAC;Y BO? ( 2+ &( N 2+2 B
? HAS BE5 %[N 6BE IMPOSSI#4 7#D7 ,AG1 IF
! CAPAC;Y IS PRES5T PRIOR 6! ACTIV;Y1 X
W 2 PRES5T = ALL "T1 EV5 :ILE ! ?+ 0 Z
YET UNG5]AT$ & NON-EXI/5T1 "?\T ! 9F9ITE
"T 9 : X 0 CAPA# ( 2+ G5]AT$4 ,AT T "T1
!N1 :5 X 0 N1 AT T SAME "T X _H !
CAPAC;Y ( 2+1 BO? ( 2+ !N &( 2+ "!AF1 &
"!=E = AN 9F9;Y ( "T4
  ,X IS CLE> AL ON O!R GR.DS T X IS
IMPOSSI# T ! DE/RUCTI# %D N AT "S "T 2
DE/ROY$4 ,= O!RWISE X W ALW 2 AT ONCE
DE/RUCTI# & 9 ACTUAL;Y 9DE/RUCTI#1 S T X
W 2 AT ! SAME "T CAPA# ( ALW EXI/+ &( N
ALW EXI/+4 ,?US ! DE/RUCTI# IS AT "S "T
ACTU,Y DE/ROY$4 ,! G5]A#1 SIMIL>LY1 HAS
BE5 G5]AT$1 = X IS CAPA# ( HAV+ BE5
G5]AT$ & ?US AL ( N ALW EXI/+4
  ,WE MAY AL SEE 9 ! FOLL[+ WAY H[
IMPOSSI# X IS EI =A ?+ : IS G5]AT$ 6BE
?;E=W>D 9DE/RUCTI#1 OR =A ?+ : IS
UNG5]AT$ & HAS ALW HI!RTO EXI/$ 6BE
DE/ROY$4 ,NO?+ T IS 0*.E C 2 9DE/RUCTI#
OR UNG5]AT$1 S9CE ! PRODUCTS ( *.E &
=TUNE >E OPPOS$ 6:AT IS1 OR -ES 6BE1 ALW
OR USU,Y1 :ILE ANY?+ : EXI/S =A "T
9F9ITE EI ABSOLUTELY OR 9 "O DIREC;N1 IS
9 EXI/;E EI ALW OR USU,Y4 ,T : IS 0*.E1
!N1 IS 0NATURE S* Z 6EXI/ AT "O "T & N
AT ANO!R4 ,B 9 ?+S ( T "* ! 3TRADICTORY
/ATES PROCE$ F "O &! SAME CAPAC;Y1 !
MATT] (! ?+ 2+ ! CAUSE EQU,Y ( XS EXI/;E
&( XS NON-EXI/;E4 ,H;E 3TRADICTORIES WD
2 PRES5T TGR 9 ACTUAL;Y4
  ,FUR!R1 X _C TRULY 2 SD (A ?+ N[ T X
EXI/S LA/ YE>1 NOR CD X 2 SD LA/ YE> T X
EXI/S N[4 ,X IS "!=E IMPOSSI# = :AT ONCE
DID N EXI/ LAT] 6BE ET]NAL4 ,= 9 XS LAT]
/ATE X W POSSESS ! CAPAC;Y ( N EXI/+1
ONLY N ( N EXI/+ AT A "T :5 X EXI/S-S9CE
!N X EXI/S 9 ACTUAL;Y-B ( N EXI/+ LA/
YE> OR 9 ! PA/4 ,N[ SUPPOSE X 6BE 9
ACTUAL;Y :AT X IS CAPA# ( 2+4 ,X W !N 2
TRUE 6SAY N[ T X DOES N EXI/ LA/ YE>4 ,B
? IS IMPOSSI#4 ,NO CAPAC;Y RELATES 62+ 9
! PA/1 B ALW 62+ 9 ! PRES5T OR FUTURE4
,X IS ! SAME )! NO;N ( AN ET]N;Y (
EXI/;E FOLL[$ LAT] 0NON-EXI/;E4 ,9 !
LAT] /ATE ! CAPAC;Y W 2 PRES5T = T : IS
N "! 9 ACTUAL;Y4 ,ACTUALIZE1 !N1 !
CAPAC;Y4 ,X W 2 TRUE 6SAY N[ T ? EXI/S
LA/ YE> OR 9 ! PA/ G5],Y4
  ,3SID],NS AL N G5]AL L ^! B PROP] 6!
SUBJECT %[ X 6BE IMPOSSI# T :AT 0 =M]LY
ET]NAL %D LAT] 2 DE/ROY$ OR T :AT =M]LY
0 N %D LAT] 2 ET]NAL4 ,:AT"E IS
DE/RUCTI# OR G5]AT$ IS ALW ALT]A#4 ,N[
ALT],N IS DUE 63TR>IES1 &! ?+S : -POSE !
NATURAL BODY >E ! V SAME T DE/ROY X4
               ,BOOK ,,II
                   #A
  ,,T ! H1V5 Z A :OLE NEI CAME 962+ NOR
ADMITS ( DE/RUC;N1 Z "S ASS]T1 B IS "O &
ET]NAL1 ) NO 5D OR 2G9N+ ( XS TOTAL
DUR,N1 3TA9+ & EMBRAC+ 9 XF ! 9F9;Y (
"T1 WE MAY 3V9CE \RVS N ONLY 0! >GU;TS
ALR SET =? B AL 0A 3SID],N (! VIEWS ( ^?
:O DI6] F U 9 PROVID+ = XS G5],N4 ,IF \R
VIEW IS A POSSI# "O1 &! MANN] ( G5],N :
!Y ASS]T IS IMPOSSI#1 ? FACT W H GRT
WEI<T 9 3V9C+ U (! IMMORTAL;Y & ET]N;Y (
! _W4 ,H;E X IS WELL 6P]SUADE "OF (!
TRU? (! ANCI5T & TRULY TRADI;NAL !ORIES1
T "! IS "S IMMORTAL & DIV9E ?+ :
POSSESSES MOVE;T1 B MOVE;T S* Z HAS NO
LIMIT & IS R XF ! LIMIT ( ALL O!R
MOVE;T4 ,A LIMIT IS A ?+ : 3TA9S2 & ?
MO;N1 2+ P]FECT1 3TA9S ^? IMP]FECT MO;NS
: H A LIMIT &A GOAL1 HAV+ XF NO 2G9N+ OR
5D1 B UNC1S+ "? ! 9F9;Y ( "T1 &( O!R
MOVE;TS1 6"S ! CAUSE ( _! 2G9N+1 6O!RS
(F]+ ! GOAL4 ,! ANCI5TS GAVE 6! ,GODS !
H1V5 OR UPP] PLACE1 Z 2+ AL"O IMMORTAL2
& \R PRES5T >GU;T TE/IFIES T X IS
9DE/RUCTI# & UNG5]AT$4 ,FUR!R1 X IS
UNA6ECT$ 0ANY MORTAL 4COM=T1 &1 9 A4I;N1
EF=T.S2 = X NE$S NO 3/RA9+ NECESS;Y
6KEEP X 6XS PA?1 & PREV5T X F MOV+ ) "S
O!R MOVE;T M NATURAL 6XF4 ,S* A 3/RA9$
MOVE;T WD NECESS>ILY 9VOLVE EF=T ! M S1
! M ET]NAL X W]E-& WD 2 9CONSI/5T )
P]FEC;N4 ,H;E WE M/ N 2LIEVE ! OLD TALE
: SAYS T ! _W NE$S "S ,ATLAS 6KEEP X
SAFE-A TALE -POS$1 X WD SEEM1 0M5 :O1 L
LAT] ?9K]S1 3CVD ( ALL ! UPP] BODIES Z
E>?Y & 5D[$ ) WEI<T1 & "!=E SUPPORT$ X 9
_! FABUL\S WAY ^U ANIMATE NECESS;Y4 ,WE
M/ NO M 2LIEVE T ?AN FOLL[ ,EMP$OCLES :5
HE SAYS T ! _W1 02+ :IRL$ R.D1 RCVD A
MOVE;T QK 5 6OV]P[] XS [N D[NW>D T5D5CY1
& ?US HAS BE5 KEPT F DE/RUC;N ALL ? "T4
,NOR1 AG1 IS X 3CEIVA# T X %D P]SI/
ET]N,Y 0! NECESSIT,N (A S\L4 ,=A S\L CD
N LIVE 9 S* 3DI;NS PA9.SLY OR HAPPILY1
S9CE ! MOVE;T 9VOLVES 3/RA9T1 2+ IMPOS$
ON ! F/ BODY1 ^: NATURAL MO;N IS DI6]5T1
& IMPOS$ 3T9U\SLY4 ,X M/ "!=E 2 UNEASY &
DEVOID ( ALL R,NAL SATISFAC;N2 = X CD N
EV51 L ! S\L ( MORTAL ANIMALS1 TAKE
RECRE,N 9 ! BODILY RELAX,N ( SLEEP4 ,AN
,IXION'S LOT M/ NE$S POSSESS X1 )\T 5D
OR RESPITE4 ,IF !N1 Z WE SD1 ! VIEW ALR
/AT$ (! F/ MO;N IS A POSSI# "O1 X IS N
ONLY M APPROPRIATE S 63CV ( XS ET]N;Y1 B
AL ON ? HYPO!SIS AL"O >E WE A# 6ADV.E A
!ORY 3SI/5T ) POPUL> DIV9,NS (! DIV9E
NATURE4 ,B ( ? 5 =! PRES5T4
                   #B
  ,S9CE "! >E "S :O SAY T "! IS A "R &A
LEFT 9 ! H1V51 ) ^? :O >E "KN Z
,PY?AGOR1NS-TO :OM 9DE$ ! VIEW RE,Y
2L;GS-WE M/ 3SID] :E!R1 IF WE >E 6APPLY
^! PR9CIPLES 6! BODY (! UNIV]SE1 WE %D
FOLL[ _! /ATE;T (! MATT] OR F9D A BETT]
WAY4 ,AT ! />T WE MAY SAY T1 IF "R &
LEFT >E APPLICA#1 "! >E PRIOR PR9CIPLES
: M/ F/ 2 APPLI$4 ,^! PR9CIPLES H BE5
ANALYS$ 9 ! 4CUS.N (! MOVE;TS ( ANIMALS1
=! R1SON T !Y >E PROP] 6ANIMAL NATURE4
,= 9 "S ANIMALS WE F9D ALL S* 4T9C;NS (
"PS Z ? ( "R & LEFT CLE>LY PRES5T1 & 9
O!RS "S2 B 9 PLANTS WE F9D ONLY ABV &
2L4 ,N[ IF WE >E 6APPLY 6! H1V5 S* A
4T9C;N ( "PS1 WE M/ EXECT1 Z WE H SD1
6F9D 9 X AL ! 4T9C;N : 9 ANIMALS IS F.D
F/ ( !M ALL4 ,! 4T9C;NS >E ?REE1 "NLY1
ABV & 2L1 FRONT & XS OPPOSITE1 "R &
LEFT-ALL ^! ?REE OPPOSI;NS WE EXPECT
6F9D 9 ! P]FECT BODY-& EA* MAY 2 CALL$ A
PR9CIPLE4 ,ABV IS ! PR9CIPLE ( L5G?1 "R
( BR1D?1 FRONT ( DEP?4 ,OR AG WE MAY
3NECT !M )! V>I\S MOVE;TS1 TAK+ PR9CIPLE
6M1N T "P1 9 A ?+ CAPA# ( MOVE;T1 F :
MOVE;T F/ 2G9S4 ,GR[? />TS F ABV1
LOCOMO;N F ! "R1 S5SEMOVE;T F 9 FRONT 7=
FRONT IS SIMPLY ! "P 6: ! S5SES >E
DIRECT$74 ,H;E WE M/ N LOOK = ABV & 2L1
"R & LEFT1 FRONT & BACK1 9 E K9D ( BODY1
B ONLY 9 ^? :1 2+ ANIMATE1 H A PR9CIPLE
( MOVE;T )9 !MVS4 ,= 9 NO 9ANIMATE ?+ D
WE OBS]VE A "P F : MOVE;T ORIG9ATES4 ,"S
D N MOVE AT ALL1 "S MOVE1 B N 9DI6]5TLY
9 ANY DIREC;N2 FIRE1 = EXAMPLE1 ONLY
UPW>D1 & E>? ONLY 6! C5TRE4 ,X IS TRUE T
WE SP1K ( ABV & 2L1 "R & LEFT1 9 ^!
BODIES RELATIVELY 6\RVS4 ,! REF];E MAY 2
6\R [N "R H&S1 Z )! DIV9]1 OR 6"S
SIMIL>;Y 6\R [N MEMB]S1 S* Z ! "PS (A
/ATUE POSSESS2 OR WE MAY TAKE ! 3TR>Y
SPATIAL ORD]1 CALL+ "R T : IS 6\R LEFT1
& LEFT T : IS 6\R "R4 ,WE OBS]VE1 H["E1
9 ! ?+S !MVS N"O ( ^! 4T9C;NS2 9DE$ IF
!Y >E TURN$ R.D WE PROCE$ 6SP1K (!
OPPOSITE "PS Z "R & LEFT1 A BOY L& 2L1
FRONT & BACK4 ,H;E X IS REM>KA# T !
,PY?AGOR1NS %D H SPOK5 ( ^! TWO
PR9CIPLES1 "R & LEFT1 ONLY1 6! EXCLU.N (
! O!R F\R1 : H Z GD A TITLE Z !Y4 ,"! IS
NO LESS DI6];E 2T ABV & 2L OR FRONT &
BACK 9 ANIMALS G5],Y ?AN 2T "R & LEFT4
,! DI6];E IS "S"TS ONLY "O ( FUNC;N1
"S"TS AL "O ( %APE2 & :ILE ! 4T9C;N (
ABV & 2L IS "*I/IC ( ALL ANIMATE ?+S1
:E!R PLANTS OR ANIMALS1 T ( "R & LEFT IS
N F.D 9 PLANTS4 ,FUR!R1 9ASM* Z L5G? IS
PRIOR 6BR1D?1 IF ABV IS ! PR9CIPLE (
L5G?1 "R ( BR1D?1 & IF ! PR9CIPLE ( T :
IS PRIOR IS XF PRIOR1 !N ABV W 2 PRIOR
6"R1 OR LET U SAY1 S9CE ,8PRIOR0' IS
AMBIGU\S1 PRIOR 9 ORD] ( G5],N4 ,IF1 9
A4I;N1 ABV IS ! REGION F : MOVE;T
ORIG9ATES1 "R ! REGION 9 : X />TS1 FRONT
! REGION 6: X IS DIRECT$1 !N ON ? GR.D
TOO ABV HAS A C]TA9 ORIG9AL "* Z -P>$ )!
O!R =MS ( POSI;N4 ,ON ^! TWO GR.DS1 !N1
!Y MAY FAIRLY 2 CRITICIZ$1 F/1 = OMITT+
! M FUNDA;TAL PR9CIPLES1 & SECONDLY1 =
?9K+ T ! TWO !Y M5;N$ 7 ATTRIBUTA# EQU,Y
6"EY?+4
  ,S9CE WE H ALR DET]M9$ T FUNC;NS ( ?
K9D 2L;G 6?+S : POSSESS1 A PR9CIPLE (
MOVE;T1 & T ! H1V5 IS ANIMATE &
POSSESSES A PR9CIPLE ( MOVE;T1 CLE>LY !
H1V5 M/ AL EXHIBIT ABV & 2L1 "R & LEFT4
,WE NE$ N 2 TR\#D 0! "Q1 >IS+ F !
SPH]ICAL %APE (! _W1 H[ "! C 2 A 4T9C;N
( "R & LEFT )9 X1 ALL "PS 2+ ALIKE & ALL
= "E 9 MO;N4 ,WE M/ ?9K (! _W Z ( "S?+ 9
: "R DI6]S F LEFT 9 %APE Z WELL Z 9 O!R
RESPECTS1 : SUBSEQU5TLY IS 9CLUD$ 9 A
SPH]E4 ,! DI6];E ( FUNC;N W P]SI/1 B W
APPE> N 60R1SON (! REGUL>;Y ( %APE4 ,9 !
SAME FA%ION M/ WE 3CV (! 2G9N+ ( XS
MOVE;T4 ,= EV5 IF X N"E 2GAN 6MOVE1 YET
X M/ POSSESS A PR9CIPLE F : X WD H 2GUN
6MOVE IF X _H 2GUN1 & F : X WD 2G9 AG IF
X CAME 6A /&4 ,N[ 0XS L5G? ,I M1N !
9T]VAL 2T XS POLES1 "O POLE 2+ ABV &!
O!R 2L2 = TWO HEMISPH]ES >E SPECI,Y
4T+UI%$ F ALL O!RS 0! IMMOBIL;Y (!
POLES4 ,FUR!R1 BY ,8TRANSV]SE0' 9 !
UNIV]SE WE -MONLY M1N1 N ABV & 2L1 B A
DIREC;N CROSS+ ! L9E (! POLES1 :1
0IMPLIC,N1 IS L5G?3 = TRANSV]SE MO;N IS
MO;N CROSS+ MO;N UP & D[N4 ,(! POLES1 T
: WE SEE ABV U IS ! L[] REGION1 & T : WE
D N SEE IS ! UPP]4 ,= "R 9 ANY?+ IS1 Z
WE SAY1 ! REGION 9 : LOCOMO;N ORIG9ATES1
&! ROT,N (! H1V5 ORIG9ATES 9 ! REGION F
: ! />S RISE4 ,S ? W 2 ! "R1 &! REGION
": !Y SET ! LEFT4 ,IF !N !Y 2G9 F ! "R &
MOVE R.D 6! "R1 ! UPP] M/ 2 ! UNSE5
POLE4 ,= IF X IS ! POLE WE SEE1 ! MOVE;T
W 2 LEFTW>D1 : WE D5Y 6BE ! FACT4
,CLE>LY !N ! 9VISI# POLE IS ABV4 ,& ^?
:O LIVE 9 ! O!R HEMISPH]E >E ABV & 6!
"R1 :ILE WE >E 2L & 6! LEFT4 ,? IS J !
OPPOSITE (! VIEW (! ,PY?AGOR1NS1 :O MAKE
U ABV & ON ! "R SIDE & ^? 9 ! O!R
HEMISPH]E 2L & ON ! LEFT SIDE2 ! FACT 2+
! EXACT OPPOSITE4 ,RELATIVELY1 H["E1 6!
SECOND>Y REVOLU;N1 ,I M1N T (! PLANETS1
WE >E ABV & ON ! "R & !Y >E 2L & ON !
LEFT4 ,=! PR9CIPLE ( _! MOVE;T HAS !
REV]SE POSI;N1 S9CE ! MOVE;T XF IS !
3TR>Y (! O!R3 H;E X FOLL[S T WE >E AT XS
2G9N+ & !Y AT XS 5D4 ,"H WE MAY 5D \R
4CUS.N (! 4T9C;NS ( "PS CR1T$ 0! ?REE
DIM5.NS &(! 3SEQU5T DI6];ES ( POSI;N4
                   #C
  ,S9CE CIRCUL> MO;N IS N ! 3TR>Y (!
REV]SE CIRCUL> MO;N1 WE M/ 3SID] :Y "!
IS M ?AN "O MO;N1 ?\< WE H 6PURSUE \R
9QUIRIES AT A 4T.E-A 4T.E CR1T$ N S M*
0\R SPATIAL POSI;N Z 0! FACT T \R S5SES
5A# U 6P]CV V FEW (! ATTRIBUTES (!
H1V5LY BODIES4 ,B LET N T DET] U4 ,!
R1SON M/ 2 S"\ 9 ! FOLL[+ FACTS4 ,"EY?+
: HAS A FUNC;N EXI/S = XS FUNC;N4 ,!
ACTIV;Y ( ,GOD IS IMMORTAL;Y1 I4E4
ET]NAL LIFE4 ,"!=E ! MOVE;T ( T : IS
DIV9E M/ 2 ET]NAL4 ,B S* IS ! H1V51 VIZ4
A DIV9E BODY1 &= T R1SON 6X IS GIV5 !
CIRCUL> BODY ^: NATURE X IS 6MOVE ALW 9
A CIRCLE4 ,:Y1 !N1 IS N ! :OLE BODY (!
H1V5 (! SAME "* Z T "P8 ,2C "! M/ 2 "S?+
AT RE/ AT ! C5TRE (! REVOLV+ BODY2 &( T
BODY NO "P C 2 AT RE/1 EI ELSE": OR AT !
C5TRE4 ,X CD D S ONLY IF ! BODY'S
NATURAL MOVE;T 7 T[>DS ! C5TRE4 ,B !
CIRCUL> MOVE;T IS NATURAL1 S9CE O!RWISE
X CD N 2 ET]NAL3 = NO?+ UNNATURAL IS
ET]NAL4 ,! UNNATURAL IS SUBSEQU5T 6!
NATURAL1 2+ A DERANGE;T (! NATURAL :
O3URS 9 ! C\RSE ( XS G5],N4 ,E>? !N HAS
6EXI/2 = X IS E>? : IS AT RE/ AT !
C5TRE4 7,AT PRES5T WE MAY TAKE ? =
GRANT$3 X % 2 EXPLA9$ LAT]47 ,B IF E>?
M/ EXI/1 S M/ FIRE4 ,=1 IF "O (A PAIR (
3TR>IES NATUR,Y EXI/S1 ! O!R1 IF X IS
RE,Y 3TR>Y1 EXI/S AL NATUR,Y4 ,9 "S =M X
M/ 2 PRES5T1 S9CE ! MATT] ( 3TR>IES IS !
SAME4 ,AL1 ! POSITIVE IS PRIOR 6XS
PRIV,N 7W>M1 = 9/.E1 6COLD71 & RE/ &
H1VI;S /& =! PRIV,N ( LI<T;S & MOVE;T4
,B FUR!R1 IF FIRE & E>? EXI/1 !
9T]M$IATE BODIES M/ EXI/ AL3 EA* ELE;T
/&S 9 A 3TR>Y REL,N 6E O!R4 7,?1 AG1 WE
W "H TAKE = GRANT$ & TRY LAT] 6EXPLA947
^! F\R ELE;TS G5],N CLE>LY IS 9VOLV$1
S9CE N"O ( !M C 2 ET]NAL3 = 3TR>IES
9T]ACT ) "O ANO!R & DE/ROY "O ANO!R4
,FUR!R1 X IS 9CONCEIVA# T A MOVA# BODY
%D 2 ET]NAL1 IF XS MOVE;T _C 2 REG>D$ Z
NATUR,Y ET]NAL3 & ^! BODIES WE "K
6POSSESS MOVE;T4 ,?US WE SEE T G5],N IS
NECESS>ILY 9VOLV$4 ,B IF S1 "! M/ 2 AT
L1/ "O O!R CIRCUL> MO;N3 =A S+LE MOVE;T
(! :OLE H1V5 WD NECESSITATE AN ID5TICAL
REL,N (! ELE;TS ( BODIES 6"O ANO!R4 ,?
MATT] AL % 2 CLE>$ UP 9 :AT FOLL[S3 B =!
PRES5T S M* IS CLE>1 T ! R1SON :Y "! IS
M ?AN "O CIRCUL> BODY IS ! NECESS;Y (
G5],N1 : FOLL[S ON ! PRES;E ( FIRE1 :1 )
T (! O!R BODIES1 FOLL[S ON T ( E>?2 &
E>? IS REQUIR$ 2C ET]NAL MOVE;T 9 "O
BODY NECESSITATES ET]NAL RE/ 9 ANO!R4
                   #D
  ,! %APE (! H1V5 IS ( NECESS;Y
SPH]ICAL2 = T IS ! %APE MO/ APPROPRIATE
6XS SUB/.E & AL 0NATURE PRIM>Y4
  ,F/1 LET U 3SID] G5],Y : %APE IS
PRIM>Y AM;G PLANES & SOLIDS ALIKE4 ,E
PLANE FIGURE M/ 2 EI RECTIL9E> OR
CURVIL9E>4 ,N[ ! RECTIL9E> IS B.D$ 0M
?AN "O L9E1 ! CURVIL9E> 0"O ONLY4 ,B
S9CE 9 ANY K9D ! "O IS NATUR,Y PRIOR 6!
_M &! SIMPLE 6! -PLEX1 ! CIRCLE W 2 ! F/
( PLANE FIGURES4 ,AG1 IF 0-PLETE1 Z
PREVI\SLY DEF9$1 WE M1N A ?+ \TSIDE : NO
"P ( XF C 2 F.D1 & IF A4I;N IS ALW
POSSI# 6! /RAI<T L9E B N"E 6! CIRCUL>1
CLE>LY ! L9E : EMBRACES ! CIRCLE IS
-PLETE4 ,IF !N ! -PLETE IS PRIOR 6!
9COMPLETE1 X FOLL[S ON ? GR.D AL T !
CIRCLE IS PRIM>Y AM;G FIGURES4 ,&! SPH]E
HOLDS ! SAME POSI;N AM;G SOLIDS4 ,= X
AL"O IS EMBRAC$ 0A S+LE SURFACE1 :ILE
RECTIL9E> SOLIDS H S"EAL4 ,! SPH]E IS
AM;G SOLIDS :AT ! CIRCLE IS AM;G PLANE
FIGURES4 ,FUR!R1 ^? :O DIVIDE BODIES
96PLANES & G5]ATE !M \ ( PLANES SEEM
6BE> WIT;S 6! TRU? ( ?4 ,AL"O AM;G
SOLIDS !Y L1VE ! SPH]E UNDIVID$1 Z N
POSSESS+ M ?AN "O SURFACE3 =! DIVI.N
96SURFACES IS N J DIVID+ A :OLE 0CUTT+ X
96XS "PS1 B DIVI.N ( ANO!R FA%ION 96"PS
DI6]5T 9 =M4 ,X IS CLE>1 !N1 T ! SPH]E
IS F/ ( SOLID FIGURES4
  ,IF1 AG1 "O ORD]S FIGURES AC 6_!
NUMB]S1 X IS MO/ NATURAL 6>RANGE !M 9 ?
WAY4 ,! CIRCLE CORRESPONDS 6! NUMB] "O1
! TRIANGLE1 2+ ! SUM ( TWO "R ANGLES1 6!
NUMB] TWO4 ,B IF "O IS ASSIGN$ 6!
TRIANGLE1 ! CIRCLE W N 2 A FIGURE AT
ALL4
  ,N[ ! F/ FIGURE 2L;GS 6! F/ BODY1 &!
F/ BODY IS T AT ! F>!/ CIRCUMF];E4 ,X
FOLL[S T ! BODY : REVOLVES )A CIRCUL>
MOVE;T M/ 2 SPH]ICAL4 ,! SAME !N W 2
TRUE (! BODY 3T9U\S ) X3 = T : IS 3T9U\S
)! SPH]ICAL IS SPH]ICAL4 ,! SAME AG
HOLDS (! BODIES 2T ^! &! C5TRE4 ,BODIES
: >E B.D$ 0! SPH]ICAL & 9 3TACT ) X M/
BE1 Z :OLES1 SPH]ICAL2 &! BODIES 2L !
SPH]E (! PLANETS >E 3TIGU\S )! SPH]E ABV
!M4 ,! SPH]E !N W 2 SPH]ICAL "?\T2 = E
BODY )9 X IS 3TIGU\S & 3T9U\S ) SPH]ES4
  ,AG1 S9CE ! :OLE REVOLVES1 PALPABLY &
0ASSUMP;N1 9 A CIRCLE1 & S9CE X HAS BE5
%[N T \TSIDE ! F>!/ CIRCUMF];E "! IS NEI
VOID NOR PLACE1 F ^! GR.DS AL X W FOLL[
NECESS>ILY T ! H1V5 IS SPH]ICAL4 ,= IF X
IS 6BE RECTIL9E> 9 %APE1 X W FOLL[ T "!
IS PLACE & BODY & VOID )\T X4 ,=A
RECTIL9E> FIGURE Z X REVOLVES N"E 3T9UES
9 ! SAME ROOM1 B ": =M]LY 0 BODY1 IS N[
N"O1 & ": N[ IS N"O1 BODY W 2 9 A MO;T
2C (! PROJEC;N AT ! CORN]S4 ,SIMIL>LY1
IF ! _W _H "S O!R FIGURE ) UNEQUAL
RADII1 IF1 = 9/.E1 X 7 L5TI=M1 OR OVI=M1
9 E CASE WE %D H 6ADMIT SPACE & VOID
\TSIDE ! MOV+ BODY1 2C ! :OLE BODY WD N
ALW O3UPY ! SAME ROOM4
  ,AG1 IF ! MO;N (! H1V5 IS ! M1SURE (
ALL MOVE;TS :AT"E 9 VIRTUE ( 2+ AL"O
3T9U\S & REGUL> & ET]NAL1 & IF1 9 EA*
K9D1 ! M1SURE IS ! M9IMUM1 &! M9IMUM
MOVE;T IS ! SWIFTE/1 !N1 CLE>LY1 !
MOVE;T (! H1V5 M/ 2 ! SWIFTE/ ( ALL
MOVE;TS4 ,N[ ( L9ES : RETURN ^U !MVS !
L9E : B.DS ! CIRCLE IS ! %ORTE/2 & T
MOVE;T IS ! SWIFTE/ : FOLL[S ! %ORTE/
L9E4 ,"!=E1 IF ! H1V5 MOVES 9 A CIRCLE &
MOVES M SWIFTLY ?AN ANY?+ ELSE1 X M/
NECESS>ILY 2 SPH]ICAL4
  ,CORROBORATIVE EVID;E MAY 2 DRAWN F !
BODIES ^: POSI;N IS AB ! C5TRE4 ,IF E>?
IS 5CLOS$ 0WAT]1 WAT] 0AIR1 AIR 0FIRE1 &
^! SIMIL>LY 0! UPP] BODIES-: :ILE N
3T9U\S >E YET 3TIGU\S ) !M-& IF !
SURFACE ( WAT] IS SPH]ICAL1 & T : IS
3T9U\S ) OR EMBRACES ! SPH]ICAL M/ XF 2
SPH]ICAL1 !N ON ^! GR.DS AL X IS CLE> T
! H1V5S >E SPH]ICAL4 ,B ! SURFACE ( WAT]
IS SE5 6BE SPH]ICAL IF WE TAKE Z \R
/>T+-PO9T ! FACT T WAT] NATUR,Y T5DS
6COLLECT 9 A HOLL[ PLACE-,8HOLL[0' M1N+
,8NE>] ! C5TRE0'4 ,DRAW F ! C5TRE ! L9ES
;,,AB1 ;,,AC1 & LET _! EXTREMITIES 2
JO9$ 0! /RAI<T L9E ,,BC4 ,! L9E ,,AD1
DRAWN 6! BASE (! TRIANGLE1 W 2 %ORT] ?AN
EI (! RADII4 ,"!=E ! PLACE 9 : X
T]M9ATES W 2 A HOLL[ PLACE4 ,! WAT] !N W
COLLECT "! UNTIL EQUAL;Y IS E/ABLI%$1 T
IS UNTIL ! L9E ,,AE IS EQUAL 6! TWO
RADII4 ,?US WAT] =CES XS WAY 6! 5DS (!
RADII1 & "! ONLY W X RE/3 B ! L9E :
3NECTS ! EXTREMITIES (! RADII IS
CIRCUL>3 "!=E ! SURFACE (! WAT] ,,BEC IS
SPH]ICAL4
  ,X IS PLA9 F ! =EGO+ T ! UNIV]SE IS
SPH]ICAL4 ,X IS PLA91 FUR!R1 T X IS
TURN$ 7S 6SP1K7 )A F9I% : NO MANUFACTUR$
?+ NOR ANY?+ ELSE )9 ! RANGE ( \R
OBS]V,N C EV5 APPROA*4 ,=! MATT] ( : ^!
>E -POS$ DOES N ADMIT ( ANY?+ L ! SAME
REGUL>;Y & F9I% Z ! SUB/.E (! 5VELOP+
BODY2 S9CE ) EA* /EP AWAY F E>? ! MATT]
MANIFE/LY 2COMES F9] 9 ! SAME PROPOR;N Z
WAT] IS F9] ?AN E>?4
                   #E
  ,N[ "! >E TWO WAYS ( MOV+ AL;G A
CIRCLE1 F ,A TO ;,B OR F ,A TO ;,C1 & WE
H ALR EXPLA9$ T ^! MOVE;TS >E N 3TR>Y
6"O ANO!R4 ,B NO?+ : 3C]NS ! ET]NAL C 2
A MATT] ( *.E OR SPONTANE;Y1 &! H1V5 &
XS CIRCUL> MO;N >E ET]NAL4 ,WE M/ "!=E
ASK :Y ? MO;N TAKES "O DIREC;N & N !
O!R4 ,EI ? IS XF AN ULTIMATE FACT OR "!
IS AN ULTIMATE FACT 2H X4 ,X MAY SEEM
EVID;E ( EXCESSIVE FOLLY OR EXCESSIVE
Z1L 6TRY 6PROVIDE AN EXPLAN,N ( "S ?+S1
OR ( "EY?+1 ADMITT+ NO EXCEP;N4 ,!
CRITICISM1 H["E1 IS N ALW J3 "O %D F/
3SID] :AT R1SON "! IS = SP1K+1 & AL :AT
K9D ( C]TA9TY IS LOOK$ =1 :E!R HUMAN
M]ELY OR (A M COG5T K9D4 ,:5 ANY "O %
SU3E$ 9 F9D+ PRO(S ( GRT] PRECI.N1
GRATITUDE W 2 DUE 6HM =! 4COV]Y1 B AT
PRES5T WE M/ 2 3T5T )A PROBA# SOLU;N4
,IF NATURE ALW FOLL[S ! BE/ C\RSE
POSSI#1 &1 J Z UPW>D MOVE;T IS ! SUP]IOR
=M ( RECTIL9E> MOVE;T1 S9CE ! UPP]
REGION IS M DIV9E ?AN ! L[]1 S =W>D
MOVE;T IS SUP]IOR 6BACKW>D1 !N FRONT &
BACK EXHIBITS1 L "R & LEFT1 Z WE SD 2F &
Z ! DI6ICULTY J /AT$ XF SU7E/S1 ! 4T9C;N
( PRIOR & PO/]IOR1 : PROVIDES A R1SON &
S SOLVES \R DI6ICULTY4 ,SUPPOS+ T NATURE
IS ORD]$ 9 ! BE/ WAY POSSI#1 ? MAY /& Z
! R1SON (! FACT M5;N$4 ,= X IS BE/ 6MOVE
)A MOVE;T SIMPLE & UNC1S+1 &1 FUR!R1 9 !
SUP]IOR ( TWO POSSI# DIREC;NS4

                   #F
  ,WE H NEXT 6%[ T ! MOVE;T (! H1V5 IS
REGUL> & N IRREGUL>4 ,? APPLIES ONLY 6!
F/ H1V5 &! F/ MOVE;T2 =! L[] SPH]ES
EXHIBIT A -POSI;N ( S"EAL MOVE;TS 96"O4
,IF ! MOVE;T IS UNEV51 CLE>LY "! W 2
A3EL],N1 MAXIMUM SPE$1 & RET>D,N1 S9CE
^! APPE> 9 ALL IRREGUL> MO;NS4 ,!
MAXIMUM MAY O3UR EI AT ! />T+-PO9T OR AT
! GOAL OR 2T ! TWO2 & WE EXPECT NATURAL
MO;N 6R1* XS MAXIMUM AT ! GOAL1
UNNATURAL MO;N AT ! />T+-PO9T1 &
MISSILES MIDWAY 2T ! TWO4 ,B CIRCUL>
MOVE;T1 HAV+ NO 2G9N+ OR LIMIT OR MI4LE
9 ! DIRECT S5SE (! ^WS1 HAS NEI :;E NOR
:I!R NOR MI4LE3 = 9 "T X IS ET]NAL1 & 9
L5G? X RETURNS ^U XF )\T A BR1K4 ,IF !N
XS MOVE;T HAS NO MAXIMUM1 X C H NO
IRREGUL>;Y1 S9CE IRREGUL>;Y IS PRODUC$
0RET>D,N & A3EL],N4 ,FUR!R1 S9CE "EY?+ T
IS MOV$ IS MOV$ 0"S?+1 ! CAUSE (!
IRREGUL>;Y ( MOVE;T M/ LIE EI 9 ! MOV]
OR 9 ! MOV$ OR BO?4 ,= IF ! MOV] MOV$ N
ALW )! SAME =CE1 OR IF ! MOV$ 7 ALT]$ &
DID N REMA9 ! SAME1 OR IF BO? 7 6*ANGE1
! RESULT MI<T WELL 2 AN IRREGUL> MOVE;T
9 ! MOV$4 ,B N"O ( ^! POSSIBILITIES C 2
3CVD Z ACTUAL 9 ! CASE (! H1V5S4 ,Z 6T :
IS MOV$1 WE H %[N T X IS PRIM>Y & SIMPLE
& UNG5]AT$ & 9DE/RUCTI# & G5],Y UN*ANG+2
&! MOV] HAS AN EV5 BETT] "R 6^!
ATTRIBUTES4 ,X IS ! PRIM>Y T MOVES !
PRIM>Y1 ! SIMPLE ! SIMPLE1 ! 9DE/RUCTI#
& UNG5]AT$ T : IS 9DE/RUCTI# & UNG5]AT$4
,S9CE !N T : IS MOV$1 2+ A BODY1 IS
N"E!.S UN*ANG+1 H[ %D ! MOV]1 : IS
9CORPOR1L1 2 *ANG$8
  ,X FOLL[S !N1 FUR!R1 T ! MO;N _C 2
IRREGUL>4 ,= IF IRREGUL>;Y O3URS1 "! M/
2 *ANGE EI 9 ! MOVE;T Z A :OLE1 F FA/
6SL[ & SL[ 6FA/1 OR 9 XS "PS4 ,T "! IS
NO IRREGUL>;Y 9 ! "PS IS OBVI\S1 S9CE1
IF "! W]E1 "S DIV]G;E (! />S WD H TAK5
PLACE 2F N[ 9 ! 9F9;Y ( "T1 Z "O MOV$
SL[] & ANO!R FA/]3 B NO ALT],N ( _!
9T]VALS IS "E OBS]V$4 ,NOR AG IS A *ANGE
9 ! MOVE;T Z A :OLE ADMISSI#4 ,RET>D,N
IS ALW DUE 69CAPAC;Y1 & 9CAPAC;Y IS
UNNATURAL4 ,! 9CAPACITIES ( ANIMALS1
AGE1 DECAY1 &! L1 >E ALL UNNATURAL1 DUE1
X SEEMS1 6! FACT T ! :OLE ANIMAL -PLEX
IS MADE UP ( MAT]IALS : DI6] 9 RESPECT (
_! PROP] PLACES1 & NO S+LE "P O3UPIES XS
[N PLACE4 ,IF "!=E T : IS PRIM>Y 3TA9S
NO?+ UNNATURAL1 2+ SIMPLE & UNMIX$ & 9
XS PROP] PLACE & HAV+ NO 3TR>Y1 !N X HAS
NO PLACE = 9CAPAC;Y1 NOR1 3SEQU5TLY1 =
RET>D,N OR 7S9CE A3EL],N 9VOLVES
RET>D,N7 = A3EL],N4 ,AG1 X IS 9CONCEIVA#
T ! MOV] %D F/ %[ 9CAPAC;Y = AN 9F9ITE
"T1 & CAPAC;Y AFWS = ANO!R 9F9;Y4 ,=
CLE>LY NO?+ :1 L 9CAPAC;Y1 UNNATURAL "E
3T9UES = AN 9F9;Y ( "T2 NOR DOES !
UNNATURAL 5DURE Z L;G Z ! NATURAL1 OR
ANY =M ( 9CAPAC;Y Z L;G Z ! CAPAC;Y4 ,B
IF ! MOVE;T IS RET>D$ X M/ NECESS>ILY 2
RET>D$ = AN 9F9ITE "T4 ,EQU,Y IMPOSSI#
IS P]PETUAL A3EL],N OR P]PETUAL RET>D,N4
,= S* MOVE;T WD 2 9F9ITE & 9DEF9ITE1 B E
MOVE;T1 9 \R VIEW1 PROCE$S F "O PO9T
6ANO!R & IS DEF9ITE 9 "*4 ,AG1 SUPPOSE
"O ASSUMES A M9IMUM "T 9 LESS ?AN : !
H1V5 CD N -PLETE XS MOVE;T4 ,=1 Z A GIV5
WALK OR A GIV5 EX]CISE ON ! H>P _C TAKE
ANY & E "T1 B E P]=M.E HAS XS DEF9ITE
M9IMUM "T : IS UNSURPASSA#1 S1 "O MI<T
SUPPOSE1 ! MOVE;T (! H1V5 CD N 2 -PLET$
9 ANY & E "T4 ,B 9 T CASE P]PETUAL
A3EL],N IS IMPOSSI# 7&1 EQU,Y1 P]PETUAL
RET>D,N3 =! >GU;T HOLDS ( BO? & EA*71 IF
WE MAY TAKE A3EL],N 6PROCE$ 0ID5TICAL OR
9CR1S+ A4I;NS ( SPE$ &= AN 9F9ITE "T4 ,!
REMA9+ ALT]NATIVE IS 6SAY T ! MOVE;T
EXHIBITS AN ALT]N,N ( SL[] & FA/]3 B ?
IS A M]E FIC;N & Q 9CONCEIVA#4 ,FUR!R1
IRREGUL>;Y ( ? K9D WD 2 "PICUL>LY
UNLIKELY 6PASS UNOBS]V$1 S9CE 3TRA/
MAKES OBS]V,N EASY4
  ,T "! IS "O H1V51 !N1 ONLY1 & T X IS
UNG5]AT$ & ET]NAL1 & FUR!R T XS MOVE;T
IS REGUL>1 HAS N[ BE5 SU6ICI5TLY
EXPLA9$4
                   #G
  ,WE H NEXT 6SP1K (! />S1 Z !Y >E
CALL$1 ( _! -POSI;N1 %APE1 & MOVE;TS4 ,X
WD 2 MO/ NATURAL & 3SEQU5T ^U :AT HAS
BE5 SD T EA* (! />S %D 2 -POS$ ( T
SUB/.E 9 : _! PA? LIES1 S9CE1 Z WE SD1
"! IS AN ELE;T ^: NATURAL MOVE;T IS
CIRCUL>4 ,9 S SAY+ WE >E ONLY FOLL[+ !
SAME L9E ( ?"\ Z ^? :O SAY T ! />S >E
FI]Y 2C !Y 2LIEVE ! UPP] BODY 6BE FIRE1
! PRESUMP;N 2+ T A ?+ IS -POS$ (! SAME
/UFF Z T 9 : X IS SITUAT$4 ,! W>M? &
LI<T : PROCE$ F !M >E CAUS$ 0! FRIC;N
SET UP 9 ! AIR 0_! MO;N4 ,MOVE;T T5DS
6CR1TE FIRE 9 WOOD1 /"O1 & IRON2 &) EV5
M R1SON %D X H T E6ECT ON AIR1 A SUB/.E
: IS CLOS] 6FIRE ?AN ^!4 ,AN EXAMPLE IS
T ( MISSILES1 : Z !Y MOVE >E !MVS FIR$ S
/R;GLY T L1D5 BALLS >E MELT$2 & IF !Y >E
FIR$ ! SURR.D+ AIR M/ 2 SIMIL>LY A6ECT$4
,N[ :ILE ! MISSILES >E H1T$ 0R1SON ( _!
MO;N 9 AIR1 : IS TURN$ 96FIRE 0! AGIT,N
PRODUC$ 0_! MOVE;T1 ! UPP] BODIES >E
C>RI$ ON A MOV+ SPH]E1 S T1 ?\< !Y >E N
!MVS FIR$1 YET ! AIR "UN1? ! SPH]E (!
REVOLV+ BODY IS NECESS>ILY H1T$ 0XS
MO;N1 & "PICUL>LY 9 T "P ": ! SUN IS
ATTA*$ 6X4 ,H;E W>M? 9CR1SES Z ! SUN
GETS NE>] OR HI<] OR OV]H1D4 ,(! FACT1
!N1 T ! />S >E NEI FI]Y NOR MOVE 9 FIRE1
5 HAS BE5 SD4
                   #H
  ,S9CE *ANGES EVID5TLY O3UR N ONLY 9 !
POSI;N (! />S B AL 9 T (! :OLE H1V51 "!
>E ?REE POSSIBILITIES4 ,EI 7#A7 BO? >E
AT RE/1 OR 7#B7 BO? >E 9 MO;N1 OR 7#C7 !
"O IS AT RE/ &! O!R 9 MO;N4
  7#A7 ,T BO? %D 2 AT RE/ IS IMPOSSI#2
=1 IF ! E>? IS AT RE/1 ! HYPO!SIS DOES N
A3.T =! OBS]V,NS2 & WE TAKE X Z GRANT$ T
! E>? IS AT RE/4 ,X REMA9S EI T BO? >E
MOV$1 OR T ! "O IS MOV$ &! O!R AT RE/4
  7#B7 ,ON ! VIEW1 F/1 T BO? >E 9 MO;N1
WE H ! ABSURD;Y T ! />S &! CIRCLES MOVE
)! SAME SPE$1 I4E4 T ! ACE ( E /> IS T (
! CIRCLE 9 X MOVES4 ,= /> & CIRCLE >E
SE5 6-E BACK 6! SAME PLACE AT ! SAME
MO;T2 F : X FOLL[S T ! /> HAS TRAV]S$ !
CIRCLE &! CIRCLE HAS -PLET$ XS [N
MOVE;T1 I4E4 TRAV]S$ XS [N CIRCUMF];E1
AT "O &! SAME MO;T4 ,B X IS DI6ICULT
63CV T ! PACE ( EA* /> %D 2 EXACTLY
PROPOR;N$ 6! SIZE ( XS CIRCLE4 ,T ! PACE
( EA* CIRCLE %D 2 PROPOR;NATE 6XS SIZE
IS N ABSURD B 9EVITA#3 B T ! SAME %D 2
TRUE (! MOVE;T (! />S 3TA9$ 9 ! CIRCLES
IS Q 9CR$I#4 ,= IF1 ON ! "O &1 WE
SUPPOSE T ! /> : MOVES ON ! GRT] CIRCLE
IS NECESS>ILY SWIFT]1 CLE>LY WE AL ADMIT
T IF />S %IFT$ _! POSI;N S Z 6EX*ANGE
CIRCLES1 ! SL[] WD 2COME SWIFT] &!
SWIFT] SL[]4 ,B ? WD %[ T _! MOVE;T 0 N
_! [N1 B DUE 6! CIRCLES4 ,IF1 ON ! O!R
H&1 ! >RANGE;T 0 A *.E -B9,N1 ! CO9CID;E
9 E CASE (A GRT] CIRCLE )A SWIFT] MOVE;T
(! /> 3TA9$ 9 X IS TOO M* 62LIEVE4 ,9 "O
OR TWO CASES X MI<T N 9CONCEIVABLY FALL
\ S1 B 6IMAG9E X 9 E CASE ALIKE IS A M]E
FIC;N4 ,2SS1 *.E HAS NO PLACE 9 T : IS
NATURAL1 & :AT HAPP5S "EY": & 9 E CASE
IS NO MATT] ( *.E4
  7#C7 ,! SAME ABSURD;Y IS EQU,Y PLA9 IF
X IS SUPPOS$ T ! CIRCLES /& / & T X IS !
/>S !MVS : MOVE4 ,= X W FOLL[ T ! \T]
/>S >E ! SWIFT]1 & T ! PACE (! />S
CORRESPONDS 6! SIZE ( _! CIRCLES4
  ,S9CE1 !N1 WE _C R1SONABLY SUPPOSE EI
T BO? >E 9 MO;N OR T ! /> AL"O MOVES1 !
REMA9+ ALT]NATIVE IS T ! CIRCLES %D
MOVE1 :ILE ! />S >E AT RE/ & MOVE )!
CIRCLES 6: !Y >E ATTA*$4 ,ONLY ON ?
SUPPOSI;N >E WE 9VOLV$ 9 NO ABSURD
3SEQU;E4 ,=1 9 ! F/ PLACE1 ! QK] MOVE;T
(! L>G] CIRCLE IS NATURAL :5 ALL !
CIRCLES >E ATTA*$ 6! SAME C5TRE4 ,:5"E
BODIES >E MOV+ ) _! PROP] MO;N1 ! L>G]
MOVES QK]4 ,X IS ! SAME "H )! REVOLV+
BODIES3 =! >E 9T]CEPT$ 0TWO RADII W 2
L>G] 9 ! L>G] CIRCLE1 & H;E X IS N
SURPRIS+ T ! REVOLU;N (! L>G] CIRCLE %D
TAKE ! SAME "T Z T (! SMALL]4 ,&
SECONDLY1 ! FACT T ! H1V5S D N BR1K 9
PIECES FOLL[S N ONLY F ? B AL F ! PRO(
ALR GIV5 (! 3T9U;Y (! :OLE4
  ,AG1 S9CE ! />S >E SPH]ICAL1 Z \R
OPPON5TS ASS]T & WE MAY 3SI/5TLY ADMIT1
9ASM* Z WE 3/RUCT !M \ (! SPH]ICAL BODY1
& S9CE ! SPH]ICAL BODY HAS TWO MOVE;TS
PROP] 6XF1 "NLY ROLL+ & SP9N+1 X FOLL[S
T IF ! />S H A MOVE;T ( _! [N1 X W 2 "O
( ^!4 ,B NEI IS OBS]V$4 7#A7 ,SUPPOSE !M
6SP94 ,!Y WD !N /AY ": !Y W]E1 & N *ANGE
_! PLACE1 Z1 0OBS]V,N & G5]AL 3S5T1 !Y
D4 ,FUR!R1 "O WD EXPECT !M ALL 6EXHIBIT
! SAME MOVE;T3 B ! ONLY /> : APPE>S
6POSSESS ? MOVE;T IS ! SUN1 AT SUNRISE
OR SUNSET1 & ? APPE>.E IS DUE N 6! SUN
XF B 6! 4T.E F : WE OBS]VE X4 ,! VISUAL
RAY 2+ EXCESSIVELY PROL;G$ 2COMES W1K &
WAV]+4 ,! SAME R1SON PROBABLY A3.TS =!
APP>5T TW9KL+ (! FIX$ />S &! ABS;E (
TW9KL+ 9 ! PLANETS4 ,! PLANETS >E NE>1 S
T ! VISUAL RAY R1*ES !M 9 XS FULL VIG\R1
B :5 X -ES 6! FIX$ />S X IS QUIV]+ 2C (!
4T.E & XS EXCESSIVE EXT5.N2 & XS TREMOR
PRODUCES AN APPE>.E ( MOVE;T 9 ! />3 = X
MAKES NO DI6];E :E!R MOVE;T IS SET UP 9
! RAY OR 9 ! OBJECT ( VI.N4
  7#B7 ,ON ! O!R H&1 X IS AL CLE> T !
/>S D N ROLL4 ,= ROLL+ 9VOLVES ROT,N3 B
! ,8FACE0'1 Z X IS CALL$1 (! MOON IS ALW
SE54 ,"!=E1 S9CE ANY MOVE;T ( _! [N : !
/>S POSSESS$ WD PRESUMABLY 2 "O PROP]
6!MVS1 & NO S* MOVE;T IS OBS]V$ 9 !M1
CLE>LY !Y H NO MOVE;T ( _! [N4
  ,"! IS1 FUR!R1 ! ABSURD;Y T NATURE HAS
2/[$ ^U !M NO ORGAN APPROPRIATE 6S*
MOVE;T4 ,= NATURE L1VES NO?+ 6*.E1 & WD
N1 :ILE C>+ = ANIMALS1 OV]LOOK ?+S S
PRECI\S4 ,9DE$1 NATURE SEEMS DELIB]ATELY
6H /RIPP$ !M ( "EY?+ : MAKES SEL=IG9AT$
PROGRES.N POSSI#1 & 6H REMOV$ !M Z F> Z
POSSI# F ?+S : H ORGANS ( MOVE;T4 ,? IS
J :Y X SEEMS PROP] T ! :OLE H1V5 & E />
%D 2 SPH]ICAL4 ,= :ILE ( ALL %APES !
SPH]E IS ! MO/ 3V5I5T = MOVE;T 9 "O
PLACE1 MAK+ POSSI#1 Z X DOES1 ! SWIFTE/
& MO/ SELFCONTA9$ MO;N1 = =W>D MOVE;T X
IS ! MO/ UNSUITA#1 L1/ ( ALL RESEMBL+
%APES : >E SELF-MOV$1 9 T X HAS NO
DEP5D5T OR PROJECT+ "P1 Z A RECTIL9E>
FIGURE HAS1 & IS 9 FACT Z F> Z POSSI#
REMOV$ 9 %APE F AMBULATORY BODIES4
,S9CE1 "!=E1 ! H1V5S H 6MOVE 9 "O LACE1
&! />S >E N REQUIR$ 6MOVE !MVS =W>D1 X
IS NATURAL T BO? %D 2 SPH]ICAL-A %APE :
BE/ SUITS ! MOVE;T (! "O &! IMMOBIL;Y (!
O!R4
                   #I
  ,F ALL ? X IS CLE> T ! !ORY T ! MOVE;T
(! />S PRODUCES A H>MONY1 I4E4 T ! S.DS
!Y MAKE >E 3CORDANT1 9 SPITE (! GRACE &
ORIG9AL;Y ) : X HAS BE5 /AT$1 IS N"E!.S
UNTRUE4 ,"S ?9K]S SUPPOSE T ! MO;N (
BODIES ( T SIZE M/ PRODUCE A NOISE1 S9CE
ON \R E>? ! MO;N ( BODIES F> 9F]IOR 9
SIZE & 9 SPE$ ( MOVE;T HAS T E6ECT4 ,AL1
:5 ! SUN &! MOON1 !Y SAY1 & ALL ! />S1 S
GRT 9 NUMB] & 9 SIZE1 >E MOV+ ) S RAPID
A MO;N1 H[ %D !Y N PRODUCE A S.D
IMM5SELY GRT8 ,/>T+ F ? >GU;T & F !
OBS]V,N T _! SPE$S1 Z M1SUR$ 0_! 4T.ES1
>E 9 ! SAME RATIOS Z MUSICAL 3CORD.ES1
!Y ASS]T T ! S.D GIV5 =? 0! CIRCUL>
MOVE;T (! />S IS A H>MONY4 ,S9CE1 H["E1
X APPE>S UNA3.TA# T WE %D N HE> ? MUSIC1
!Y EXPLA9 ? 0SAY+ T ! S.D IS 9 \R E>S F
! V MO;T ( BIR? & IS ?US 9DIST+UI%A# F
XS 3TR>Y SIL;E1 S9CE S.D & SIL;E >E
4CRIM9AT$ 0MUTUAL 3TRA/4 ,:AT HAPP5S
6M51 !N1 IS J :AT HAPP5S 6COPP]SMI?S1 :O
>E S A3U/OM$ 6! NOISE (! SMI?Y T X MAKES
NO DI6];E 6!M4 ,B1 Z WE SD 2F1 MELODI\S
& POETICAL Z ! !ORY IS1 X _C 2 A TRUE
A3.T (! FACTS4 ,"! IS N ONLY ! ABSURD;Y
( \R HE>+ NO?+1 ! GR.D ( : !Y TRY
6REMOVE1 B AL ! FACT T NO E6ECT O!R ?AN
S5SITIVE IS PRODUC$ ^U U4 ,EXCESSIVE
NOISES1 WE "K1 %ATT] ! SOLID BODIES EV5
( 9ANIMATE ?+S3 ! NOISE ( ?"U1 = 9/.E1
SPLITS ROCKS &! /R;GE/ ( BODIES4 ,B IF !
MOV+ BODIES >E S GRT1 &! S.D : P5ETRATES
6U IS PROPOR;NATE 6_! SIZE1 T S.D M/
NE$S R1* U 9 AN 9T5S;Y _M "TS T ( ?"U1 &
! =CE ( XS AC;N M/ 2 IMM5SE4 ,9DE$ !
R1SON :Y WE D N HE>1 & %[ 9 \R BODIES
N"O (! E6ECTS ( VIOL5T =CE1 IS EASILY
GIV53 X IS T "! IS NO NOISE4 ,B N ONLY
IS ! EXPLAN,N EVID5T2 X IS AL A
CORROBOR,N (! TRU? (! VIEWS WE H ADV.ED4
,=! V DI6ICULTY : MADE ! ,PY?AGOR1NS SAY
T ! MO;N (! />S PRODUCES A 3CORD
CORROBORATES \R VIEW4 ,BODIES : >E !MVS
9 MO;N1 PRODUCE NOISE & FRIC;N3 B ^? :
>E ATTA*$ OR FIX$ 6A MOV+ BODY1 Z ! "PS
6A %IP1 C NO M CR1TE NOISE1 ?AN A %IP ON
A RIV] MOV+ )! /R1M4 ,YET 0! SAME >GU;T
"O MI<T SAY X 0 ABSURD T ON A L>GE
VESSEL ! MO;N ( MA/ & POOP %D N MAKE A
GRT NOISE1 &! L MI<T 2 SD (! MOVE;T (!
VESSEL XF4 ,B S.D IS CAUS$ :5 A MOV+
BODY IS 5CLOS$ 9 AN UNMOV$ BODY1 & _C 2
CAUS$ 0"O 5CLOS$ IN1 & 3T9U\S )1 A MOV+
BODY : CR1TES NO FRIC;N4 ,WE MAY SAY1
!N1 9 ? MATT] T IF ! H1V5LY BODIES MOV$
9 A G5],Y DI6US$ MASS ( AIR OR FIRE1 Z E
"O SUPPOSES1 _! MO;N WD NECESS>ILY CAUSE
A NOISE ( TREM5D\S /R5G? & S* A NOISE WD
NECESS>ILY R1* & %ATT] U4 ,S9CE1 "!=E1 ?
E6ECT IS EVID5TLY N PRODUC$1 X FOLL[S T
N"O ( !M C MOVE )! MO;N EI ( ANIMATE
NATURE OR ( 3/RA9T4 ,X IS Z ?\< NATURE
_H =ESE5 ! RESULT1 T IF _! MOVE;T 7 O!R
?AN X IS1 NO?+ ON ? E>? CD MA9TA9 XS "*4
  ,T ! />S >E SPH]ICAL & >E N SELFMOV$1
HAS N[ BE5 EXPLA9$4
                  #AJ
  ,) _! ORD]-,I M1N ! POSI;N ( EA*1 Z
9VOLV+ ! PRIOR;Y ( "S &! PO/]IOR;Y (
O!RS1 & _! RESPECTIVE 4T.ES F !
EXTREM;Y-) ? A/RONOMY MAY 2 LEFT 6D1L1
S9CE ! A/RONOMICAL 4CUS.N IS ADEQUATE4
,? 4CUS.N %[S T ! MOVE;TS (! S"EAL />S
DEP5D1 Z REG>DS ! V>IETIES ( SPE$ : !Y
EXHIBIT1 ON ! 4T.E ( EA* F ! EXTREM;Y4
,X IS E/ABLI%$ T ! \T]MO/ REVOLU;N (!
H1V5S IS A SIMPLE MOVE;T &! SWIFTE/ (
ALL1 & T ! MOVE;T ( ALL O!R BODIES IS
-POSITE & RELATIVELY SL[1 =! R1SON T EA*
IS MOV+ ON XS [N CIRCLE )! REV]SE MO;N
6T (! H1V5S4 ,? AT ONCE L1DS U 6EXPECT T
! BODY : IS NE>E/ 6T F/ SIMPLE REVOLU;N
%D TAKE ! L;GE/ "T 6-PLETE XS CIRCLE1 &
T : IS F>!/ F X ! %ORTE/1 ! O!RS TAK+ A
L;G] "T ! NE>] !Y >E &A %ORT] "T ! F>!R
AWAY !Y >E4 ,= X IS ! NE>E/ BODY : IS
MO/ /R;GLY 9FLU;ED1 &! MO/ REMOTE1
0R1SON ( XS 4T.E1 : IS L1/ A6ECT$1 !
9FLU;E ON ! 9T]M$IATE BODIES V>Y+1 Z !
MA!MATICIANS %[1 ) _! 4T.E4
                  #AA
  ,) REG>D 6! %APE ( EA* />1 ! MO/
R1SONA# VIEW IS T !Y >E SPH]ICAL4 ,X HAS
BE5 %[N T X IS N 9 _! NATURE 6MOVE !MVS1
&1 S9CE NATURE IS NO WANTON OR R&OM
CR1TOR1 CLE>LY %E W H GIV5 ?+S : POSSESS
NO MOVE;T A %APE "PICUL>LY UNADAPT$
6MOVE;T4 ,S* A %APE IS ! SPH]E1 S9CE X
POSSESSES NO 9/RU;T ( MOVE;T4 ,CLE>LY !N
_! MASS W H ! =M (A SPH]E4 ,AG1 :AT
HOLDS ( "O HOLDS ( ALL1 &! EVID;E ( \R
EYES %[S U T ! MOON IS SPH]ICAL4 ,= H[
ELSE %D ! MOON Z X WAXES & WANES %[ =!
MO/ "P A CRESC5T-%AP$ OR GI2\S FIGURE1 &
ONLY AT "O MO;T A HALF-MOON8 ,&
A/RONOMICAL >GU;TS GIVE FUR!R 3FIRM,N2 =
NO O!R HYPO!SIS A3.TS =! CRESC5T %APE (!
SUN'S ECLIPSES4 ,"O1 !N1 (! H1V5LY
BODIES 2+ SPH]ICAL1 CLE>LY ! RE/ W 2
SPH]ICAL AL4
                  #AB
  ,"! >E TWO DI6ICULTIES1 : MAY V
R1SONABLY "H 2 RAIS$1 ( : WE M/ N[
ATTEMPT 6/ATE ! PROBA# SOLU;N3 = WE
REG>D ! Z1L ( "O ^: ?IR/ AF PHILOSOPHY
L1DS HM 6A3EPT EV5 SLI<T 9DIC,NS ": X IS
V DI6ICULT 6SEE "O'S WAY1 Z A PRO( R (
MODE/Y ?AN ( OV]CONFID;E4
  ,( _M S* PRO#MS "O (! /RANGE/ IS !
PRO#M :Y WE F9D ! GRTE/ NUMB] ( MOVE;TS
9 ! 9T]M$IATE BODIES1 & N1 R1 9 EA*
SU3ESSIVE BODY A V>IETY ( MOVE;T
PROPOR;NATE 6XS 4T.E F ! PRIM>Y MO;N4 ,=
WE %D EXPECT1 S9CE ! PRIM>Y BODY %[S "O
MO;N ONLY1 T ! BODY : IS NE>E/ 6X %D
MOVE )! FEWE/ MOVE;TS1 SAY TWO1 &! "O
NEXT AF T ) ?REE1 OR "S SIMIL> >RANGE;T4
,B ! OPPOSITE IS ! CASE4 ,! MOVE;TS (!
SUN & MOON >E FEW] ?AN ^? ( "S (!
PLANETS4 ,YET ^! PLANETS >E F>!R F !
C5TRE & ?US NE>] 6! PRIM>Y BODY ?AN !Y1
Z OBS]V,N HAS XF REV1L$4 ,= WE H SE5 !
MOON1 HALF-FULL1 PASS 2N ! PLANET ,M>S1
: VANI%$ ON XS %AD[ SIDE & CAME =? 0!
B"R & %9+ "P4 ,SIMIL> A3.TS ( O!R />S >E
GIV5 0! ,EGYPTIANS & ,BABYLONIANS1 ^:
OBS]V,NS H BE5 KEPT = V _M YE>S PA/1 & F
:OM M* ( \R EVID;E AB "PICUL> />S IS
DERIV$4 ,A SECOND DI6ICULTY : MAY )
EQUAL JU/ICE 2 RAIS$ IS ?4 ,:Y IS X T !
PRIM>Y MO;N 9CLUDES S* A MULTITUDE ( />S
T _! :OLE >RAY SEEMS 6DEFY C.T+1 :ILE (!
O!R />S EA* "O IS SEP>AT$ (F1 & 9 NO
CASE D WE F9D TWO OR M ATTA*$ 6! SAME
MO;N8
  ,ON ^! "QS1 ,I SAY1 X IS WELL T WE %D
SEEK 69CR1SE \R "U/&+1 ?\< WE H B LL 6G
^U1 & >E PLAC$ AT S GRT A 4T.E F ! FACTS
9 "Q4 ,N"E!.S "! >E C]TA9 PR9CIPLES ON :
IF WE BASE \R 3SID],N WE % N F9D ?
DI6ICULTY 0ANY M1NS 9SOLU#4 ,WE MAY
OBJECT T WE H BE5 ?9K+ (! />S Z M]E
BODIES1 & Z UNITS )A S]IAL ORD] 9DE$ B
5TIRELY 9ANIMATE2 B %D R 3CV !M Z 5JOY+
LIFE & AC;N4 ,ON ? VIEW ! FACTS C1SE
6APPE> SURPRIS+4 ,= X IS NATURAL T !
BE/-3DI;N$ ( ALL ?+S %D H XS GD )\T
AC;N1 T : IS NE>E/ 6X %D A*IEVE X 0LL &
SIMPLE AC;N1 & T : IS F>!R REMOV$ 0A
-PLEX;Y ( AC;NS1 J Z ) M5'S BODIES "O IS
9 GD 3DI;N )\T EX]CISE AT ALL1 ANO!R AF
A %ORT WALK1 :ILE ANO!R REQUIRES RUNN+ &
WRE/L+ & H>D TRA9+1 & "! >E YET O!RS :O
H["E H>D !Y "W$ !MVS CD N"E SECURE ? GD1
B ONLY "S SUB/ITUTE = X4 ,6SU3E$ (T5 OR
9 _M ?+S IS DI6ICULT4 ,= 9/.E1 6?R[ T5
?\S& ,COAN ?R[S )! DICE WD 2 IMPOSSI#1 B
6?R[ "O OR TWO IS -P>ATIVELY EASY4 ,9
AC;N1 AG1 :5 ,A HAS 6BE D"O 6GET ;,B1
;,B 6GET ;,C1 & ;,C 6GET ;,D1 "O /EP OR
TWO PRES5T LL DI6ICULTY1 B Z ! S]IES
EXT5DS ! DI6ICULTY GR[S4 ,WE M/1 !N1 ?9K
(! AC;N (! L[] />S Z SIMIL> 6T ( ANIMALS
& PLANTS4 ,= ON \R E>? X IS MAN T HAS !
GRTE/ V>IETY ( AC;NS-= "! >E _M GDS T
MAN C SECURE2 H;E 8 AC;NS >E V>I\S &
DIRECT$ 65DS 2Y !M-:ILE ! P]FECTLY
3DI;N$ HAS NO NE$ ( AC;N1 S9CE X IS XF !
5D1 & AC;N ALW REQUIRES TWO T]MS1 5D &
M1NS4 ,! L[] ANIMALS H LESS V>IETY (
AC;N ?AN MAN2 & PLANTS P]H H LL AC;N &(
"O K9D ONLY4 ,= EI !Y H B "O ATTA9A# GD
7Z 9DE$ MAN HAS71 OR1 IF S"EAL1 EA*
3TRIBUTES DIRECTLY 6_! ULTIMATE GD4 ,"O
?+ !N HAS & 5JOYS ! ULTIMATE GD1 O!R ?+S
ATTA9 6X1 "O IMMLY 0FEW /EPS1 ANO!R 0_M1
:ILE YET ANO!R DOES N EV5 ATTEMPT
6SECURE X B IS SATISFI$ 6R1* A PO9T N F>
REMOV$ F T 3SUMM,N4 ,?US1 TAK+ H1L? Z !
5D1 "! W 2 "O ?+ T ALW POSSESSES H1L?1
O!RS T ATTA9 X1 "O 0REDUC+ FLE%1 ANO!R
0RUNN+ & ?US REDUC+ FLE%1 ANO!R 0TAK+
/EPS 65A# HMF 6RUN1 ?US FUR!R 9CR1S+ !
NUMB] ( MOVE;TS1 :ILE ANO!R _C ATTA9
H1L? XF1 B ONLY RUNN+ OR REDUC;N ( FLE%1
S T "O OR O!R ( ^! IS = S* A 2+ ! 5D4 ,=
:ILE X IS CLE>LY BE/ = ANY 2+ 6ATTA9 !
R1L 5D1 YET1 IF T _C BE1 ! NE>] X IS 6!
BE/ ! BETT] W 2 XS /ATE4 ,X IS = ? R1SON
T ! E>? MOVES N AT ALL &! BODIES NE> 6X
) FEW MOVE;TS4 ,= !Y D N ATTA9 ! F9AL
5D1 B ONLY -E Z NE> 6X Z _! %>E 9 !
DIV9E PR9CIPLE P]MITS4 ,B ! F/ H1V5 F9DS
X IMMLY )A S+LE MOVE;T1 &! BODIES
9T]M$IATE 2T ! F/ & LA/ H1V5S ATTA9 X
9DE$1 B AT ! CO/ (A MULTIPLIC;Y (
MOVE;T4
  ,Z 6! DI6ICULTY T 96! "O PRIM>Y MO;N
IS CR[D$ A VA/ MULTITUDE ( />S1 :ILE (!
O!R />S EA* HAS BE5 SEP>ATELY GIV5
SPECIAL MOVE;TS ( XS [N1 "! IS 9 ! F/
PLACE ? R1SON = REG>D+ ! >RANGE;T Z A
NATURAL "O4 ,9 ?9K+ (! LIFE & MOV+
PR9CIPLE (! S"EAL H1V5S "O M/ REG>D ! F/
Z F> SUP]IOR 6! O!RS4 ,S* A SUP]IOR;Y WD
2 R1SONA#4 ,= ? S+LE F/ MO;N HAS 6MOVE
_M (! DIV9E BODIES1 :ILE ! NUM]\S O!R
MO;NS MOVE ONLY "O EA*1 S9CE EA* S+LE
PLANET MOVES )A V>IETY ( MO;NS4 ,?US1
!N1 NATURE MAKES MATT]S EQUAL &
E/ABLI%ES A C]TA9 ORD]1 GIV+ 6! S+LE
MO;N _M BODIES & 6! S+LE BODY _M MO;NS4
,& "! IS A SECOND R1SON :Y ! O!R MO;NS H
EA* ONLY "O BODY1 9 T EA* ( !M EXCEPT !
LA/1 I4E4 T : 3TA9S ! "O />1 IS RE,Y
MOV+ _M BODIES4 ,= ? LA/ SPH]E MOVES )
_M O!RS1 6: X IS FIX$1 EA* SPH]E 2+
ACTU,Y A BODY2 S T XS MOVE;T W 2 A JO9T
PRODUCT4 ,EA* SPH]E1 9 FACT1 HAS XS
"PICUL> NATURAL MO;N1 6: ! G5]AL MOVE;T
IS1 Z X W]E1 A4$4 ,B ! =CE ( ANY LIMIT$
BODY IS ONLY ADEQUATE 6MOV+ A LIMIT$
BODY4
  ,! "*I/ICS (! />S : MOVE )A CIRCUL>
MO;N1 9 RESPECT ( SUB/.E & %APE1 MOVE;T
& ORD]1 H N[ BE5 SU6ICI5TLY EXPLA9$4
                  #AC
  ,X REMA9S 6SP1K (! E>?1 ( XS POSI;N1 (
! "Q :E!R X IS AT RE/ OR 9 MO;N1 &( XS
%APE4
  ,I4 ,Z 6XS POSI;N "! IS "S DI6];E (
OP9ION4 ,MO/ P-ALL1 9 FACT1 :O REG>D !
:OLE H1V5 Z F9ITE-SAY X LIES AT ! C5TRE4
,B ! ,ITALIAN PHILOSOPH]S "KN Z
,PY?AGOR1NS TAKE ! 3TR>Y VIEW4 ,AT !
C5TRE1 !Y SAY1 IS FIRE1 &! E>? IS "O (!
/>S1 CR1T+ NI<T & "D 0XS CIRCUL> MO;N AB
! C5TRE4 ,!Y FUR!R 3/RUCT ANO!R E>? 9
OPPOSI;N 6\RS 6: !Y GIVE ! "N C.T]E>?4
,9 ALL ? !Y >E N SEEK+ = !ORIES & CAUSES
6A3.T = OBS]V$ FACTS1 B R =C+ _!
OBS]V,NS & TRY+ 6A3OMMODATE !M 6C]TA9
!ORIES & OP9IONS ( _! [N4 ,B "! >E _M
O!RS :O WD AGREE T X IS WR;G 6GIVE ! E>?
! C5TRAL POSI;N1 LOOK+ = 3FIRM,N R 6!ORY
?AN 6! FACTS ( OBS]V,N4 ,_! VIEW IS T !
MO/ PRECI\S PLACE 2FITS ! MO/ PRECI\S
?+3 B FIRE1 !Y SAY1 IS M PRECI\S ?AN
E>?1 &! LIMIT ?AN ! 9T]M$IATE1 &!
CIRCUMF];E &! C5TRE >E LIMITS4 ,R1SON+
ON ? BASIS !Y TAKE ! VIEW T X IS N E>? T
LIES AT ! C5TRE (! SPH]E1 B R FIRE4 ,!
,PY?AGOR1NS H A FUR!R R1SON4 ,!Y HOLD T
! MO/ IMPORTANT "P (! _W1 : IS ! C5TRE1
%D 2 MO/ /RICTLY GU>D$1 & "N X1 OR R !
FIRE : O3UPIES T PLACE1 ! ,8,GU>DH\SE (
,ZEUS0'1 Z IF ! ^W ,8C5TRE0' 7 Q
UNEQUIVOCAL1 &! C5TRE (! MA!MATICAL
FIGURE 7 ALW ! SAME ) T (! ?+ OR !
NATURAL C5TRE4 ,B X IS BETT] 63CV (!
CASE (! :OLE H1V5 Z ANALOG\S 6T (
ANIMALS1 9 : ! C5TRE (! ANIMAL & T (!
BODY >E DI6]5T4 ,= ? R1SON !Y H NO NE$
6BE S 4TURB$ AB ! _W1 OR 6CALL 9 A GU>D
= XS C5TRE3 R LET !M LOOK =! C5TRE 9 !
O!R S5SE & TELL U :AT X IS L & ": NATURE
HAS SET X4 ,T C5TRE W 2 "S?+ PRIM>Y &
PRECI\S2 B 6! M]E POSI;N WE %D GIVE !
LA/ PLACE R ?AN ! F/4 ,=! MI4LE IS :AT
IS DEF9$1 & :AT DEF9ES X IS ! LIMIT1 & T
: 3TA9S OR LIMITS IS M PRECI\S ?AN T :
IS LIMIT$1 SEE 9G T ! LATT] IS ! MATT] &
! =M] ! ESS;E (! SY/EM4
  ,,II4 ,Z 6! POSI;N (! E>?1 !N1 ? IS !
VIEW : "S ADV.E1 &! VIEWS ADV.ED 3C]N+
XS RE/ OR MO;N >E SIMIL>4 ,= "H TOO "!
IS NO G5]AL AGREE;T4 ,ALL :O D5Y T ! E>?
LIES AT ! C5TRE ?9K T X REVOLVES AB !
C5TRE1 & N ! E>? ONLY B1 Z WE SD 2F1 !
C.T]-E>? Z WELL4 ,"S ( !M EV5 3SID] X
POSSI# T "! >E S"EAL BODIES S MOV+1 : >E
9VISI# 6U [+ 6! 9T]POSI;N (! E>?4 ,?1 !Y
SAY1 A3.TS =! FACT T ECLIPSES (! MOON >E
M FREQU5T ?AN ECLIPSES (! SUN3 = 9 A4I;N
6! E>? EA* ( ^! MOV+ BODIES C OB/RUCT X4
,9DE$1 Z 9 ANY CASE ! SURFACE (! E>? IS
N ACTU,Y A C5TRE B 4TANT F X A FULL
HEMISPH]E1 "! IS NO M DI6ICULTY1 !Y ?9K1
9 A3.T+ =! OBS]V$ FACTS ON _! VIEW T WE
D N DWELL AT ! C5TRE1 ?AN ON ! -MON VIEW
T ! E>? IS 9 ! MI4LE4 ,EV5 Z X IS1 "! IS
NO?+ 9 ! OBS]V,NS 6SU7E/ T WE >E REMOV$
F ! C5TRE 0HALF ! DIAMET] (! E>?4 ,O!RS1
AG1 SAY T ! E>?1 : LIES AT ! C5TRE1 IS
,8ROLL$0'1 & ?US 9 MO;N1 AB ! AXIS (!
:OLE H1V51 ,S X /&S WRITT5 9 ! ,TIMAEUS4
  ,,III4 ,"! >E SIMIL> 4PUTES AB ! %APE
(! E>?4 ,"S ?9K X IS SPH]ICAL1 O!RS T X
IS FLAT & DRUM-%AP$4 ,= EVID;E !Y BR+ !
FACT T1 Z ! SUN RISES & SETS1 ! "P 3C1L$
0! E>? %[S A /RAI<T & N A CURV$ $GE1
":AS IF ! E>? 7 SPH]ICAL ! L9E ( SEC;N
WD H 6BE CIRCUL>4 ,9 ? !Y L1VE \ ( A3.T
! GRT 4T.E (! SUN F ! E>? &! GRT SIZE (!
CIRCUMF];E1 :1 SE5 F A 4T.E ON ^!
APP>5TLY SMALL CIRCLES APPE>S /RAI<T4
,S* AN APPE>.E "\ N 6MAKE !M D\BT !
CIRCUL> %APE (! E>?4 ,B !Y H ANO!R
>GU;T4 ,!Y SAY T 2C X IS AT RE/1 ! E>?
M/ NECESS>ILY H ? %APE4 ,= "! >E _M
DI6]5T WAYS 9 : ! MOVE;T OR RE/ (! E>?
HAS BE5 3CVD4
  ,! DI6ICULTY M/ H O3URR$ 6E "O4 ,X WD
9DE$ 2 A -PLAC5T M9D T FELT NO SURPRISE
T1 :ILE A LL BIT ( E>?1 LET LOOSE 9 MID-
AIR MOVES & W N /AY /1 & M "! IS ( X !
FA/] X MOVES1 ! :OLE E>?1 FREE 9 MIDAIR1
%D %[ NO MOVE;T AT ALL4 ,YET "H IS ? GRT
WEI<T ( E>?1 & X IS AT RE/4 ,& AG1 F 2N
"O ( ^! MOV+ FRAG;TS ( E>?1 2F X FALLS1
TAKE AWAY ! E>?1 & X W 3T9UE XS D[NW>D
MOVE;T ) NO?+ 6/OP X4 ,! DI6ICULTY !N1
HAS NATUR,Y PASS$ 96A -MON PLACE (
PHILOSOPHY2 & "O MAY WELL WOND] T !
SOLU;NS (F]$ >E N SE5 69VOLVE GRT]
ABSURDITIES ?AN ! PRO#M XF4
  ,0^! 3SID],NS "S H BE5 L$ 6ASS]T T !
E>? 2L U IS 9F9ITE1 SAY+1 ) ,X5OPHANES (
,COLOPHON1 T X HAS ,8PU%$ XS ROOTS
69F9;Y0'1-IN ORD] 6SAVE ! TR\# ( SEEK+ =
! CAUSE4 ,H;E ! %>P REBUKE ( ,EMP$OCLES1
9 ! ^WS ,8IF ! DEEPS (! E>? >E 5D.S &
5D.S ! AMPLE E!R-S* IS ! VA9 TALE TOLD
0_M A T;GUE1 P\R$ F ! M\?S ( ^? :O H SE5
B LL (! :OLE4 ,O!RS SAY ! E>? RE/S ^U
WAT]4 ,?1 9DE$1 IS ! OLDE/ !ORY T HAS
BE5 PRES]V$1 & IS ATTRIBUT$ 6,?ALES (
,MILETUS4 ,X 0 SUPPOS$ 6/AY / 2C X
FLOAT$ L WOOD & O!R SIMIL> SUB/.ES1 : >E
S 3/ITUT$ Z 6RE/ ^U B N ^U AIR4 ,Z IF !
SAME A3.T _H N 6BE GIV5 (! WAT] : C>RIES
! E>? Z (! E>? XF6 ,X IS N ! NATURE (
WAT]1 ANY M ?AN ( E>?1 6/AY 9 MID-AIR3 X
M/ H "S?+ 6RE/ ^U4 ,AG1 Z AIR IS LI<T]
?AN WAT]1 S IS WAT] ?AN E>?3 H[ !N C !Y
?9K T ! NATUR,Y LI<T] SUB/.E LIES 2L !
H1VI]8 ,AG1 IF ! E>? Z A :OLE IS CAPA# (
FLOAT+ ^U WAT]1 T M/ OBVI\SLY 2 ! CASE )
ANY "P ( X4 ,B OBS]V,N %[S T ? IS N !
CASE4 ,ANY PIECE ( E>? GOES 6! BOTTOM1 !
QK] ! L>G] X IS4 ,^! ?9K]S SEEM 6PU% _!
9QUIRIES "S WAY 96! PRO#M1 B N S F> Z !Y
MI<T4 ,X IS :AT WE >E ALL 9CL9$ 6D1
6DIRECT \R 9QUIRY N 0! MATT] XF1 B 0!
VIEWS ( \R OPPON5TS3 & EV5 :5 9T]ROGAT+
"OF "O PU%ES ! 9QUIRY ONLY 6! PO9T AT :
"O C NO L;G] (F] ANY OPPOSI;N4 ,H;E A GD
9QUIR] W 2 "O :O IS R1DY 9 BR++ =W>D !
OBJEC;NS PROP] 6! G5US1 & T HE W 2 :5 HE
HAS GA9$ AN "U/&+ ( ALL ! DI6];ES4
  ,ANAXIM5ES & ,ANAXAGORAS & ,DEMOCRITUS
GIVE ! FLAT;S (! E>? Z ! CAUSE ( XS /AY+
/4 ,?US1 !Y SAY1 X DOES N CUT1 B COV]S L
A LID1 ! AIR 2N X4 ,? SEEMS 6BE ! WAY (
FLAT-%AP$ BODIES3 = EV5 ! W9D C SC>CELY
MOVE !M 2C ( _! P[] ( RESI/.E4 ,! SAME
IMMOBIL;Y1 !Y SAY1 IS PRODUC$ 0! FLAT;S
(! SURFACE : ! E>? PRES5TS 6! AIR :
"ULIES X2 :ILE ! AIR1 N HAV+ ROOM 5
6*ANGE XS PLACE 2C X IS "UN1? ! E>?1
/AYS "! 9 A MASS1 L ! WAT] 9 ! CASE (!
WAT]-CLOCK4 ,& !Y A4UCE AN AM.T ( EVID;E
6PROVE T AIR1 :5 CUT (F & AT RE/1 C BE>
A 3SID]A# WEI<T4
  ,N[1 F/1 IF ! %APE (! E>? IS N FLAT1
XS FLAT;S _C 2 ! CAUSE ( XS IMMOBIL;Y4
,B 9 _! [N A3.T X IS R ! SIZE (! E>? ?AN
XS FLAT;S T CAUSES X 6REMA9 AT RE/4 ,=!
R1SON :Y ! AIR IS S CLOSELY 3F9$ T X _C
F9D A PASSAGE1 & "!=E /AYS ": X IS1 IS
XS GRT AM.T3 & ? AM.T GRT 2C ! BODY :
ISOLATES X1 ! E>?1 IS V L>GE4 ,? RESULT1
!N1 W FOLL[1 EV5 IF ! E>? IS SPH]ICAL1 S
L;G Z X RETA9S XS SIZE4 ,S F> Z _!
>GU;TS G1 ! E>? W / 2 AT RE/4
  ,9 G5]AL1 \R QU>REL ) ^? :O SP1K (
MOVE;T 9 ? WAY _C 2 3F9$ 6! "PS2 X 3C]NS
! :OLE UNIV]SE4 ,"O M/ DECIDE AT ! \TSET
:E!R BODIES H A NATURAL MOVE;T OR N1
:E!R "! IS NO NATURAL B ONLY 3/RA9$
MOVE;T4 ,SEE+1 H["E1 T WE H ALR DECID$ ?
MATT] 6! BE/ ( \R ABIL;Y1 WE >E 5TITL$
6TR1T \R RESULTS Z REPRES5T+ FACT4
,BODIES1 WE SAY1 : H NO NATURAL MOVE;T1
H NO 3/RA9$ MOVE;T2 & ": "! IS NO
NATURAL & NO 3/RA9$ MOVE;T "! W 2 NO
MOVE;T AT ALL4 ,? IS A 3CLU.N1 !
NECESS;Y ( : WE H ALR DECID$1 & WE H SE5
FUR!R T RE/ AL W 2 9CONCEIVA#1 S9CE RE/1
L MOVE;T1 IS EI NATURAL OR 3/RA9$4 ,B IF
"! IS ANY NATURAL MOVE;T1 3/RA9T W N 2 !
SOLE PR9CIPLE ( MO;N OR ( RE/4 ,IF1 !N1
X IS 03/RA9T T ! E>? N[ KEEPS XS PLACE1
! S-CALL$ ,8:IRL+0' MOVE;T 0: XS "PS
CAME TGR AT ! C5TRE 0 AL 3/RA9$4 7,! =M
( CAUS,N SUPPOS$ !Y ALL BORR[ F OBS]V,NS
( LIQUIDS &( AIR1 9 : ! L>G] & H1VI]
BODIES ALW MOVE 6! C5TRE (! :IRL4 ,? IS
?"\ 0ALL ^? :O TRY 6G5]ATE ! H1V5S
6EXPLA9 :Y ! E>? CAME TGR AT ! C5TRE4
,!Y !N SEEK A R1SON = XS /AY+ "!2 & "S
SAY1 9 ! MANN] EXPLA9$1 T ! R1SON IS XS
SIZE & FLAT;S1 O!RS1 ) ,EMP$OCLES1 T !
MO;N (! H1V5S1 MOV+ AB X AT A HI<] SPE$1
PREV5TS MOVE;T (! E>?1 Z ! WAT] 9 A CUP1
:5 ! CUP IS GIV5 A CIRCUL> MO;N1 ?\< X
IS (T5 "UN1? ! BRONZE1 IS = ? SAME R1SON
PREV5T$ F MOV+ )! D[NW>D MOVE;T : IS
NATURAL 6X47 ,B SUPPOSE BO? ! ,8:IRL0' &
XS FLAT;S 7! AIR 2N 2+ )DRAWN7 C1SE
6PREV5T ! E>?'S MO;N1 ": W ! E>? MOVE
6!N8 ,XS MOVE;T 6! C5TRE 0 3/RA9$1 & XS
RE/ AT ! C5TRE IS DUE 63/RA9T2 B "! M/ 2
"S MO;N : IS NATURAL 6X4 ,W ? 2 UPW>D
MO;N OR D[NW>D OR :AT8 ,X M/ H "S MO;N2
& IF UPW>D & D[NW>D MO;N >E ALIKE 6X1 &!
AIR ABV ! E>? DOES N PREV5T UPW>D
MOVE;T1 !N NO M CD AIR 2L X PREV5T
D[NW>D MOVE;T4 ,=! SAME CAUSE M/
NECESS>ILY H ! SAME E6ECT ON ! SAME ?+4
  ,FUR!R1 AG/ ,EMP$OCLES "! IS ANO!R
PO9T : MI<T 2 MADE4 ,:5 ! ELE;TS 7
SEP>AT$ (F 0,HATE1 :AT CAUS$ ! E>? 6KEEP
XS PLACE8 ,SURELY ! ,8:IRL0' _C H BE5 !N
AL ! CAUSE4 ,X IS ABSURD TOO N 6P]CV T1
:ILE ! :IRL+ MOVE;T MAY H BE5 RESPONSI#
=! ORIG9AL -+ TGR (! >T ( E>? AT !
C5TRE1 ! "Q REMA9S1 :Y N[ D ALL H1VY
BODIES MOVE 6! E>?4 ,=! :IRL SURELY DOES
N -E NE> U4 ,:Y1 AG1 DOES FIRE MOVE
UPW>D8 ,N1 SURELY1 2C (! :IRL4 ,B IF
FIRE IS NATUR,Y S* Z 6MOVE 9 A C]TA9
DIREC;N1 CLE>LY ! SAME MAY 2 SUPPOS$
6HOLD ( E>?4 ,AG1 X _C 2 ! :IRL :
DET]M9ES ! H1VY &! LI<T4 ,R T MOVE;T
CAUS$ ! PRE-EXI/5T H1VY & LI<T ?+S 6G 6!
MI4LE & /AY ON ! SURFACE RESPECTIVELY4
,?US1 2F "E ! :IRL 2GAN1 H1VY & LI<T
EXI/$2 & :AT C H BE5 ! GR.D ( _! 4T9C;N1
OR ! MANN] & DIREC;N ( _! NATURAL
MOVE;TS8 ,9 ! 9F9ITE *AOS "! C H BE5 NEI
ABV NOR 2L1 & X IS 0^! T H1VY & LI<T >E
DET]M9$4
  ,X IS 6^! CAUSES T MO/ WRIT]S PAY
ATT5;N3 B "! >E "S1 ,ANAXIM&]1 = 9/.E1
AM;G ! ANCI5TS1 :O SAY T ! E>? KEEPS XS
PLACE 2C ( XS 9DI6];E4 ,MO;N UPW>D &
D[NW>D & SIDEWAYS 7 ALL1 !Y ?"\1 EQU,Y
9APPROPRIATE 6T : IS SET AT ! C5TRE &
9DI6]5TLY RELAT$ 6E EXTREME PO9T2 &
6MOVE 9 3TR>Y DIREC;NS AT ! SAME "T 0
IMPOSSI#3 S X M/ NE$S REMA9 /4 ,? VIEW
IS 9G5I\S B N TRUE4 ,! >GU;T WD PROVE T
"EY?+1 :AT"E X BE1 : IS PUT AT ! C5TRE1
M/ /AY "!4 ,FIRE1 !N1 W RE/ AT ! C5TRE3
=! PRO( TURNS ON NO PECULI> PROP]TY (
E>?4 ,B ? DOES N FOLL[4 ,! OBS]V$ FACTS
AB E>? >E N ONLY T X REMA9S AT ! C5TRE1
B AL T X MOVES 6! C5TRE4 ,! PLACE 6: ANY
FRAG;T ( E>? MOVES M/ NECESS>ILY 2 !
PLACE 6: ! :OLE MOVES2 & 9 ! PLACE 6: A
?+ NATUR,Y MOVES1 X W NATUR,Y RE/4 ,!
R1SON !N IS N 9 ! FACT T ! E>? IS
9DI6]5TLY RELAT$ 6E EXTREME PO9T3 = ? WD
APPLY 6ANY BODY1 ":AS MOVE;T 6! C5TRE IS
PECULI> 6E>?4 ,AG X IS ABSURD 6LOOK =A
R1SON :Y ! E>? REMA9S AT ! C5TRE & N =A
R1SON :Y FIRE REMA9S AT ! EXTREM;Y4 ,IF
! EXTREM;Y IS ! NATURAL PLACE ( FIRE1
CLE>LY E>? M/ AL H A NATURAL PLACE4 ,B
SUPPOSE T ! C5TRE IS N XS PLACE1 & T !
R1SON ( XS REMA9+ "! IS ? NECESS;Y (
9DI6];E-ON ! ANALOGY (! HAIR :1 X IS SD1
H["E GRT ! T5.N1 W N BR1K "U X1 IF X 2
EV5LY 4TRIBUT$1 OR (! M5 :O1 ?\<
EXCE$+LY HUNGRY & ?IR/Y1 & BO? EQU,Y1
YET 2+ EQUIDISTANT F FOOD & DR9K1 IS
"!=E B.D 6/AY ": HE IS-EV5 S1 X / REMA9S
6EXPLA9 :Y FIRE /AYS AT ! EXTREMITIES4
,X IS /RANGE1 TOO1 6ASK AB ?+S /AY+ / B
N AB _! MO;N1-:Y1 ,I M1N1 "O ?+1 IF NO?+
/OPS X1 MOVES UP1 & ANO!R ?+ 6! C5TRE4
,AG1 _! /ATE;TS >E N TRUE4 ,X HAPP5S1
9DE$1 6BE ! CASE T A ?+ 6: MOVE;T ? WAY
& T IS EQU,Y 9APPROPRIATE IS OBLIG$
6REMA9 AT ! C5TRE4 ,B S F> Z _! >GU;T
GOES1 9/1D ( REMA9+ "!1 X W MOVE1 ONLY N
Z A MASS B 9 FRAG;TS4 ,=! >GU;T APPLIES
EQU,Y 6FIRE4 ,FIRE1 IF SET AT ! C5TRE1
%D /AY "!1 L E>?1 S9CE X W 2 9DI6]5TLY
RELAT$ 6E PO9T ON ! EXTREM;Y4 ,N"E!.S X
W MOVE1 Z 9 FACT X ALW DOES MOVE :5 NO?+
/OPS X1 AWAY F ! C5TRE 6! EXTREM;Y4 ,X W
N1 H["E1 MOVE 9 A MASS 6A S+LE PO9T ON !
CIRCUMF];E-! ONLY POSSI# RESULT ON !
L9ES (! 9DI6];E !ORY-B R EA* CORRESPOND+
POR;N ( FIRE 6! CORRESPOND+ "P (!
EXTREM;Y1 EA* F\R? "P1 = 9/.E1 6A F\R?
"P (! CIRCUMF];E4 ,= S9CE NO BODY IS A
PO9T1 X W H "PS4 ,! EXPAN.N1 :5 ! BODY
9CR1S$ ! PLACE O3UPI$1 WD 2 ON ! SAME
PR9CIPLE Z ! 3TRAC;N1 9 : ! PLACE 0
DIM9I%$4 ,?US1 = ALL ! 9DI6];E !ORY %[S
6! 3TR>Y1 E>? AL WD H MOV$ 9 ? MANN]
AWAY F ! C5TRE1 UN.S ! C5TRE _H BE5 XS
NATURAL PLACE4
  ,WE H N[ \TL9$ ! VIEWS HELD Z 6! %APE1
POSI;N1 & RE/ OR MOVE;T (! E>?4
                  #AD
  ,LET U F/ DECIDE ! "Q :E!R ! E>? MOVES
OR IS AT RE/4 ,=1 Z WE SD1 "! >E "S :O
MAKE X "O (! />S1 & O!RS :O1 SETT+ X AT
! C5TRE1 SUPPOSE X 6BE ,8ROLL$0' & 9
MO;N AB ! POLE Z AXIS4 ,T BO? VIEWS >E
UNT5A# W 2 CLE> IF WE TAKE Z \R />T+-
PO9T ! FACT T ! E>?'S MO;N1 :E!R ! E>? 2
AT ! C5TRE OR AWAY F X1 M/ NE$S 2 A
3/RA9$ MO;N4 ,X _C 2 ! MOVE;T (! E>? XF4
,IF X W]E1 ANY POR;N ( X WD H ? MOVE;T2
B 9 FACT E "P MOVES 9 A /RAI<T L9E 6!
C5TRE4 ,2+1 !N1 3/RA9$ & UNNATURAL1 !
MOVE;T CD N 2 ET]NAL4 ,B ! ORD] (!
UNIV]SE IS ET]NAL4 ,AG1 "EY?+ T MOVES )!
CIRCUL> MOVE;T1 EXCEPT ! F/ SPH]E1 IS
OBS]V$ 6BE PASS$1 & 6MOVE ) M ?AN "O
MO;N4 ,! E>?1 !N1 AL1 :E!R X MOVE AB !
C5TRE OR Z /,N>Y AT X1 M/ NECESS>ILY
MOVE ) TWO MO;NS4 ,B IF ? 7 S1 "! WD H
6BE PASS+S & TURN+S (! FIX$ />S4 ,YET NO
S* ?+ IS OBS]V$4 ,! SAME />S ALW RISE &
SET 9 ! SAME "PS (! E>?4
  ,FUR!R1 ! NATURAL MOVE;T (! E>?1 "P &
:OLE ALIKE1 IS ! C5TRE (! :OLE-:;E !
FACT T X IS N[ ACTU,Y SITUAT$ AT !
C5TRE-B X MI<T 2 "Q$ S9CE BO? C5TRES >E
! SAME1 : C5TRE X IS T POR;NS ( E>? &
O!R H1VY ?+S MOVE TO4 ,IS ? _! GOAL 2C X
IS ! C5TRE (! E>? OR 2C X IS ! C5TRE (!
:OLE8 ,! GOAL1 SURELY1 M/ 2 ! C5TRE (!
:OLE4 ,= FIRE & O!R LI<T ?+S MOVE 6!
EXTREM;Y (! >EA : 3TA9S ! C5TRE4 ,X
HAPP5S1 H["E1 T ! C5TRE (! E>? &(! :OLE
IS ! SAME4 ,?US !Y D MOVE 6! C5TRE (!
E>?1 B A3ID5T,Y1 9 VIRTUE (! FACT T !
E>?'S C5TRE LIES AT ! C5TRE (! :OLE4 ,T
! C5TRE (! E>? IS ! GOAL ( _! MOVE;T IS
9DICAT$ 0! FACT T H1VY BODIES MOV+ T[>DS
! E>? D N P>ALLEL B S Z 6MAKE EQUAL
ANGLES1 & ?US 6A S+LE C5TRE1 T (! E>?4
,X IS CLE>1 !N1 T ! E>? M/ 2 AT ! C5TRE
& IMMOVA#1 N ONLY =! R1SONS ALR GIV51 B
AL 2C H1VY BODIES =CIBLY ?R[N Q /RAI<T
UPW>D RETURN 6! PO9T F : !Y />T$1 EV5 IF
!Y >E ?R[N 6AN 9F9ITE 4T.E4 ,F ^!
3SID],NS !N X IS CLE> T ! E>? DOES N
MOVE & DOES N LIE ELSE": ?AN AT ! C5TRE4
  ,F :AT WE H SD ! EXPLAN,N (! E>?'S
IMMOBIL;Y IS AL APP>5T4 ,IF X IS !
NATURE ( E>?1 Z OBS]V,N %[S1 6MOVE F ANY
PO9T 6! C5TRE1 Z ( FIRE 3TR>IWISE 6MOVE
F ! C5TRE 6! EXTREM;Y1 X IS IMPOSSI# T
ANY POR;N ( E>? %D MOVE AWAY F ! C5TRE
EXCEPT 03/RA9T4 ,=A S+LE ?+ HAS A S+LE
MOVE;T1 &A SIMPLE ?+ A SIMPLE3 3TR>Y
MOVE;TS _C 2L;G 6! SAME ?+1 & MOVE;T
AWAY F ! C5TRE IS ! 3TR>Y ( MOVE;T 6X4
,IF !N NO POR;N ( E>? C MOVE AWAY F !
C5TRE1 OBVI\SLY / LESS C ! E>? Z A :OLE
S MOVE4 ,= X IS ! NATURE (! :OLE 6MOVE
6! PO9T 6: ! "P NATUR,Y MOVES4 ,S9CE1
!N1 X WD REQUIRE A =CE GRT] ?AN XF 6MOVE
X1 X M/ NE$S /AY AT ! C5TRE4 ,? VIEW IS
FUR!R SUPPORT$ 0! 3TRIBU;NS (
MA!MATICIANS 6A/RONOMY1 S9CE ! OBS]V,NS
MADE Z ! %APES *ANGE 0: ! ORD] (! />S IS
DET]M9$1 >E FULLY A3.T$ = ON ! HYPO!SIS
T ! E>? LIES AT ! C5TRE4 ,(! POSI;N (!
E>? &(! MANN] ( XS RE/ OR MOVE;T1 \R
4CUS.N MAY "H 5D4
  ,XS %APE M/ NECESS>ILY 2 SPH]ICAL4 ,=
E POR;N ( E>? HAS WEI<T UNTIL X R1*ES !
C5TRE1 &! JO/L+ ( "PS GRT] & SMALL] WD
BR+ AB N A WAV$ SURFACE1 B R -PRES.N &
3V]G;E ( "P & "P UNTIL ! C5TRE IS R1*$4
,! PROCESS %D 2 3CVD 0SUPPOS+ ! E>? 6-E
962+ 9 ! WAY T "S (! NATURAL PHILOSOPH]S
DESCRIBE4 ,ONLY !Y ATTRIBUTE ! D[NW>D
MOVE;T 63/RA9T1 & X IS BETT] 6KEEP 6!
TRU? & SAY T ! R1SON ( ? MO;N IS T A ?+
: POSSESSES WEI<T IS NATUR,Y 5D[$ )A
C5TRIPETAL MOVE;T4 ,:5 ! MIXTURE1 !N1 0
M]ELY POT5TIAL1 ! ?+S T 7 SEP>AT$ (F
MOV$ SIMIL>LY F E SIDE T[>DS ! C5TRE4
,:E!R ! "PS : CAME TGR AT ! C5TRE 7
4TRIBUT$ AT ! EXTREMITIES EV5LY1 OR 9 "S
O!R WAY1 MAKES NO DI6];E4 ,IF1 ON ! "O
H&1 "! 7 A SIMIL> MOVE;T F EA* QU>T] (!
EXTREM;Y 6! S+LE C5TRE1 X IS OBVI\S T !
RESULT+ MASS WD 2 SIMIL> ON E SIDE4 ,=
IF AN EQUAL AM.T IS A4$ ON E SIDE !
EXTREM;Y (! MASS W 2 "EY": EQUIDISTANT F
XS C5TRE1 I4E4 ! FIGURE W 2 SPH]ICAL4 ,B
NEI W X 9 ANY WAY A6ECT ! >GU;T IF "! IS
N A SIMIL> A3ES.N ( 3CURR5T FRAG;TS F E
SIDE4 ,=! GRT] QUANT;Y1 F9D+ A LESS] 9
FRONT ( X1 M/ NECESS>ILY DRIVE X ON1 BO?
HAV+ AN IMPULSE ^: GOAL IS ! C5TRE1 &!
GRT] WEI<T DRIV+ ! LESS] =W>D TILL ?
GOAL IS R1*$4 ,9 ? WE H AL ! SOLU;N (A
POSSI# DI6ICULTY4 ,! E>?1 X MI<T 2 >GU$1
IS AT ! C5TRE & SPH]ICAL 9 %APE3 IF1 !N1
A WEI<T _M "TS T (! E>? 7 A4$ 6"O
HEMISPH]E1 ! C5TRE (! E>? &(! :OLE W NO
L;G] 2 CO9CID5T4 ,S T EI ! E>? W N /AY /
AT ! C5TRE1 OR IF X DOES1 X W 2 AT RE/
)\T HAV+ XS C5TRE AT ! PLACE 6: X IS /
XS NATURE 6MOVE4 ,S* IS ! DI6ICULTY4 ,A
%ORT 3SID],N W GIVE U AN EASY ANSW]1 IF
WE F/ GIVE PRECI.N 6\R PO/ULATE T ANY
BODY 5D[$ ) WEI<T1 ( :AT"E SIZE1 MOVES
T[>DS ! C5TRE4 ,CLE>LY X W N /OP :5 XS
$GE T\*ES ! C5TRE4 ,! GRT] QUANT;Y M/
PREVAIL UNTIL ! BODY'S C5TRE O3UPIES !
C5TRE4 ,= T IS ! GOAL ( XS IMPULSE4 ,N[
X MAKES NO DI6];E :E!R WE APPLY ? 6A
CLOD OR -MON FRAG;T ( E>? OR 6! E>? Z A
:OLE4 ,! FACT 9DICAT$ DOES N DEP5D ^U
DEGREES ( SIZE B APPLIES UNIV]S,Y 6"EY?+
T HAS ! C5TRIPETAL IMPULSE4 ,"!=E E>? 9
MO;N1 :E!R 9 A MASS OR 9 FRAG;TS1
NECESS>ILY 3T9UES 6MOVE UNTIL X O3UPIES
! C5TRE EQU,Y E WAY1 ! LESS 2+ =C$
6EQUALIZE XF 0! GRT] [+ 6! =W>D DRIVE (!
IMPULSE4
  ,IF ! E>? 0 G5]AT$1 !N1 X M/ H BE5 =M$
9 ? WAY1 & S CLE>LY XS G5],N 0 SPH]ICAL2
& IF X IS UNG5]AT$ & HAS REMA9$ S ALW1
XS "* M/ 2 T : ! 9ITIAL G5],N1 IF X _H
O3URR$1 WD H GIV5 X4 ,B ! SPH]ICAL %APE1
NECESSITAT$ 0? >GU;T1 FOLL[S AL F ! FACT
T ! MO;NS ( H1VY BODIES ALW MAKE EQUAL
ANGLES1 & >E N P>ALLEL4 ,? WD 2 !
NATURAL =M ( MOVE;T T[>DS :AT IS NATUR,Y
SPH]ICAL4 ,EI !N ! E>? IS SPH]ICAL OR X
IS AT L1/ NATUR,Y SPH]ICAL4 ,& X IS "R
6CALL ANY?+ T : NATURE 9T5DS X 6BE1 & :
2L;GS 6X1 R ?AN T : X IS 03/RA9T & 3TR>Y
6NATURE4 ,! EVID;E (! S5SES FUR!R
CORROBORATES ?4 ,H[ ELSE WD ECLIPSES (!
MOON %[ SEG;TS %AP$ Z WE SEE !M8 ,Z X
IS1 ! %APES : ! MOON XF EA* MON? %[S >E
( E K9D /RAI<T1 GI2\S1 & 3CAVE-B 9
ECLIPSES ! \TL9E IS ALW CURV$3 &1 S9CE X
IS ! 9T]POSI;N (! E>? T MAKES ! ECLIPSE1
! =M ( ? L9E W 2 CAUS$ 0! =M (! E>?'S
SURFACE1 : IS "!=E SPH]ICAL4 ,AG1 \R
OBS]V,NS (! />S MAKE X EVID5T1 N ONLY T
! E>? IS CIRCUL>1 B AL T X IS A CIRCLE (
NO GRT SIZE4 ,= Q A SMALL *ANGE ( POSI;N
6S\? OR NOR? CAUSES A MANIFE/ ALT],N (!
HORIZON4 ,"! IS M* *ANGE1 ,I M1N1 9 !
/>S : >E OV]H1D1 &! />S SE5 >E DI6]5T1 Z
"O MOVES NOR?W>D OR S\?W>D4 ,9DE$ "! >E
"S />S SE5 9 ,EGYPT & 9 ! NEI<B\RHOOD (
,CYPRUS : >E N SE5 9 ! NOR!RLY REGIONS2
& />S1 : 9 ! NOR? >E N"E 2Y ! RANGE (
OBS]V,N1 9 ^? REGIONS RISE & SET4 ,ALL (
: GOES 6%[ N ONLY T ! E>? IS CIRCUL> 9
%APE1 B AL T X IS A SPH]E ( NO GRT SIZE3
= O!RWISE ! E6ECT ( S SLI<T A *ANGE (
PLACE WD N 2 QKLY APP>5T4 ,H;E "O %D N 2
TOO SURE (! 9CR$IBIL;Y (! VIEW ( ^? :O
3CV T "! IS 3T9U;Y 2T ! "PS AB ! PILL>S
( ,H]CULES &! "PS AB ,9DIA1 & T 9 ? WAY
! OC1N IS "O4 ,Z FUR!R EVID;E 9 FAV\R (
? !Y QUOTE ! CASE ( ELEPHANTS1 A SPECIES
O3URR+ 9 EA* ( ^! EXTREME REGIONS1
SU7E/+ T ! -MON "*I/IC ( ^! EXTREMES IS
EXPLA9$ 0_! 3T9U;Y4 ,AL1 ^? MA!MATICIANS
:O TRY 6CALCULATE ! SIZE (! E>?'S
CIRCUMF];E >RIVE AT ! FIGURE #DJJ1JJJ
/ADES4 ,? 9DICATES N ONLY T ! E>?'S MASS
IS SPH]ICAL 9 %APE1 B AL T Z -P>$ )! />S
X IS N ( GRT SIZE4
              ,BOOK ,,III
                   #A
  ,,WE H ALR 4CUSS$ ! F/ H1V5 & XS "PS1
! MOV+ />S )9 X1 ! MATT] ( : ^! >E -POS$
& _! BODILY 3/ITU;N1 & WE H AL %[N T !Y
>E UNG5]AT$ & 9DE/RUCTI#4 ,N[ ?+S T WE
CALL NATURAL >E EI SUB/.ES OR FUNC;NS &
ATTRIBUTES ( SUB/.ES4 ,Z SUB/.ES ,I
CLASS ! SIMPLE BODIES-FIRE1 E>?1 &! O!R
T]MS (! S]IES-& ALL ?+S -POS$ ( !M2 =
EXAMPLE1 ! H1V5 Z A :OLE & XS "PS1
ANIMALS1 AG1 & PLANTS & _! "PS4
,0ATTRIBUTES & FUNC;NS ,I M1N ! MOVE;TS
( ^! &( ALL O!R ?+S 9 : !Y H P[] 9 !MVS
6CAUSE MOVE;T1 & AL _! ALT],NS &
RECIPROCAL TRANS=M,NS4 ,X IS OBVI\S1 !N1
T ! GRT] "P (! 9QUIRY 96NATURE 3C]NS
BODIES3 =A NATURAL SUB/.E IS EI A BODY
OR A ?+ : _C -E 96EXI/;E )\T BODY &
MAGNITUDE4 ,? APPE>S PLA9LY F AN
ANALYSIS (! "* ( NATURAL ?+S1 & EQU,Y F
AN 9SPEC;N (! 9/.ES ( 9QUIRY 96NATURE4
,S9CE1 !N1 WE H SPOK5 (! PRIM>Y ELE;T1 (
XS BODILY 3/ITU;N1 &( XS FREEDOM F
DE/RUC;N & G5],N1 X REMA9S 6SP1K (! O!R
TWO4 ,9 SP1K+ ( !M WE % 2 OBLIG$ AL
69QUIRE 96G5],N & DE/RUC;N4 ,= IF "! IS
G5],N ANY":1 X M/ 2 9 ^! ELE;TS & ?+S
-POS$ ( !M4
  ,? IS 9DE$ ! F/ "Q WE H 6ASK3 IS G5],N
A FACT OR N8 ,E>LI] SPECUL,N 0 AT V>I.E
BO? ) XF &)! VIEWS "H PUT =W>D Z 6! TRUE
ANSW] 6? "Q4 ,"S REMOV$ G5],N & DE/RUC;N
F ! _W ALT4 ,NO?+ T IS1 !Y SD1 IS G5]AT$
OR DE/ROY$1 & \R 3VIC;N 6! 3TR>Y IS AN
ILLU.N4 ,S MA9TA9$ ! S*OOL ( ,MELISSUS &
,P>M5IDES4 ,B H["E EXCELL5T _! !ORIES
MAY O!RWISE BE1 ANYH[ !Y _C 2 HELD 6SP1K
Z /UD5TS ( NATURE4 ,"! MAY 2 ?+S N
SUBJECT 6G5],N OR ANY K9D ( MOVE;T1 B IF
S !Y 2L;G 6ANO!R &A HI<] 9QUIRY ?AN !
/UDY ( NATURE4 ,!Y1 H["E1 _H NO IDEA (
ANY =M ( 2+ O!R ?AN ! SUB/.E ( ?+S
P]CVD2 & :5 !Y SAW1 :AT NO "O PREVI\SLY
_H SE51 T "! CD 2 NO K OR WISDOM )\T "S
S* UN*ANG+ 5TITIES1 !Y NATUR,Y TRANSF]R$
:AT 0 TRUE ( !M 6?+S P]CVD4 ,O!RS1 P]H
9T5;N,Y1 MA9TA9 PRECISELY ! 3TR>Y OP9ION
6?4 ,X HAS BE5 ASS]T$ T "EY?+ 9 ! _W 0
SUBJECT 6G5],N & NO?+ 0 UNG5]AT$1 B T AF
2+ G5]AT$ "S ?+S REMA9$ 9DE/RUCTI# :ILE
! RE/ 7 AG DE/ROY$4 ,? _H BE5 ASS]T$ 9 !
F/ 9/.E 0,HESIOD & 8 FOLL[]S1 B AFWS
\TSIDE 8 CIRCLE 0! E>LIE/ NATURAL
PHILOSOPH]S4 ,B :AT ^! ?9K]S MA9TA9$ 0 T
ALL ELSE HAS BE5 G5]AT$ &1 Z !Y SD1 ,8IS
FL[+ AWAY1 NO?+ HAV+ ANY SOLID;Y1 EXCEPT
"O S+LE ?+ : P]SI/S Z ! BASIS ( ALL ^!
TRANS=M,NS4 ,S WE MAY 9T]PRET ! /ATE;TS
( ,H]ACLITUS ( ,EPHESUS & _M O!RS4 ,& "S
SUBJECT ALL BODIES :AT"E 6G5],N1 0M1NS (
! -POSI;N & SEP>,N ( PLANES4
  ,4CUS.N (! O!R VIEWS MAY 2 PO/PON$4 ,B
? LA/ !ORY : -POSES E BODY ( PLANES IS1
Z ! MO/ SUP]FICIAL OBS]V,N %[S1 9 _M
RESPECTS 9 PLA9 3TRADIC;N ) MA!MATICS4
,X IS1 H["E1 WR;G 6REMOVE ! F.D,NS (A
SCI;E UN.S Y C REPLACE !M ) O!RS M
3V9C+4 ,&1 SECONDLY1 ! SAME !ORY :
-POSES SOLIDS ( PLANES CLE>LY -POSES
PLANES ( L9ES & L9ES ( PO9TS1 S T A "P (
A L9E NE$ N 2 A L9E4 ,? MATT] HAS BE5
ALR 3SID]$ 9 \R 4CUS.N ( MOVE;T1 ": WE H
%[N T AN 9DIVISI# L5G? IS IMPOSSI#4 ,B )
RESPECT 6NATURAL BODIES "! >E
IMPOSSIBILITIES 9VOLV$ 9 ! VIEW : ASS]TS
9DIVISI# L9ES1 : WE MAY BRIEFLY 3SID] AT
? PO9T4 ,=! IMPOSSI# 3SEQU;ES : RESULT F
? VIEW 9 ! MA!MATICAL SPH]E W REPRODUCE
!MVS :5 X IS APPLI$ 6PHYSICAL BODIES1 B
"! W 2 DI6ICULTIES 9 PHYSICS : >E N
PRES5T 9 MA!MATICS2 = MA!MATICS D1LS )
AN AB/RACT & PHYSICS )A M 3CRETE OBJECT4
,"! >E _M ATTRIBUTES NECESS>ILY PRES5T 9
PHYSICAL BODIES : >E NECESS>ILY EXCLUD$
09DIVISIBIL;Y2 ALL ATTRIBUTES1 9 FACT1 :
>E DIVISI#4 ,"! C 2 NO?+ DIVISI# 9 AN
9DIVISI# ?+1 B ! ATTRIBUTES ( BODIES >E
ALL DIVISI# 9 "O ( TWO WAYS4 ,!Y >E
DIVISI# 96K9DS1 Z COL\R IS DIVID$ 96:ITE
& BLACK1 & !Y >E DIVISI# P] A3ID5S :5 T
: HAS !M IS DIVISI#4 ,9 ? LATT] S5SE
ATTRIBUTES : >E SIMPLE >E N"E!.S
DIVISI#4 ,ATTRIBUTES ( ? K9D W S]VE1
"!=E1 6ILLU/RATE ! IMPOSSIBIL;Y (! VIEW4
,X IS IMPOSSI#1 IF TWO "PS (A ?+ H NO
WEI<T1 T ! TWO TGR %D H WEI<T4 ,B EI ALL
P]CEPTI# BODIES OR "S1 S* Z E>? & WAT]1
H WEI<T1 Z ^! ?9K]S WD !MVS ADMIT4 ,N[
IF ! PO9T HAS NO WEI<T1 CLE>LY ! L9ES H
N EI1 &1 IF !Y H N1 NEI H ! PLANES4
,"!=E NO BODY HAS WEI<T4 ,X IS1 FUR!R1
MANIFE/ T _! PO9T _C H WEI<T4 ,= :ILE A
H1VY ?+ MAY ALW 2 H1VI] ?AN "S?+ &A LI<T
?+ LI<T] ?AN "S?+1 A ?+ : IS H1VI] OR
LI<T] ?AN "S?+ NE$ N 2 XF H1VY OR LI<T1
J Z A L>GE ?+ IS L>G] ?AN O!RS1 B :AT IS
L>G] IS N ALW L>GE4 ,A ?+ :1 JUDG$
ABSOLUTELY1 IS SMALL MAY N"O ! LESS 2
L>G] ?AN O!R ?+S4 ,:AT"E1 !N1 IS H1VY &
AL H1VI] ?AN "S?+ ELSE1 M/ EXCE$ ? 0"S?+
: IS H1VY4 ,A H1VY ?+ "!=E IS ALW
DIVISI#4 ,B X IS -MON GR.D T A PO9T IS
9DIVISI#4 ,AG1 SUPPOSE T :AT IS H1VY OR
WEI<T IS A D5SE BODY1 & :AT IS LI<T R>E4
,D5SE DI6]S F R>E 9 3TA9+ M MATT] 9 !
SAME CUBIC >EA4 ,A PO9T1 !N1 IF X MAY 2
H1VY OR LI<T1 MAY 2 D5SE OR R>E4 ,B !
D5SE IS DIVISI# :ILE A PO9T IS 9DIVISI#4
,& IF :AT IS H1VY M/ 2 EI H>D OR S(T1 AN
IMPOSSI# 3SEQU;E IS EASY 6DRAW4 ,=A ?+
IS S(T IF XS SURFACE C 2 PRESS$ IN1 H>D
IF X _C2 & IF X C 2 PRESS$ 9 X IS
DIVISI#4
  ,MOREOV]1 NO WEI<T C 3SI/ ( "PS N
POSSESS+ WEI<T4 ,= H[1 EXCEPT 0! M]E/
FIC;N1 C !Y SPECIFY ! NUMB] & "* (! "PS
: W PRODUCE WEI<T8 ,&1 FUR!R1 :5 "O
WEI<T IS GRT] ?AN ANO!R1 ! DI6];E IS A
?IRD WEI<T2 F : X W FOLL[ T E 9DIVISI#
"P POSSESSES WEI<T4 ,= SUPPOSE T A BODY
( F\R PO9TS POSSESSES WEI<T4 ,A BODY
-POS$ ( M ?AN F\R PO9TS W SUP]IOR 9
WEI<T 6X1 A ?+ : HAS WEI<T4 ,B ! DI6];E
2T WEI<T & WEI<T M/ 2 A WEI<T1 Z !
DI6];E 2T :ITE & :IT] IS :ITE4 ,"H !
DI6];E : MAKES ! SUP]IOR WEI<T H1VI] IS
! S+LE PO9T : REMA9S :5 ! -MON NUMB]1
F\R1 IS SUBTRACT$4 ,A S+LE PO9T1 "!=E1
HAS WEI<T4
  ,FUR!R1 6ASSUME1 ON ! "O H&1 T !
PLANES C ONLY 2 PUT 9 L9E> 3TACT WD 2
RIDICUL\S4 ,= J Z "! >E TWO WAYS ( PUTT+
L9ES TGR1 "NLY1 5D 6& SIDE 0SIDE1 S "!
M/ 2 TWO WAYS ( PUTT+ PLANES TGR4 ,L9ES
C 2 PUT TGR S T 3TACT IS L9E> 0LAY+ "O
AL;G ! O!R1 ?\< N 0PUTT+ !M 5D 65D4 ,B
IF1 SIMIL>LY1 9 PUTT+ ! LANES TGR1
SUP]FICIAL 3TACT IS ALL[$ Z AN
ALT]NATIVE 6L9E>1 T ME?OD W GIVE !M
BODIES : >E N ANY ELE;T NOR -POS$ (
ELE;TS4 ,AG1 IF X IS ! NUMB] ( PLANES 9
A BODY T MAKES "O H1VI] ?AN ANO!R1 Z !
,TIMAEUS EXPLA9S1 CLE>LY ! L9E &! PO9T W
H WEI<T4 ,=! ?REE CASES >E1 Z WE SD 2F1
ANALOG\S4 ,B IF ! R1SON ( DI6];ES (
WEI<T IS N ?1 B R ! H1VI;S ( E>? &!
LI<T;S ( FIRE1 !N "S (! PLANES W 2 LI<T
& O!RS H1VY 7: 9VOLVES A SIMIL> 4T9C;N 9
! L9ES &! PO9TS72 ! E>?PLANE1 ,I M1N1 W
2 H1VI] ?AN ! FIRE-PLANE4 ,9 G5]AL1 !
RESULT IS EI T "! IS NO MAGNITUDE AT
ALL1 OR T ALL MAGNITUDE CD 2 D"O AWAY )4
,=A PO9T IS 6A L9E Z A L9E IS 6A PLANE &
Z A PLANE IS 6A BODY4 ,N[ ! V>I\S =MS 9
PASS+ 96"O ANO!R W EA* 2 RESOLV$ 96XS
ULTIMATE 3/ITU5TS4 ,X MI<T HAPP5 "!=E T
NO?+ EXI/$ EXCEPT PO9TS1 & T "! 0 NO
BODY AT ALL4 ,A FUR!R 3SID],N IS T IF "T
IS SIMIL>LY 3/ITUT$1 "! WD BE1 OR MI<T
BE1 A "T AT : X 0 D"O AWAY )4 ,=!
9DIVISI# N[ IS L A PO9T 9 A L9E4 ,! SAME
3SEQU;ES FOLL[ F -POS+ ! H1V5 ( NUMB]S1
Z "S (! ,PY?AGOR1NS D :O MAKE ALL NATURE
\ ( NUMB]S4 ,= NATURAL BODIES >E
MANIFE/LY 5D[$ ) WEI<T & LI<T;S1 B AN
ASSEMBLAGE ( UNITS C NEI 2 -POS$ 6=M A
BODY NOR POSSESS WEI<T4
                   #B
  ,! NECESS;Y T EA* (! SIMPLE BODIES %D
H A NATURAL MOVE;T MAY 2 %[N Z FOLL[S4
,!Y MANIFE/LY MOVE1 & IF !Y H NO PROP]
MOVE;T !Y M/ MOVE 03/RA9T3 &! 3/RA9$ IS
! SAME Z ! UNNATURAL4 ,N[ AN UNNATURAL
MOVE;T PRESUPPOSES A NATURAL MOVE;T : X
3TRAV5ES1 & :1 H["E _M ! UNNATURAL
MOVE;TS1 IS ALW "O4 ,= NATUR,Y A ?+
MOVES 9 "O WAY1 :ILE XS UNNATURAL
MOVE;TS >E MANIFOLD4 ,! SAME MAY 2 %[N1
F ! FACT ( RE/4 ,RE/1 AL1 M/ EI 2 3/RA9$
OR NATURAL1 3/RA9$ 9 A PLACE 6: MOVE;T 0
3/RA9$1 NATURAL 9 A PLACE MOVE;T 6: 0
NATURAL4 ,N[ MANIFE/LY "! IS A BODY : IS
AT RE/ AT ! C5TRE4 ,IF !N ? RE/ IS
NATURAL 6X1 CLE>LY MO;N 6? PLACE IS
NATURAL 6X4 ,IF1 ON ! O!R H&1 XS RE/ IS
3/RA9$1 :AT IS H9D]+ XS MO;N8 ,"S?+1 :
IS AT RE/3 B IF S1 WE % SIMPLY REP1T !
SAME >GU;T2 & EI WE % -E 6AN ULTIMATE
"S?+ 6: RE/ ": X IS OR WE % H AN 9F9ITE
PROCESS1 : IS IMPOSSI#4 ,! H9DR.E 6XS
MOVE;T1 !N1 WE W SUPPOSE1 IS A MOV+ ?+-Z
,EMP$OCLES SAYS T X IS ! VORTEX : KEEPS
! E>? /-3 B 9 T CASE WE ASK1 ": WD X H
MOV$ 6B =! VORTEX8 ,X CD N MOVE
9F9ITELY2 = 6TRAV]SE AN 9F9ITE IS
IMPOSSI#1 & IMPOSSIBILITIES D N HAPP54
,S ! MOV+ ?+ M/ /OP "S":1 & "! RE/ N
03/RA9T B NATUR,Y4 ,B A NATURAL RE/
PROVES A NATURAL MOVE;T 6! PLACE ( RE/4
,H;E ,LEUCIPPUS & ,DEMOCRITUS1 :O SAY T
! PRIM>Y BODIES >E 9 P]PETUAL MOVE;T 9 !
VOID OR 9F9ITE1 MAY 2 ASK$ 6EXPLA9 !
MANN] ( _! MO;N &! K9D ( MOVE;T : IS
NATURAL 6!M4 ,= IF ! V>I\S ELE;TS >E
3/RA9$ 0"O ANO!R 6MOVE Z !Y D1 EA* M/ /
H A NATURAL MOVE;T : ! 3/RA9$ 3TRAV5ES1
&! PRIME MOV] M/ CAUSE MO;N N 03/RA9T B
NATUR,Y4 ,IF "! IS NO ULTIMATE NATURAL
CAUSE ( MOVE;T & EA* PREC$+ T]M 9 !
S]IES IS ALW MOV$ 03/RA9T1 WE % H AN
9F9ITE PROCESS4 ,! SAME DI6ICULTY IS
9VOLV$ EV5 IF X IS SUPPOS$1 Z WE R1D 9 !
,TIMAEUS1 T 2F ! ORD]$ _W 0 MADE !
ELE;TS MOV$ )\T ORD]4 ,_! MOVE;T M/ H
BE5 DUE EI 63/RA9T OR 6_! NATURE4 ,& IF
_! MOVE;T 0 NATURAL1 A MO;T'S 3SID],N
%[S T "! 0 ALR AN ORD]$ _W4 ,=! PRIME
MOV] M/ CAUSE MO;N 9 VIRTUE ( XS [N
NATURAL MOVE;T1 &! O!R BODIES1 MOV+ )\T
3/RA9T1 Z !Y CAME 6RE/ 9 _! PROP]
PLACES1 WD FALL 96! ORD] 9 : !Y N[ /&1 !
H1VY BODIES MOV+ T[>DS ! C5TRE &! LI<T
BODIES AWAY F X4 ,B T IS ! ORD] ( _!
4TRIBU;N 9 \R _W4 ,"! IS A FUR!R "Q1
TOO1 : MI<T 2 ASK$4 ,IS X POSSI# OR
IMPOSSI# T BODIES 9 UNORD]$ MOVE;T %D
-B9E 9 "S CASES 96-B9,NS L ^? ( : BODIES
( NATURE'S -POS+ >E -POS$1 S*1 ,I M1N1 Z
B"OS & FLE%8 ,YET ? IS :AT ,EMP$OCLES
ASS]TS 6H O3URR$ "U ,LOVE4 ,8,_M A
H1D0'1 SAYS HE1 ,8CAME 6BIR? )\T A
NECK40' ,! ANSW] 6! VIEW T "! >E 9F9ITE
BODIES MOV+ 9 AN 9F9ITE IS T1 IF ! CAUSE
( MOVE;T IS S+LE1 !Y M/ MOVE )A S+LE
MO;N1 & "!=E N )\T ORD]2 & IF1 ON ! O!R
H&1 ! CAUSES >E ( 9F9ITE V>IETY1 _!
MO;NS TOO M/ 2 9F9ITELY V>I$4 ,=A F9ITE
NUMB] ( CAUSES WD PRODUCE A K9D ( ORD]1
S9CE ABS;E ( ORD] IS N PROV$ 0DIV]S;Y (
DIREC;N 9 MO;NS3 9DE$1 9 ! _W WE "K1 N
ALL BODIES1 B ONLY BODIES (! SAME K9D1 H
A -MON GOAL ( MOVE;T4 ,AG1 4ORD]LY
MOVE;T M1NS 9 R1L;Y UNNATURAL MOVE;T1
S9CE ! ORD] PROP] 6P]CEPTI# ?+S IS _!
NATURE4 ,& "! IS AL ABSURD;Y &
IMPOSSIBIL;Y 9 ! NO;N T ! 4ORD]LY MOVE;T
IS 9F9ITELY 3T9U$4 ,=! NATURE ( ?+S IS !
NATURE : MO/ ( !M POSSESS = MO/ (! "T4
,?US _! VIEW BR+S !M 96! 3TR>Y POSI;N T
4ORD] IS NATURAL1 & ORD] OR SY/EM
UNNATURAL4 ,B NO NATURAL FACT C ORIG9ATE
9 *.E4 ,? IS A PO9T : ,ANAXAGORAS SEEMS
6H ?OR\<LY GRASP$2 = HE />TS 8 COSMOGONY
F UNMOV$ ?+S4 ,! O!RS1 X IS TRUE1 MAKE
?+S COLLECT TGR "SH[ 2F !Y TRY 6PRODUCE
MO;N & SEP>,N4 ,B "! IS NO S5SE 9 />T+
G5],N F AN ORIG9AL /ATE 9 : BODIES >E
SEP>AT$ & 9 MOVE;T4 ,H;E ,EMP$OCLES 2G9S
AF ! PROCESS RUL$ 0,LOVE3 = HE CD N H
3/RUCT$ ! H1V5 0BUILD+ X UP \ ( BODIES 9
SEP>,N1 MAK+ !M 6-B9E 0! P[] ( ,LOVE1
S9CE \R _W HAS XS 3/ITU5T ELE;TS 9
SEP>,N1 & "!=E PRESUPPOSES A PREVI\S
/ATE ( UN;Y & -B9,N4
  ,^! >GU;TS MAKE X PLA9 T E BODY HAS XS
NATURAL MOVE;T1 : IS N 3/RA9$ OR 3TR>Y
6XS NATURE4 ,WE G ON 6%[ T "! >E C]TA9
BODIES ^: NEC IMPETUS IS T ( WEI<T &
LI<T;S4 ,( NECESS;Y1 WE ASS]T1 !Y M/
MOVE1 &A MOV$ ?+ : HAS NO NATURAL
IMPETUS _C MOVE EI T[>DS OR AWAY F !
C5TRE4 ,SUPPOSE A BODY ,A )\T WEI<T1 &A
BODY ;,B 5D[$ ) WEI<T4 ,SUPPOSE !
WEI<T.S BODY 6MOVE ! 4T.E ;,,CD1 :ILE
;,B 9 ! SAME "T MOVES ! 4T.E ,,CE1 : W 2
GRT] S9CE ! H1VY ?+ M/ MOVE FUR!R4 ,LET
! H1VY BODY !N 2 DIVID$ 9 ! PROPOR;N
,,CE3 ;,,CD 7= "! IS NO R1SON :Y A "P (
;,B %D N /& 9 ? REL,N 6! :OLE74 ,N[ IF !
:OLE MOVES ! :OLE 4T.E ,,CE1 ! "P M/ 9 !
SAME "T MOVE ! 4T.E ;,,CD4 ,A WEI<T.S
BODY1 "!=E1 & "O : HAS WEI<T W MOVE !
SAME 4T.E1 : IS IMPOSSI#4 ,&! SAME >GU;T
WD FIT ! CASE ( LI<T;S4 ,AG1 A BODY : IS
9 MO;N B HAS NEI WEI<T NOR LI<T;S1 M/ 2
MOV$ 03/RA9T1 & M/ 3T9UE XS 3/RA9$
MOVE;T 9F9ITELY4 ,= "! W 2 A =CE : MOVES
X1 &! SMALL] & LI<T] A BODY IS ! FUR!R W
A GIV5 =CE MOVE X4 ,N[ LET ;,A1 !
WEI<T.S BODY1 2 MOV$ ! 4T.E ,,CE1 & ;,B1
: HAS WEI<T1 2 MOV$ 9 ! SAME "T ! 4T.E
;,,CD4 ,DIVID+ ! H1VY BODY 9 ! PROPOR;N
,,CE3,,CD1 WE SUBTRACT F ! H1VY BODY A
"P : W 9 ! SAME "T MOVE ! 4T.E ,,CE1
S9CE ! :OLE MOV$ ;,,CD3 =! RELATIVE
SPE$S (! TWO BODIES W 2 9 9V]SE RATIO
6_! RESPECTIVE SIZES4 ,?US ! WEI<T.S
BODY W MOVE ! SAME 4T.E Z ! H1VY 9 !
SAME "T4 ,B ? IS IMPOSSI#4 ,H;E1 S9CE !
MO;N (! WEI<T.S BODY W COV] A GRT] 4T.E
?AN ANY T IS SU7E/$1 X W 3T9UE 9F9ITELY4
,X IS "!=E OBVI\S T E BODY M/ H A
DEF9ITE WEI<T OR LI<T;S4 ,B S9CE
,8NATURE0' M1NS A S\RCE ( MOVE;T )9 ! ?+
XF1 :ILE A =CE IS A S\RCE ( MOVE;T 9
"S?+ O!R ?AN X OR 9 XF QUA O!R1 & S9CE
MOVE;T IS ALW DUE EI 6NATURE OR 63/RA9T1
MOVE;T : IS NATURAL1 Z D[NW>D MOVE;T IS
6A /"O1 W 2 M]ELY A3EL]AT$ 0AN EXT]NAL
=CE1 :ILE AN UNNATURAL MOVE;T W 2 DUE 6!
=CE AL"O4 ,9 EI CASE ! AIR IS Z X 7
9/RU;TAL 6! =CE4 ,= AIR IS BO? LI<T &
H1VY1 & ?US QUA LI<T PRODUCES UPW>D
MO;N1 2+ PROPELL$ & SET 9 MO;N 0! =CE1 &
QUA H1VY PRODUCES A D[NW>D MO;N4 ,9 EI
CASE ! =CE TRANSMITS ! MOVE;T 6! BODY
0F/1 Z X W]E1 IMPREGNAT+ ! AIR4 ,T IS :Y
A BODY MOV$ 03/RA9T 3T9UES 6MOVE :5 T :
GAVE ! IMPULSE C1SES 6A3OMPANY X4
,O!RWISE1 I4E4 IF ! AIR 7 N 5D[$ ) ?
FUNC;N1 3/RA9$ MOVE;T WD 2 IMPOSSI#4 ,&!
NATURAL MOVE;T (A BODY MAY 2 HELP$ ON 9
! SAME WAY4 ,? 4CUS.N SU6ICES 6%[ 7#A7 T
ALL BODIES >E EI LI<T OR H1VY1 & 7#B7 H[
UNNATURAL MOVE;T TAKES PLACE4
  ,F :AT HAS BE5 SD E>LI] X IS PLA9 T "!
_C 2 G5],N EI ( "EY?+ OR 9 AN ABSOLUTE
S5SE ( ANY?+4 ,X IS IMPOSSI# T "EY?+ %D
2 G5]AT$1 UN.S AN EXTRA-CORPOR1L VOID IS
POSSI#4 ,=1 ASSUM+ G5],N1 ! PLACE : IS
6BE O3UPI$ 0T : IS -+ 6BE1 M/ H BE5
PREVI\SLY O3UPI$ 0VOID 9 : NO BODY WAS4
,N[ X IS Q POSSI# = "O BODY 6BE G5]AT$ \
( ANO!R1 AIR = 9/.E \ ( FIRE1 B 9 !
ABS;E ( ANY PRE-EXI/+ MASS G5],N IS
IMPOSSI#4 ,T : IS POT5TI,Y A C]TA9 K9D (
BODY MAY1 X IS TRUE1 2COME S* 9
ACTUAL;Y1 ,B IF ! POT5TIAL BODY 0 N ALR
9 ACTUAL;Y "S O!R K9D ( BODY1 ! EXI/;E (
AN EXTRA-CORPOR1L VOID M/ 2 ADMITT$4
                   #C
  ,X REMA9S 6SAY :AT BODIES >E SUBJECT
6G5],N1 & :Y4 ,S9CE 9 E CASE K DEP5DS ON
:AT IS PRIM>Y1 &! ELE;TS >E ! PRIM>Y
3/ITU5TS ( BODIES1 WE M/ ASK : ( S*
BODIES >E ELE;TS1 & :Y2 & AF T :AT IS _!
NUMB] & "*4 ,! ANSW] W 2 PLA9 IF WE F/
EXPLA9 :AT K9D ( SUB/.E AN ELE;T IS4 ,AN
ELE;T1 WE TAKE X1 IS A BODY 96: O!R
BODIES MAY 2 ANALYS$1 PRES5T 9 !M
POT5TI,Y OR 9 ACTUAL;Y 7: ( ^!1 IS /
4PUTA#71 & N XF DIVISI# 96BODIES DI6]5T
9 =M4 ,T1 OR "S?+ L X1 IS :AT ALL M5 9 E
CASE M1N 0ELE;T4 ,N[ IF :AT WE H
DESCRIB$ IS AN ELE;T1 CLE>LY "! M/ 2 S*
BODIES4 ,= FLE% & WOOD & ALL O!R SIMIL>
BODIES 3TA9 POT5TI,Y FIRE & E>?1 S9CE "O
SEES ^! ELE;TS EXUD$ F !M2 &1 ON ! O!R
H&1 NEI 9 POT5TIAL;Y NOR 9 ACTUAL;Y DOES
FIRE 3TA9 FLE% OR WOOD1 OR X WD EXUDE
!M4 ,SIMIL>LY1 EV5 IF "! 7 ONLY "O
ELE;T>Y BODY1 X WD N 3TA9 !M4 ,= ?\< X W
2 EI FLE% OR B"O OR "S?+ ELSE1 T DOES N
AT ONCE %[ T X 3TA9$ ^! 9 POT5TIAL;Y3 !
FUR!R "Q REMA9S1 9 :AT MANN] X 2COMES
!M4 ,N[ ,ANAXAGORAS OPPOSES ,EMP$OCLES'
VIEW (! ELE;TS4 ,EMP$OCLES SAYS T FIRE &
E>? &! RELAT$ BODIES >E ELE;T>Y BODIES (
: ALL ?+S >E -POS$2 B ? ,ANAXAGORAS
D5IES4 ,8 ELE;TS >E ! HOMOEOM]\S ?+S1
VIZ4 FLE%1 B"O1 &! L4 ,E>? & FIRE >E
MIXTURES1 -POS$ ( !M & ALL ! O!R SE$S1
EA* 3SI/+ (A COLLEC;N ( ALL ! HOMOEOM]\S
BODIES1 SEP>ATELY 9VISI#2 & T EXPLA9S :Y
F ^! TWO BODIES ALL O!RS >E G5]AT$4
7,6HM FIRE & AI!R >E ! SAME ?+47 ,B S9CE
E NATURAL BODY HAS X PROP] MOVE;T1 &
MOVE;TS >E EI SIMPLE OR MIX$1 MIX$ 9
MIX$ BODIES & SIMPLE 9 SIMPLE1 "! M/
OBVI\SLY 2 SIMPLE BODIES2 = "! >E SIMPLE
MOVE;TS4 ,X IS PLA91 !N1 T "! >E ELE;TS1
& :Y4
                   #D
  ,! NEXT "Q 63SID] IS :E!R ! ELE;TS >E
F9ITE OR 9F9ITE 9 NUMB]1 &1 IF F9ITE1
:AT _! NUMB] IS4 ,LET U F/ %[ R1SON OR
D5Y+ T _! NUMB] IS 9F9ITE1 Z "S SUPPOSE4
,WE 2G9 )! VIEW ( ,ANAXAGORAS T ALL !
HOMOEOM]\S BODIES >E ELE;TS4 ,ANY "O :O
ADOPTS ? VIEW MISAPPREH5DS ! M1N+ (
ELE;T4 ,OBS]V,N %[S T EV5 MIX$ BODIES >E
(T5 DIVISI# 96HOMOEOM]\S "PS2 EXAMPLES
>E FLE%1 B"O1 WOOD1 & /"O4 ,S9CE !N !
-POSITE _C 2 AN ELE;T1 N E HOMOEOM]\S
BODY C 2 AN ELE;T2 ONLY1 Z WE SD 2F1 T :
IS N DIVISI# 96BODIES DI6]5T 9 =M4 ,B
EV5 TAK+ ,8ELE;T0' Z !Y D1 !Y NE$ N
ASS]T AN 9F9;Y ( ELE;TS1 S9CE ! HYPO!SIS
(A F9ITE NUMB] W GIVE ID5TICAL RESULTS4
,9DE$ EV5 TWO OR ?REE S* BODIES S]VE !
PURPOSE Z WELL1 Z ,EMP$OCLES' ATTEMPT
%[S4 ,AG1 EV5 ON _! VIEW X TURNS \ T ALL
?+S >E N -POS$ ( HOMOCOM]\S BODIES4 ,!Y
D N PRET5D T A FACE IS -POS$ ( FACES1 OR
T ANY O!R NATURAL 3=M,N IS -POS$ ( "PS L
XF4 ,OBVI\SLY !N X WD 2 BETT] 6ASSUME A
F9ITE NUMB] ( PR9CIPLES4 ,!Y %D1 9 FACT1
2 Z FEW Z POSSI#1 3SI/5TLY ) PROV+ :AT
HAS 6BE PROV$4 ,? IS ! -MON DEM& (
MA!MATICIANS1 :O ALW ASSUME Z PR9CIPLES
?+S F9ITE EI 9 K9D OR 9 NUMB]4 ,AG1 IF
BODY IS 4T+UI%$ F BODY 0! APPROPRIATE
QUALITATIVE DI6];E1 & "! IS A LIMIT 6!
NUMB] ( DI6];ES 7=! DI6];E LIES 9
QUALITIES APPREH5D$ 0S5SE1 : >E 9 FACT
F9ITE 9 NUMB]1 ?\< ? REQUIRES PRO(71 !N
MANIFE/LY "! IS NECESS>ILY A LIMIT 6!
NUMB] ( ELE;TS4
  ,"! IS1 FUR!R1 ANO!R VIEW-T (
,LEUCIPPUS & ,DEMOCRITUS ( ,ABD]A-!
IMPLIC,NS ( : >E AL UNA3EPTA#4 ,! PRIM>Y
MASSES1 AC 6!M1 >E 9F9ITE 9 NUMB] &
9DIVISI# 9 MASS3 "O _C TURN 96_M NOR _M
96"O2 & ALL ?+S >E G5]AT$ 0_! -B9,N &
9VOLU;N4 ,N[ ? VIEW 9 A S5SE MAKES ?+S \
6BE NUMB]S OR -POS$ ( NUMB]S4 ,!
EXPOSI;N IS N CLE>1 B ? IS XS R1L M1N+4
,& FUR!R1 !Y SAY T S9CE ! ATOMIC BODIES
DI6] 9 %APE1 & "! IS AN 9F9;Y ( %APES1
"! IS AN 9F9;Y ( SIMPLE BODIES4 ,B !Y H
N"E EXPLA9$ 9 DETAIL ! %APES (! V>I\S
ELE;TS1 EXCEPT S F> 6ALLOT ! SPH]E
6FIRE4 ,AIR1 WAT]1 &! RE/ !Y 4T+UI%$ 0!
RELATIVE SIZE (! ATOM1 ASSUM+ T ! ATOMIC
SUB/.E 0 A SORT ( MA/]-SE$ = EA* & E
ELE;T4 ,N[1 9 ! F/ PLACE1 !Y MAKE !
MISTAKE ALR NOTIC$4 ,! PR9CIPLES : !Y
ASSUME >E N LIMIT$ 9 NUMB]1 ?\< S*
LIMIT,N WD NECESSITATE NO O!R ALT],N 9
_! !ORY4 ,FUR!R1 IF ! DI6];ES ( BODIES
>E N 9F9ITE1 PLA9LY ! ELE;TS W N 2 AN
9F9;Y4 ,2SS1 A VIEW : ASS]TS ATOMIC
BODIES M/ NE$S -E 963FLICT )! MA!MATICAL
SCI;ES1 9 A4I;N 69VALIDAT+ _M -MON
OP9IONS & APP>5T DATA ( S5SE P]CEP;N4 ,B
( ^! ?+S WE H ALR SPOK5 9 \R 4CUS.N ( "T
& MOVE;T4 ,!Y >E AL B.D 63TRADICT !MVS4
,= IF ! ELE;TS >E ATOMIC1 AIR1 E>?1 &
WAT] _C 2 DI6]5TIAT$ 0! RELATIVE SIZES (
_! ATOMS1 S9CE !N !Y CD N 2 G5]AT$ \ (
"O ANO!R4 ,! EXTRU.N (! L>GE/ ATOMS IS A
PROCESS T W 9 "T EXHAU/ ! SUPPLY2 & X IS
0S* A PROCESS T !Y A3.T =! G5],N ( WAT]1
AIR1 & E>? F "O ANO!R4 ,AG1 EV5 ON _! [N
PRESUPPOSI;NS X DOES N SEEM Z IF !
CLE;TS WD 2 9F9ITE 9 NUMB]4 ,! ATOMS
DI6] 9 FIGURE1 & ALL FIGURES >E -POS$ (
PYRAMIDS1 RECTIL9E> ! CASE ( RECTIL9E>
FIGURES1 :ILE ! SPH]E HAS EI<T PYRAMIDAL
"PS4 ,! FIGURES M/ H _! PR9CIPLES1 &1
:E!R ^! >E "O OR TWO OR M1 ! SIMPLE
BODIES M/ 2 ! SAME 9 NUMB] Z !Y4 ,AG1 IF
E ELE;T HAS XS PROP] MOVE;T1 &A SIMPLE
BODY HAS A SIMPLE MOVE;T1 &! NUMB] (
SIMPLE MOVE;TS IS N 9F9ITE1 2C ! SIMPLE
MO;NS >E ONLY TWO &! NUMB] ( PLACES IS N
9F9ITE1 ON ^! GR.DS AL WE %D H 6D5Y T !
NUMB] ( ELE;TS IS 9F9ITE4
                   #E
  ,S9CE ! NUMB] (! ELE;TS M/ 2 LIMIT$1 X
REMA9S 69QUIRE :E!R "! IS M ?AN "O
ELE;T4 ,"S ASSUME "O ONLY1 : IS AC 6"S
WAT]1 6O!RS AIR1 6O!RS FIRE1 6O!RS AG
"S?+ F9] ?AN WAT] & D5S] ?AN AIR1 AN
9F9ITE BODY-S !Y SAY-BRAC+ ALL ! H1V5S4
  ,N[ ^? :O DECIDE =A S+LE ELE;T1 : IS
EI WAT] OR AIR OR A BODY F9] ?AN WAT] &
D5S] ?AN AIR1 & PROCE$ 6G5]ATE O!R ?+S \
( X 0USE (! ATTRIBUTES D5S;Y & R>;Y1 ALL
ALIKE FAIL 6OBS]VE ! FACT T !Y >E
DEPRIV+ ! ELE;T ( XS PRIOR;Y4 ,G5],N \ (
! ELE;TS IS1 Z !Y SAY1 SYN!SIS1 & G5],N
96! ELE;TS IS ANALYSIS1 S T ! BODY )!
F9] "PS M/ H PRIOR;Y 9 ! ORD] ( NATURE4
,B !Y SAY T FIRE IS ( ALL BODIES ! F9E/4
,H;E FIRE W 2 F/ 9 ! NATURAL ORD]4 ,&
:E!R ! F9E/ BODY IS FIRE OR N MAKES NO
DI6];E2 ANYH[ X M/ 2 "O (! O!R BODIES T
IS PRIM>Y & N T : IS 9T]M$IATE4 ,AG1
D5S;Y & R>;Y1 Z 9/RU;TS ( G5],N1 >E
EQUIVAL5T 6F9E;S & CO>SE;S1 S9CE ! F9E
IS R>E1 & CO>SE 9 _! USE M1NS D5SE4 ,B
F9E;S & CO>SE;S1 AG1 >E EQUIVAL5T 6GRT;S
& SMALL;S1 S9CE A ?+ ) SMALL "PS IS F9E
&A ?+ ) L>GE "PS CO>SE4 ,= T : SPR1DS XF
\ WIDELY IS F9E1 &A ?+ -POS$ ( SMALL "PS
IS S SPR1D \4 ,9 ! 5D1 !N1 !Y 4T+UI% !
V>I\S O!R SUB/.ES F ! ELE;T 0! GRT;S &
SMALL;S ( _! "PS4 ,? ME?OD ( 4T9C;N
MAKES ALL JUDGE;T RELATIVE4 ,"! W 2 NO
ABSOLUTE 4T9C;N 2T FIRE1 WAT]1 & AIR1 B
"O &! SAME BODY W 2 RELATIVELY 6? FIRE1
RELATIVELY 6"S?+ ELSE AIR4 ,! SAME
DI6ICULTY IS 9VOLV$ EQU,Y 9 ! VIEW
ELE;TS & 4T+UI%ES !M 0_! GRT;S &
SMALL;S4 ,! PR9CIPLE ( 4T9C;N 2T BODIES
2+ QUANT;Y1 ! V>I\S SIZES W 2 9 A
DEF9ITE RATIO1 & :AT"E BODIES >E 9 ?
RATIO 6"O ANO!R M/ 2 AIR1 FIRE1 E>?1 &
WAT] RESPECTIVELY4 ,=! RATIOS ( SMALL]
BODIES MAY 2 REP1T$ AM;G GRT] BODIES4
  ,^? :O />T F FIRE Z ! S+LE ELE;T1 :ILE
AVOID+ ? DI6ICULTY1 9VOLVE !MVS 9 _M
O!RS4 ,"S ( !M GIVE FIRE A "PICUL> %APE1
L ^? :O MAKE X A PYRAMID1 & ? ON "O (
TWO GR.DS4 ,! R1SON GIV5 MAY BE-M
CRUDELY-T ! PYRAMID IS ! MO/ PI]C+ (
FIGURES Z FIRE IS ( BODIES1 OR-M
9G5I\SLY-! POSI;N MAY 2 SUPPORT$ 0!
FOLL[+ >GU;T4 ,Z ALL BODIES >E -POS$ ( T
: HAS ! F9E/ "PS1 S ALL SOLID FIGURES >E
-POS$ ( PRYAMIDS3 B ! F9E/ BODY IS FIRE1
:ILE AM;G FIGURES ! PYRAMID IS PRIM>Y &
HAS ! SMALLE/ "PS2 &! PRIM>Y BODY M/ H !
PRIM>Y FIGURE3 "!=E FIRE W 2 A PYRAMID4
,O!RS1 AG1 EXPRESS NO OP9ION ON !
SUBJECT ( XS FIGURE1 B SIMPLY REG>D X Z
! (! F9E/ "PS1 : 9 -B9,N W =M O!R
BODIES1 Z ! FUS+ ( GOLD-DU/ PRODUCES
SOLID GOLD4 ,BO? ( ^! VIEWS 9VOLVE !
SAME DI6ICULTIES4 ,= 7#A7 IF1 ON ! "O
H&1 !Y MAKE ! PRIM>Y BODY AN ATOM1 !
VIEW W 2 OP5 6! OBJEC;NS ALR ADV.ED AG/
! ATOMIC !ORY4 ,& FUR!R ! !ORY IS
9CONSI/5T )A REG>D =! FACTS ( NATURE4 ,=
IF ALL BODIES >E QUANTITATIVELY
-M5SURA#1 &! RELATIVE SIZE (! V>I\S
HOMOEOM]\S MASSES &( _! S"EAL ELE;TS >E
9 ! SAME RATIO1 S T ! TOTAL MASS ( WAT]1
= 9/.E1 IS RELAT$ 6! TOTAL MASS ( AIR Z
! ELE;TS ( EA* >E 6"O ANO!R1 & S ON1 &
IF "! IS M AIR ?AN WAT] &1 G5],Y1 M (!
F9] BODY ?AN (! CO>S]1 OBVI\SLY ! ELE;T
( WAT] W 2 SMALL] ?AN T ( AIR4 ,B !
LESS] QUANT;Y IS 3TA9$ 9 ! GRT]4 ,"!=E !
AIR ELE;T IS DIVISI#4 ,&! SAME CD 2 %[N
( FIRE &( ALL BODIES ^: "PS >E
RELATIVELY F9E4 7#B7 ,IF1 ON ! O!R H&1 !
PRIM>Y BODY IS DIVISI#1 !N 7A7 ^? :O
GIVE FIRE A SPECIAL %APE W H 6SAY T A "P
( FIRE IS N FIRE1 2C A PYRAMID IS N
-POS$ ( PYRAMIDS1 & AL T N E BODY IS EI
AN ELE;T OR -POS$ ( ELE;TS1 S9CE A "P (
FIRE W 2 NEI FIRE NOR ANY O!R ELE;T4 ,&
7B7 ^? ^: GR.D ( 4T9C;N IS SIZE W H
6RECOGNIZE AN ELE;T PRIOR 6! ELE;T1 A
REGRESS : 3T9UES 9F9ITELY1 S9CE E BODY
IS DIVISI# & T : HAS ! SMALLE/ "PS IS !
ELE;T4 ,FUR!R1 !Y TOO W H 6SAY T ! SAME
BODY IS RELATIVELY 6? FIRE & RELATIVELY
6T AIR1 6O!RS AG WAT] & E>?4
  ,! -MON ]ROR ( ALL VIEWS : ASSUME A
S+LE ELE;T IS T !Y ALL[ ONLY "O NATURAL
MOVE;T1 : IS ! SAME = E BODY4 ,= X IS A
MATT] ( OBS]V,N T A NATURAL BODY
POSSESSES A PR9CIPLE ( MOVE;T4 ,IF !N
ALL BODIES >E "O1 ALL W H "O MOVE;T4 ,)
? MO;N ! GRT] _! QUANT;Y ! M !Y W MOVE1
J Z FIRE1 9 PROPOR;N Z XS QUANT;Y IS
GRT]1 MOVES FA/] )! UPW>D MO;N : 2L;GS
6X4 ,B ! FACT IS T 9CR1SE ( QUANT;Y
MAKES _M ?+S MOVE ! FA/] D[NW>D4 ,= ^!
R1SONS1 !N1 Z WELL Z F ! 4T9C;N ALR
E/ABLI%$ (A PLURAL;Y ( NATURAL MOVE;TS1
X IS IMPOSSI# T "! %D 2 ONLY "O ELE;T4
,B IF ! ELE;TS >E N AN 9F9;Y & N REDUCI#
6"O1 !Y M/ 2 S"EAL & F9ITE 9 NUMB]4
                   #F
  ,F/ WE M/ 9QUIRE :E!R ! ELE;TS >E
ET]NAL OR SUBJECT 6G5],N & DE/RUC;N2 =
:5 ? "Q HAS BE5 ANSW]$ _! NUMB] & "* W 2
MANIFE/4 ,9 ! F/ PLACE1 !Y _C 2 ET]NAL4
,X IS A MATT] ( OBS]V,N T FIRE1 WAT]1 &
E SIMPLE BODY "UGO A PROCESS ( ANALYSIS1
: M/ EI 3T9UE 9F9ITELY OR /OP "S":4 7#A7
,SUPPOSE X 9F9ITE4 ,!N ! "T O3UPI$ 0!
PROCESS W 2 9F9ITE1 & AL T O3UPI$ 0!
REV]SE PROCESS ( SYN!SIS4 ,=! PROCESSES
( ANALYSIS & SYN!SIS SU3E$ "O ANO!R 9 !
V>I\S "PS4 ,X W FOLL[ T "! >E TWO 9F9ITE
"TS : >E MUTU,Y EXCLUSIVE1 ! "T O3UPI$
0! SYN!SIS1 : IS 9F9ITE1 2+ PREC$$ 0!
P]IOD ( ANALYSIS4 ,"! >E ?US TWO MUTU,Y
EXCLUSIVE 9F9ITES1 : IS IMPOSSI#4 7#B7
,SUPPOSE1 ON ! O!R H&1 T ! ANALYSIS /OPS
"S":4 ,!N ! BODY AT : X /OPS W 2 EI
ATOMIC OR1 Z ,EMP$OCLES SEEMS 6H 9T5D$1
A DIVISI# BODY : W YET N"E 2 DIVID$4 ,!
=EGO+ >GU;TS %[ T X _C 2 AN ATOM2 B NEI
C X 2 A DIVISI# BODY : ANALYSIS W N"E
R1*4 ,=A SMALL] BODY IS M EASILY DE/ROY$
?AN A L>G]2 &A DE/RUCTIVE PROCESS :
SU3E$S 9 DE/ROY+1 T IS1 9 RESOLV+
96SMALL] BODIES1 A BODY ( "S SIZE1 _C
R1SONABLY 2 EXPECT$ 6FAIL )! SMALL]
BODY4 ,N[ 9 FIRE WE OBS]VE A DE/RUC;N (
TWO K9DS3 X IS DE/ROY$ 0XS 3TR>Y :5 X IS
QU5*$1 & 0XF :5 X DIES \4 ,B ! E6ECT IS
PRODUC$ 0A GRT] QUANT;Y ^U A LESS]1 &! M
QKLY ! SMALL] X IS4 ,! ELE;TS ( BODIES
M/ "!=E 2 SUBJECT 6DE/RUC;N & G5],N4
  ,S9CE !Y >E G5]AT$1 !Y M/ 2 G5]AT$ EI
F "S?+ 9CORPOR1L OR F A BODY1 & IF F A
BODY1 EI F "O ANO!R OR F "S?+ ELSE4 ,!
!ORY : G5]ATES !M F "S?+ 9CORPOR1L
REQUIRES AN EXTRA-CORPOR1L VOID4 ,=
"EY?+ T -ES 6BE -ES 6BE 9 "S?+1 & T 9 :
! G5],N TAKES PLACE M/ EI 2 9CORPOR1L OR
POSSESS BODY2 & IF X HAS BODY1 "! W 2
TWO BODIES 9 ! SAME PLACE AT ! SAME "T1
VIZ4 T : IS -+ 6BE & T : 0 PREVI\SLY "!1
:ILE IF X IS 9CORPOR1L1 "! M/ 2 AN
EXTRA-CORPOR1L VOID4 ,B WE H ALR %[N T ?
IS IMPOSSI#4 ,B1 ON ! O!R H&1 X IS EQU,Y
IMPOSSI# T ! ELE;TS %D 2 G5]AT$ F "S K9D
( BODY4 ,T WD 9VOLVE A BODY 4T9CT F !
ELE;TS & PRIOR 6!M4 ,B IF ? BODY
POSSESSES WEI<T OR LI<T;S1 X W 2 "O (!
ELE;TS2 & IF X HAS NO T5D5CY 6MOVE;T1 X
W 2 AN IMMOVA# OR MA!MATICAL 5T;Y1 &
"!=E N 9 A PLACE AT ALL4 ,A PLACE 9 : A
?+ IS AT RE/ IS A PLACE 9 : X MI<T MOVE1
EI 03/RA9T1 I4E4 UNNATUR,Y1 OR 9 ! ABS;E
( 3/RA9T1 I4E4 NATUR,Y4 ,IF1 !N1 X IS 9
A PLACE & "S":1 X W 2 "O (! ELE;TS2 & IF
X IS N 9 A PLACE1 NO?+ C -E F X1 S9CE T
: -ES 962+ & T \ ( : X -ES M/ NE$S 2
TGR4 ,! ELE;TS "!=E _C 2 G5]AT$ F "S?+
9CORPOR1L NOR F A BODY : IS N AN ELE;T1
&! ONLY REMA9+ ALT]NATIVE IS T !Y >E
G5]AT$ F "O ANO!R4
                   #G
  ,WE M/1 "!=E1 TURN 6! "Q1 :AT IS !
MANN] ( _! G5],N F "O ANO!R8 ,IS X Z
,EMP$OCLES & ,DEMOCRITUS SAY1 OR Z ^? :O
RESOLVE BODIES 96PLANES SAY1 OR IS "!
YET ANO!R POSSIBIL;Y8 7#A7 ,:AT !
FOLL[]S ( ,EMP$OCLES D1 ?\< )\T OBS]V+ X
!MVS1 IS 6REDUCE ! G5],N ( ELE;TS \ ( "O
ANO!R 6AN ILLU.N4 ,!Y MAKE X A PROCESS (
EXCRE;N F A BODY ( :AT 0 9 X ALL ! "T-Z
?\< G5],N REQUIR$ A VESSEL R ?AN A
MAT]IAL-S T X 9VOLVES NO *ANGE ( ANY?+4
,& EV5 IF ? 7 A3EPT$1 "! >E O!R
IMPLIC,NS EQU,Y UNSATISFACTORY4 ,WE D N
EXPECT A MASS ( MATT] 6BE MADE H1VI]
0-PRES.N4 ,B !Y W 2 B.D 6MA9TA9 ?1 IF !Y
SAY T WAT] IS A BODY PRES5T 9 AIR &
EXCRET$ F AIR1 S9CE AIR 2COMES H1VI] :5
X TURNS 96WAT]4 ,AG1 :5 ! MIX$ BODY IS
DIVID$1 !Y C %[ NO R1SON :Y "O (!
3/ITU5TS M/ 0XF TAKE UP M ROOM ?AN !
BODY DID3 B :5 WAT] TURNS 96AIR1 ! ROOM
O3UPI$ IS 9CR1S$4 ,! FACT IS T ! F9]
BODY TAKES UP M ROOM1 Z IS OBVI\S 9 ANY
CASE ( TRANS=M,N4 ,Z ! LIQUID IS 3V]T$
96VAP\R OR AIR ! VESSEL : 3TA9S X IS (T5
BUR/ 2C X DOES N 3TA9 ROOM 5\<4 ,N[1 IF
"! IS NO VOID AT ALL1 & IF1 Z ^? :O TAKE
? VIEW SAY1 "! IS NO EXPAN.N ( BODIES1 !
IMPOSSIBIL;Y ( ? IS MANIFE/3 & IF "! IS
VOID & EXPAN.N1 "! IS NO A3.T+ =! FACT T
! BODY : RESULTS F DIVI.N CFPIES (
NECESS;Y A GRT] SPACE4 ,X IS 9EVITA#1
TOO1 T G5],N ( "O \ ( ANO!R %D -E 6A
/OP1 S9CE A F9ITE QUANTUM _C 3TA9 AN
9F9;Y ( F9ITE QUANTA4 ,:5 E>? PRODUCES
WAT] "S?+ IS TAK5 AWAY F ! E>?1 =!
PROCESS IS "O ( EXCRE;N4 ,! SAME ?+
HAPP5S AG :5 ! RESIDUE PRODUCES WAT]4 ,B
? C ONLY G ON = "E1 IF ! F9ITE BODY
3TA9S AN 9F9;Y1 : IS IMPOSSI#4 ,"!=E !
G5],N ( ELE;TS \ ( "O ANO!R W N ALW
3T9UE4
  7#B7 ,WE H N[ EXPLA9$ T ! MUTUAL
TRANS=M,NS (! ELE;TS _C TAKE PLACE 0M1NS
( EXCRE;N4 ,! REMA9+ ALT]NATIVE IS T !Y
%D 2 G5]AT$ 0*ANG+ 96"O ANO!R4 ,& ? 9 "O
( TWO WAYS1 EI 0*ANGE ( %APE1 Z ! SAME
WAX TAKES ! %APE BO? (A SPH]E &(A CUBE1
OR1 Z "S ASS]T1 0RESOLU;N 96PLANES4 7A7
,G5],N 0*ANGE ( %APE WD NECESS>ILY
9VOLVE ! ASS];N ( ATOMIC BODIES4 ,= IF !
"PICLES 7 DIVISI# "! WD 2 A "P ( FIRE :
0 N FIRE &A "P ( E>? : 0 N E>?1 =! R1SON
T N E "P (A PYRAMID IS A PYRAMID NOR (A
CUBE A CUBE4 ,B IF 7B7 ! PROCESS IS
RESOLU;N 96PLANES1 ! F/ DI6ICULTY IS T !
ELE;TS _C ALL 2 G5]AT$ \ ( "O ANO!R4 ,?
!Y >E OBLIG$ 6ASS]T1 & D ASS]T4 ,X IS
ABSURD1 2C X IS UNR1SONA# T "O ELE;T
AL"O %D H NO "P 9 ! TRANS=M,NS1 & AL
3TR>Y 6! OBS]V$ DATA ( S5SE1 AC 6: ALL
ALIKE *ANGE 96"O ANO!R4 ,9 FACT _!
EXPLAN,N (! OBS]V,NS IS N 3SI/5T )!
OBS]V,NS4 ,&! R1SON IS T _! ULTIMATE
PR9CIPLES >E WR;GLY ASSUM$3 !Y _H C]TA9
PREDET]M9$ VIEWS1 & 7 RESOLV$ 6BR+ "EY?+
96L9E ) !M4 ,X SEEMS T P]CEPTI# ?+S
REQUIRE P]CEPTI# PR9CIPLES1 ET]NAL ?+S
ET]NAL PR9CIPLES1 CORRUPTI# ?+S
CORRUPTI# PR9CIPLES2 &1 9 G5]AL1 E
SUBJECT MATT] PR9CIPLES HOMOG5E\S ) XF4
,B !Y1 [+ 6_! LOVE = _! PR9CIPLES1 FALL
96! ATTITUDE ( M5 :O "UTAKE ! DEF;E (A
POSI;N 9 >GU;T4 ,9 ! 3FID;E T !
PR9CIPLES >E TRUE !Y >E R1DY 6A3EPT ANY
3SEQU;E ( _! APPLIC,N4 ,Z ?\< "S
PR9CIPLES DID N REQUIRE 6BE JUDG$ F _!
RESULTS1 & "PICUL>LY F _! F9AL ISSUE6 ,&
T ISSUE1 : 9 ! CASE ( PRODUCTIVE K IS !
PRODUCT1 9 ! K ( NATURE IS ! UNIMP1*A#
EVID;E (! S5SES Z 6EA* FACT4
  ,! RESULT ( _! VIEW IS T E>? HAS ! BE/
"R 6! "N ELE;T1 & IS AL"O 9DE/RUCTI#2 =
T : IS 9DISSOLU# IS 9DE/RUCTI# &
ELE;T>Y1 & E>? AL"O _C 2 4SOLV$ 96ANY
BODY B XF4 ,AG1 9 ! CASE ( ^? ELE;TS : D
SU6] 4SOLU;N1 ! ,8SUSP5.N0' (! TRIANGLES
IS UNSATISFACTORY4 ,B ? TAKES PLACE :5"E
"O IS 4SOLV$ 96ANO!R1 2C (! NUM]ICAL
9EQUAL;Y (! TRIANGLES : -POSE !M4
,FUR!R1 ^? :O HOLD ^! VIEWS M/ NE$S
SUPPOSE T G5],N DOES N />T F A BODY4 ,=
:AT IS G5]AT$ \ ( PLANES _C 2 SD 6H BE5
G5]AT$ F A BODY4 ,& !Y M/ AL ASS]T T N
ALL BODIES >E DIVISI#1 -+ ?US 963FLICT )
\R MO/ A3URATE SCI;ES1 "NLY !
MA!MATICAL1 : ASSUME T EV5 ! 9TELLIGI#
IS DIVISI#1 :ILE !Y1 9 _! ANXIETY 6SAVE
_! HYPO!SIS1 _C EV5 ADMIT ? ( E P]CEPTI#
?+4 ,= ANY "O :O GIVES EA* ELE;T A %APE
( XS [N1 & MAKES ? ! GR.D ( 4T9C;N 2T !
SUB/.ES1 HAS 6ATTRIBUTE 6!M
9DIVISIBIL;Y2 S9CE DIVI.N (A PYRAMID OR
A SPH]E M/ L1VE "S": AT L1/ A RESIDUE :
IS N SPH]E OR A PYRAMID4 ,EI1 !N1 A "P (
FIRE IS N FIRE1 S T "! IS A BODY PRIOR
6! ELE;T-= E BODY IS EI AN ELE;T OR
-POS$ ( ELE;TS-OR N E BODY IS DIVISI#4
                   #H
  ,9 G5]AL1 ! ATTEMPT 6GIVE A %APE 6EA*
(! SIMPLE BODIES IS UNS.D1 =! R1SON1 F/1
T !Y W N SU3E$ 9 FILL+ ! :OLE4 ,X IS
AGRE$ T "! >E ONLY ?REE PLANE FIGURES :
C FILL A SPACE1 ! TRIANGLE1 ! SQU>E1 &!
HEXAGON1 & ONLY TWO SOLIDS1 ! PYRAMID &!
CUBE4 ,B ! !ORY NE$S M ?AN ^! 2C !
ELE;TS : X RECOGNIZES >E M 9 NUMB]4
,SECONDLY1 X IS MANIFE/ T ! SIMPLE
BODIES >E (T5 GIV5 A %APE 0! PLACE 9 :
!Y >E 9CLUD$1 "PICUL>LY WAT] & AIR4 ,9
S* A CASE ! %APE (! ELE;T _C P]SI/2 =1
IF X DID1 ! 3TA9$ MASS WD N 2 9 3T9U\S
3TACT )! 3TA9+ BODY2 :ILE1 IF XS %APE IS
*ANG$1 X W C1SE 6BE WAT]1 S9CE !
4T9CTIVE QUAL;Y IS %APE4 ,CLE>LY1 !N1 _!
%APES >E N FIX$4 ,9DE$1 NATURE XF SEEMS
6(F] CORROBOR,N ( ? !ORETICAL 3CLU.N4 ,J
Z 9 O!R CASES ! SUB/RATUM M/ 2 =M.S &
UN%AP5-= ?US ! ,8ALL-RECEPTIVE0'1 Z WE
R1D 9 ! ,TIMAEUS1 W 2 BE/ = MODELL+-S !
ELE;TS %D 2 3CVD Z A MAT]IAL = -POSITE
?+S2 & T IS :Y !Y C PUT (F _!
QUALITATIVE 4T9C;NS & PASS 96"O ANO!R4
,FUR!R1 H[ C !Y A3.T =! G5],N ( FLE% &
B"O OR ANY O!R 3T9U\S BODY8 ,! ELE;TS
AL"O _C PRODUCE !M 2C _! COLLOC,N _C
PRODUCE A 3T9UUM4 ,NOR C ! -POSI;N (
PLANES2 = ? PRODUCES ! ELE;TS !MVS1 N
BODIES MADE UP ( !M4 ,ANY "O !N :O 9SI/S
^U AN EXACT /ATE;T ( ? K9D ( !ORY1 9/1D
( ASS5T+ AF A PASS+ GL.E AT X1 W SEE T X
REMOVES G5],N F ! _W4
  ,FUR!R1 ! V PROP]TIES1 P[]S1 & MO;NS1
6: !Y PD "PICUL> ATT5;N 9 ALLOTT+ %APES1
%[ ! %APES N 6BE 9 A3ORD )! BODIES4 ,2C
FIRE IS MOBILE & PRODUCTIVE ( H1T &
-BUS;N1 "S MADE X A SPH]E1 O!RS A
PYRAMID4 ,^! %APES1 !Y ?"\1 7 ! MO/
MOBILE 2C !Y (F] ! FEWE/ PO9TS ( 3TACT &
>E ! L1/ /A# ( ANY2 !Y 7 AL ! MO/ APT
6PRODUCE W>M? & -BUS;N1 2C ! "O IS
ANGUL> "?\T :ILE ! O!R HAS ! MO/ ACUTE
ANGLES1 &! ANGLES1 !Y SAY1 PRODUCE W>M?
& -BUS;N4 ,N[1 9 ! F/ PLACE1 ) REG>D
6MOVE;T BO? >E 9 ]ROR4 ,^! MAY 2 !
FIGURES BE/ ADAPT$ 6MOVE;T2 !Y >E N1
H["E1 WELL ADAPT$ 6! MOVE;T ( FIRE1 : IS
AN UPW>D & RECTIL9E> MOVE;T1 B R 6T =M (
CIRCUL> MOVE;T : WE CALL ROLL+4 ,E>?1
AG1 !Y CALL A CUBE 2C X IS /A# & AT RE/4
,B X RE/S ONLY 9 XS [N PLACE1 N ANY":2 F
ANY O!R X MOVES IF NO?+ H9D]S1 & FIRE &!
O!R BODIES D ! SAME4 ,! OBVI\S 9F];E1
"!=E1 IS T FIRE & EA* S"EAL ELE;T IS 9 A
=EIGN PLACE A SPH]E OR A PYRAMID1 B 9 XS
[N A CUBE4 ,AG1 IF ! POSSES.N ( ANGLES
MAKES A BODY PRODUCE H1T & -BUS;N1 E
ELE;T PRODUCES H1T1 ?\< "O MAY D S M ?AN
ANO!R4 ,= !Y ALL POSSESS ANGLES1 !
OCTAH$RON & DODECAH$RON Z WELL Z !
PYRAMID2 & ,DEMOCRITUS MAKES EV5 ! SPH]E
A K9D ( ANGLE1 : CUTS ?+S 2C ( XS
MOBIL;Y4 ,! DI6];E1 !N1 W 2 "O ( DEGREE3
& ? IS PLA9LY FALSE4 ,!Y M/ AL A3EPT !
9F];E T ! MA!MATICAL PRODUCE H1T &
-BUS;N1 S9CE !Y TOO POSSESS ANGLES &
3TA9 ATOMIC SPH]ES & PYRAMIDS1 ESPECI,Y
IF "! >E1 Z !Y ALLEGE1 ATOMIC FIGURES4
,ANYH[ IF ^! FUNC;NS 2L;G 6"S ( ^! ?+S &
N 6O!RS1 !Y %D EXPLA9 ! DI6];E1 9/1D (
SP1K+ 9 Q G5]AL T]MS Z !Y D4 ,AG1 -BUS;N
(A BODY PRODUCES FIRE1 & FIRE IS A SPH]E
OR A PYRAMID4 ,! BODY1 !N1 IS TURN$
96SPH]ES OR PYRAMIDS4 ,LET U GRANT T ^!
FIGURES MAY R1SONABLY 2 SUPPOS$ 6CUT &
BR1K UP BODIES Z FIRE DOES2 / X REMA9S Q
9EXPLICA# T A PYRAMID M/ NE$S PRODUCE
PYRAMIDS OR A SPH]E SPH]ES4 ,"O MI<T Z
WELL PO/ULATE T A KNIFE OR A SAW DIVIDES
?+S 96KNIVES OR SAWS4 ,X IS AL RIDICUL\S
6?9K ONLY ( DIVI.N :5 ALLOTT+ FIRE XS
%APE4 ,FIRE IS G5],Y ?"\ ( Z -B9+ &
3NECT+ R ?AN Z SEP>AT+4 ,= ?\< X
SEP>ATES BODIES DI6]5T 9 K9D1 X -B9ES ^?
: >E ! SAME2 &! -B9+ IS ESS5TIAL 6X1 !
FUNC;NS ( 3NECT+ & UNIT+ 2+ A M>K (
FIRE1 :ILE ! SEP>AT+ IS 9CID5TAL4 ,=!
EXPUL.N (! =EIGN BODY IS AN 9CID5T 9 !
-PACT+ (! HOMOG5E\S4 ,9 *OOS+ ! %APE1
!N1 !Y %D H ?"\ EI ( BO? FUNC;NS OR
PREF]ABLY (! -B9+ FUNC;N4 ,9 A4I;N1 S9CE
HOT & COLD >E 3TR>Y P[]S1 X IS IMPOSSI#
6ALLOT ANY %APE 6! COLD4 ,=! %APE GIV5
M/ 2 ! 3TR>Y ( T GIV5 6! HOT1 B "! IS NO
3TR>IETY 2T FIGURES4 ,T IS :Y !Y H ALL
LEFT ! COLD \1 ?\< PROP]LY EI ALL OR N"O
%D H _! 4T+UI%+ FIGURES4 ,"S ( !M1 H["E1
D ATTEMPT 6EXPLA9 ? P[]1 & !Y 3TRADICT
!MVS4 ,A BODY ( L>GE "PICLES1 !Y SAY1 IS
COLD 2C 9/1D ( P5ETRAT+ "? ! PASSAGES X
CRU%ES4 ,CLE>LY1 !N1 T : IS HOT IS T :
P5ETRATES ^! PASSAGES1 OR 9 O!R ^WS T :
HAS F9E "PICLES4 ,X RESULTS T HOT & COLD
>E 4T+UI%$ N 0! FIGURE B 0! SIZE (!
"PICLES4 ,AG1 IF ! PYRAMIDS >E UNEQUAL 9
SIZE1 ! L>GE "OS W N 2 FIRE1 & T FIGURE
W PRODUCE N -BUS;N B XS 3TR>Y4
  ,F :AT HAS BE5 SD X IS CLE> T ! DI6];E
(! ELE;TS DOES N DEP5D ^U _! %APE4 ,N[
_! MO/ IMPORTANT DI6];ES >E ^? (
PROP]TY1 FUNC;N1 & P[]2 = E NATURAL BODY
HAS1 WE MA9TA91 XS [N FUNC;NS1
PROP]TIES1 & P[]S4 ,\R F/ BUSI;S1 !N1 W
2 6SP1K ( ^!1 & T 9QUIRY W 5A# U 6EXPLA9
! DI6];ES ( EA* F EA*4
               ,BOOK ,,IV
                   #A
  ,,WE H N[ 63SID] ! T]MS ,8H1VY0' &
,8LI<T0'4 ,WE M/ ASK :AT ! BODIES S
CALL$ >E1 H[ !Y >E 3/ITUT$1 & :AT IS !
R1SON ( _! POSSESS+ ^! P[]S4 ,! 3SID],N
( ^! "QS IS A PROP] "P (! !ORY ( MOVE;T1
S9CE WE CALL ?+S H1VY & LI<T 2C !Y H !
P[] ( 2+ MOV$ NATUR,Y 9 A C]TA9 WAY4 ,!
ACTIVITIES CORRESPOND+ 6^! P[]S H N BE5
GIV5 ANY "N1 UN.S X IS ?"\ T ,8IMPETUS0'
IS S* A "N4 ,B 2C ! 9QUIRY 96NATURE IS
3C]N$ ) MOVE;T1 & ^! ?+S H 9 !MVS "S
SP>K 7Z X W]E7 ( MOVE;T1 ALL 9QUIR]S
AVAIL !MVS ( ^! P[]S1 ?\< 9 ALL B A FEW
CASES )\T EXACT 4CRIM9,N4 ,WE M/ !N F/
LOOK AT :AT"E O!RS H SD1 & =MULATE ! "QS
: REQUIRE SETTLE;T 9 ! 9T]E/S ( ?
9QUIRY1 2F WE G ON 6/ATE \R [N VIEW (!
MATT]4
  ,LANGUAGE RECOGNIZES 7A7 AN ABSOLUTE1
7B7 A RELATIVE H1VY & LI<T4 ,( TWO H1VY
?+S1 S* Z WOOD & BRONZE1 WE SAY T ! "O
IS RELATIVELY LI<T1 ! O!R RELATIVELY
H1VY4 ,\R PR$ECESSORS H N D1LT AT ALL )!
ABSOLUTE USE1 (! T]MS1 B ONLY )!
RELATIVE4 ,I M1N1 !Y D N EXPLA9 :AT !
H1VY IS OR :AT ! LI<T IS1 B ONLY !
RELATIVE H1VI;S & LI<T;S ( ?+S POSSESS+
WEI<T4 ,? C 2 MADE CLE>] Z FOLL[S4 ,"!
>E ?+S ^: 3/ANT NATURE X IS 6MOVE AWAY F
! C5TRE1 :ILE O!RS MOVE 3/ANTLY T[>DS !
C5TRE2 &( ^! MOVE;TS T : IS AWAY F !
C5TRE ,I CALL UPW>D MOVE;T & T : IS
T[>DS X ,I CALL D[NW>D MOVE;T4 7,! VIEW1
URG$ 0"S1 T "! IS NO UP & NO D[N 9 !
H1V51 IS ABSURD4 ,"! C BE1 !Y SAY1 NO UP
& NO D[N1 S9CE ! UNIV]SE IS SIMIL> E
WAY1 & F ANY PO9T ON ! E>?'S SURFACE A
MAN 0ADVANC+ F> 5 W -E 6/& FOOT 6FOOT )
HMF4 ,B ! EXTREM;Y (! :OLE1 : WE CALL
,8ABV0'1 IS 9 POSI;N ABV & 9 NATURE
PRIM>Y4 ,& S9CE ! UNIV]SE HAS AN
EXTREM;Y &A C5TRE1 X M/ CLE>LY H AN UP &
D[N4 ,-MON USAGE IS ?US CORRECT1 ?\<
9ADEQUATE4 ,&! R1SON ( XS 9ADEQUACY IS T
M5 ?9K T ! UNIV]SE IS N SIMIL> E WAY4
,!Y RECOGNIZE ONLY ! HEMISPH]E : IS OV]
U4 ,B IF !Y W5T ON 6?9K (! _W Z =M$ ON ?
PATT]N ALL R.D1 )A C5TRE ID5TIC,Y RELAT$
6EA* PO9T ON ! EXTREM;Y1 !Y WD H 6ADMIT
T ! EXTREM;Y 0 ABV &! C5TRE 2L47
,0ABSOLUTELY LI<T1 !N1 WE M1N T : MOVES
UPW>D OR 6! EXTREM;Y1 & 0ABSOLUTELY H1VY
T : MOVES D[NW>D OR 6! C5TRE4 ,0LI<T] OR
RELATIVELY LI<T WE M1N T "O1 ( TWO
BODIES 5D[$ ) WEI<T & EQUAL 9 BULK1 : IS
EXCE$$ 0! O!R 9 ! SPE$ ( XS NATURAL
D[NW>D MOVE;T4
                   #B
  ,^? ( \R PR$ECESSORS :O H 5T]$ ^U ?
9QUIRY H =! MO/ "P SPOK5 ( LI<T & H1VY
?+S ONLY 9 ! S5SE 9 : "O ( TWO ?+S BO?
5D[$ ) WEI<T IS SD 6BE ! LI<T]4 ,& ?
TR1T;T !Y 3SID] A SU6ICI5T ANALYSIS AL (
! NO;NS ( ABSOLUTE H1VI;S1 6: _! A3.T
DOES N APPLY4 ,?1 H["E1 W 2COME CLE>] Z
WE ADV.E4 ,"O USE (! T]MS ,8LI<T]0' &
,8H1VI]0' IS T : IS SET =? 9 WRIT+ 9 !
,TIMAEUS1 T ! BODY : IS -POS$ (! GRT]
NUMB] ( ID5TICAL "PS IS RELATIVELY H1VY1
:ILE T : IS -POS$ (A SMALL] NUMB] IS
RELATIVELY LI<T4 ,Z A L>G] QUANT;Y ( L1D
OR ( BRONZE IS H1VI] ?AN A SMALL]-& ?
HOLDS GD ( ALL HOMOG5E\S MASSES1 !
SUP]IOR WEI<T ALW DEP5D+ ^U A NUM]ICAL
SUP]IOR;Y ( EQUAL "PS-IN PRECISELY !
SAME WAY1 !Y ASS]T1 L1D IS H1VI] ?AN
WOOD4 ,= ALL BODIES1 9 SPITE (! G5]AL
OP9ION 6! 3TR>Y1 >E -POS$ ( ID5TICAL "PS
&(A S+LE MAT]IAL4 ,B ? ANALYSIS SAYS
NO?+ (! ABSOLUTELY H1VY & LI<T4 ,! FACTS
>E T FIRE IS ALW LI<T & MOVES UPW>D1
:ILE E>? & ALL E>?Y ?+S MOVE D[NW>DS OR
T[>DS ! C5TRE4 ,X _C !N 2 ! FEW;S (!
TRIANGLES 7( :1 9 _! VIEW1 ALL ^! BODIES
>E -POS$7 : 4POSES FIRE 6MOVE UPW>D4 ,IF
X W]E1 ! GRT] ! QUANT;Y ( FIRE ! SL[] X
WD MOVE1 [+ 6! 9CR1SE ( WEI<T DUE 6!
9CR1S$ NUMB] ( TRIANGLES4 ,B ! PALPA#
FACT1 ON ! 3TR>Y1 IS T ! GRT] ! QUANT;Y1
! LI<T] ! MASS IS &! QK] XS UPW>D
MOVE;T3 &1 SIMIL>LY1 9 ! REV]SE MOVE;T F
ABV D[NW>D1 ! SMALL MASS W MOVE QK] &!
L>GE SL[]4 ,FUR!R1 S9CE 6BE LI<T] IS 6H
FEW] ( ^! HOMOG5E\S "PS & 6BE H1VI] IS
6H M1 & AIR1 WAT]1 & FIRE >E -POS$ (!
SAME TRIANGLES1 ! ONLY DI6];E 2+ 9 !
NUMB] ( S* "PS1 : M/ "!=E EXPLA9 ANY
4T9C;N ( RELATIVELY LI<T & H1VY 2T ^!
BODIES1 X FOLL[S T "! M/ 2 A C]TA9
QUANTUM ( AIR : IS H1VI] ?AN WAT]4 ,B !
FACTS >E DIRECTLY OPPOS$ 6?4 ,! L>G] !
QUANT;Y ( AIR ! M R1DILY X MOVES UPW>D1
& ANY POR;N ( AIR )\T EXCEP;N W RISE UP
\ (! WAT]4
  ,S M* = "O VIEW (! 4T9C;N 2T LI<T &
H1VY4 ,6O!RS ! ANALYSIS SEEMS 9SU6ICI5T2
& _! VIEWS ON ! SUBJECT1 ?\< !Y 2L;G 6AN
OLD] G5],N ?AN \RS1 H AN AIR ( NOVELTY4
,X IS APP>5T T "! >E BODIES :1 :5 SMALL]
9 BULK ?AN O!RS1 YET EXCE$ !M 9 WEI<T4
,X IS "!=E OBVI\SLY 9SU6ICI5T 6SAY T
BODIES ( EQUAL WEI<T >E -POS$ ( AN EQUAL
NUMB] ( PRIM>Y "PS3 = T WD GIVE EQUAL;Y
( BULK4 ,^? :O MA9TA9 T ! PRIM>Y OR
ATOMIC "PS1 ( : BODIES 5D[$ ) WEI<T >E
-POS$1 >E PLANES1 _C S SP1K )\T
ABSURD;Y2 B ^? :O REG>D !M Z SOLIDS >E 9
A BETT] POSI;N 6ASS]T T ( S* BODIES !
L>G] IS ! H1VI]4 ,B S9CE 9 -POSITE
BODIES ! WEI<T OBVI\SLY DOES N
CORRESPOND 9 ? WAY 6! BULK1 ! LESS] BULK
2+ (T5 SUP]IOR 9 WEI<T 7Z1 = 9/.E1 IF "O
2 WOOL &! O!R BRONZE71 "! >E "S :O ?9K &
SAY T ! CAUSE IS 6BE F.D ELSE":4 ,!
VOID1 !Y SAY1 : IS IMPRISON$ 9 BODIES1
LI<T5S !M & "S"TS MAKES ! L>G] BODY !
LI<T]4 ,! R1SON IS T "! IS M VOID4 ,& ?
WD AL A3.T =! FACT T A BODY -POS$ (A
NUMB] ( SOLID "PS EQUAL TO1 OR EV5
SMALL] ?AN1 T ( ANO!R IS "S"TS L>G] 9
BULK ?AN X4 ,9 %ORT1 G5],Y & 9 E CASE A
BODY IS RELATIVELY LI<T :5 X 3TA9S A
RELATIVELY L>GE AM.T ( VOID4 ,? IS ! WAY
!Y PUT X !MVS1 B _! A3.T REQUIRES AN
A4I;N4 ,RELATIVE LI<T;S M/ DEP5D N ONLY
ON AN EXCESS ( VOID1 B AL AN A DEFECT (
SOLID3 = IF ! RATIO ( SOLID 6VOID EXCE$S
A C]TA9 PROPOR;N1 ! RELATIVE LI<T;S W
4APPE>4 ,?US FIRE1 !Y SAY1 IS ! LI<TE/ (
?+S J = ? R1SON T X HAS ! MO/ VOID4 ,B X
WD FOLL[ T A L>GE MASS ( GOLD1 Z 3TA9+ M
VOID ?AN A SMALL MASS ( FIRE1 IS LI<T]
?AN X1 UN.S X AL 3TA9S _M "TS Z M*
SOLID4 ,! A4I;N IS "!=E NEC4
  ,( ^? :O D5Y ! EXI/;E (A VOID "S1 L
,ANAXAGORAS & ,EMP$OCLES1 H N TRI$
6ANALYSE ! NO;NS ( LI<T & H1VY AT ALL2 &
^? :O1 :ILE / D5Y+ ! EXI/;E (A VOID1 H
ATTEMPT$ ?1 H FAIL$ 6EXPLA9 :Y "! >E
BODIES : >E ABSOLUTELY H1VY & LI<T1 OR 9
O!R ^WS :Y "S MOVE UPW>D & O!RS D[NW>D4
,! FACT1 AG1 T ! BODY ( GRT] BULK IS
"S"TS LI<T] ?AN SMALL] BODIES IS "O : !Y
H PASS$ OV] 9 SIL;E1 & :AT !Y H SD GIVES
NO OBVI\S SU7ES;N = RECONCIL+ _! VIEWS )
! OBS]V$ FACTS4
  ,B ^? :O ATTRIBUTE ! LI<T;S ( FIRE 6XS
3TA9+ S M* VOID >E NECESS>ILY 9VOLV$ 9
PRACTIC,Y ! SAME DI6ICULTIES4 ,= ?\<
FIRE 2 SUPPOS$ 63TA9 LESS SOLID ?AN ANY
O!R BODY1 Z WELL Z M VOID1 YET "! W 2 A
C]TA9 QUANTUM ( FIRE 9 : ! AM.T ( SOLID
OR PL5UM IS 9 EXCESS (! SOLIDS 3TA9$ 9
"S SMALL QUANT;Y ( E>?4 ,!Y MAY REPLY T
"! IS AN EXCESS ( VOID AL4 ,B ! "Q IS1
H[ W !Y 4CRIM9ATE ! ABSOLUTELY H1VY8
,PRESUMABLY1 EI 0XS EXCESS ( SOLID OR
0XS DEFECT ( VOID4 ,ON ! =M] VIEW "! CD
2 AN AM.T ( E>? S SMALL Z 63TA9 LESS
SOLID ?AN A L>GE MASS ( FIRE4 ,&
SIMIL>LY1 IF ! 4T9C;N RE/S ON ! AM.T (
VOID1 "! W 2 A BODY1 LI<T] ?AN !
ABSOLUTELY LI<T1 : N"E!.S MOVES D[NW>D Z
3/ANTLY Z ! O!R MOVES UPW>D4 ,B T _C 2
S1 S9CE ! ABSOLUTELY LI<T IS ALW LI<T]
?AN BODIES : H WEI<T & MOVE D[NW>D1
:ILE1 ON ! O!R H&1 T : IS LI<T] NE$ N 2
LI<T1 2C 9 -MON SPEE* WE 4T+UI% A LI<T]
&A H1VI] 7VIZ4 WAT] & E>?7 AM;G BODIES
5D[$ ) WEI<T4 ,AG1 ! SU7ES;N (A C]TA9
RATIO 2T ! VOID &! SOLID 9 A BODY IS NO
M EQUAL 6SOLV+ ! PRO#M 2F U4 ,! MANN] (
SP1K+ W ISSUE 9 A SIMIL> IMPOSSIBIL;Y4
,= ANY TWO POR;NS ( FIRE1 SMALL OR GRT1
W EXHIBIT ! SAME RATIO ( SOLID 6VOID1 B
! UPW>D MOVE;T (! GRT] IS QK] ?AN T (!
LESS1 J Z ! D[NW>D MOVE;T (A MASS ( GOLD
OR L1D1 OR ( ANY O!R BODY 5D[$ ) WEI<T1
IS QK] 9 PROPOR;N 6XS SIZE4 ,?1 H["E1 %D
N 2 ! CASE IF ! RATIO IS ! GR.D ( 4T9C;N
2T H1VY ?+S & LI<T4 ,"! IS AL AN
ABSURD;Y 9 ATTRIBUT+ ! UPW>D MOVE;T (
BODIES 6A VOID : DOES N XF MOVE4 ,IF1
H["E1 X IS ! NATURE (A VOID 6MOVE UPW>D
&(A PL5UM 6MOVE D[NW>D1 & "!=E EA*
CAUSES A L MOVE;T 9 O!R ?+S1 "! 0 NO NE$
6RAISE ! "Q :Y -POSITE BODIES >E "S LI<T
& "S H1VY2 !Y _H ONLY 6EXPLA9 :Y ^! TWO
?+S >E !MVS LI<T & H1VY RESPECTIVELY1 &
6GIVE1 FUR!R1 ! R1SON :Y ! PL5UM &! VOID
>E N ET]N,Y SEP>AT$4 ,X IS AL UNR1SONA#
6IMAG9E A PLACE =! VOID1 Z IF ! VOID 7 N
XF A K9D ( PLACE4 ,B IF ! VOID IS 6MOVE1
X M/ H A PLACE \ ( : & 96: ! *ANGE
C>RIES X4 ,AL :AT IS ! CAUSE ( XS
MOVE;T8 ,N1 SURELY1 XS VOID;S3 = X IS N
! VOID ONLY : IS MOV$1 B AL ! SOLID4
  ,SIMIL> DI6ICULTIES >E 9VOLV$ 9 ALL
O!R ME?ODS ( 4T9C;N1 :E!R !Y A3.T =!
RELATIVE LI<T;S & H1VI;S ( BODIES
04T9C;NS ( SIZE1 OR PROCE$ ON ANY O!R
PR9CIPLE1 S L;G Z !Y ATTRIBUTE 6EA* !
SAME MATT]1 OR EV5 IF !Y RECOGNIZE M ?AN
"O MATT]1 S L;G Z T M1NS ONLY A PAIR (
3TR>IES4 ,IF "! IS A S+LE MATT]1 Z ) ^?
:O -POSE ?+S ( TRIANGLES1 NO?+ C 2
ABSOLUTELY H1VY OR LI<T3 & IF "! IS "O
MATT] & XS 3TR>Y-! VOID1 = 9/.E1 &!
PL5UM-NO R1SON C 2 GIV5 =! RELATIVE
LI<T;S & H1VI;S (! BODIES 9T]M$IATE 2T !
ABSOLUTELY LI<T & H1VY :5 -P>$ EI ) "O
ANO!R OR ) ^! !MVS4 ,! VIEW : BASES !
4T9C;N ^U DI6];ES ( SIZE IS M L A M]E
FIC;N ?AN ^? PREVI\SLY M5;N$1 B1 9 T X
IS A# 6MAKE 4T9C;NS 2T ! F\R ELE;TS1 X
IS 9 A /R;G] POSI;N = MEET+ ! =EGO+
DI6ICULTIES4 ,S9CE1 H["E1 X IMAG9ES T ^!
BODIES : DI6] 9 SIZE >E ALL MADE ( "O
SUB/.E1 X IMPLIES1 EQU,Y )! VIEW T "! IS
B "O MATT]1 T "! IS NO?+ ABSOLUTELY LI<T
& NO?+ : MOVES UPW>D 7EXCEPT Z 2+ PASS$
0O!R ?+S OR =C$ UP 0!M72 & S9CE A
MULTITUDE ( SMALL ATOMS >E H1VI] ?AN A
FEW L>GE "OS1 X W FOLL[ T M* AIR OR FIRE
IS H1VI] ?AN A LL WAT] OR E>?1 : IS
IMPOSSI#4

                   #C
  ,^!1 !N1 >E ! VIEWS : H BE5 ADV.ED
0O!RS &! T]MS 9 : !Y /ATE !M4 ,WE MAY
2G9 \R [N /ATE;T 0SETTL+ A "Q : 6"S HAS
BE5 ! MA9 DI6ICULTY-! "Q :Y "S BODIES
MOVE ALW & NATUR,Y UPW>D & O!RS D[NW>D1
:ILE O!RS AG MOVE BO? UPW>D & D[NW>D4
,AF T WE W 9QUIRE 96LI<T & H1VY &(!
V>I\S PH5OM5A 3NECT$ ) !M4 ,! LOCAL
MOVE;T ( EA* BODY 96XS [N PLACE M/ 2
REG>D$ Z SIMIL> 6:AT HAPP5S 9 3NEXION )
O!R =MS ( G5],N & *ANGE4 ,"! >E1 9 FACT1
?REE K9DS ( MOVE;T1 A6ECT+ RESPECTIVELY
! SIZE1 ! =M1 &! PLACE (A ?+1 & 9 EA* X
IS OBS]VA# T *ANGE PROCE$S F A 3TR>Y 6A
3TR>Y OR 6"S?+ 9T]M$IATE3 X IS N"E !
*ANGE ( ANY *.E SUBJECT 9 ANY *.E
DIREC;N1 NOR1 SIMIL>LY1 IS ! REL,N (!
MOV] 6XS OBJECT =TUIT\S3 ! ?+ ALT]$ IS
DI6]5T F ! ?+ 9CR1S$1 & PRECISELY ! SAME
DI6];E HOLDS 2T T : PRODUCES ALT],N & T
: PRODUCES 9CR1SE4 ,9 ! SAME MANN] X M/
2 ?"\ T PRODUCES LOCAL MO;N & T : IS S
MOV$ >E N =TUIT\SLY RELAT$4 ,N[1 T :
PRODUCES UPW>D & D[NW>D MOVE;T IS T :
PRODUCES WEI<T & LI<T;S1 & T : IS MOV$
IS T : IS POT5TI,Y H1VY OR LI<T1 &!
MOVE;T ( EA* BODY 6XS [N PLACE IS MO;N
T[>DS XS [N =M4 7,X IS BE/ 69T]PRET 9 ?
S5SE ! -MON /ATE;T (! OLD] WRIT]S T ,8L
MOVES 6L0'4 ,=! ^WS >E N 9 E S5SE TRUE
6FACT4 ,IF "O 7 6REMOVE ! E>? 6": ! MOON
N[ IS1 ! V>I\S FRAG;TS ( E>? WD EA* MOVE
N T[>DS X B 6! PLACE 9 : X N[ IS4 ,9
G5]AL1 :5 A NUMB] ( SIMIL> &
UNDI6]5TIAT$ BODIES >E MOV$ )! SAME MO;N
? RESULT IS NECESS>ILY PRODUC$1 VIZ4 T !
PLACE : IS ! NATURAL GOAL (! MOVE;T (
EA* S+LE "P IS AL T (! :OLE4 ,B S9CE !
PLACE (A ?+ IS ! B.D>Y ( T : 3TA9S X1 &!
3T95T ( ALL ?+S T MOVE UPW>D OR D[NW>D
IS ! EXTREM;Y &! C5TRE1 & ? B.D>Y -ES
6BE1 9 A S5SE1 ! =M ( T : IS 3TA9$1 X IS
6XS L T A BODY MOVES :5 X MOVES 6XS [N
PLACE4 ,=! SU3ESSIVE MEMB]S (! SCRIES >E
L "O ANO!R3 WAT]1 ,I M1N1 IS L AIR & AIR
L FIRE1 & 2T 9T]M$IATES ! REL,N MAY 2
3V]T$1 ?\< N 2T !M &! EXTREMES2 ?US AIR
IS L WAT]1 B WAT] IS L E>?3 =! REL,N (
EA* \T] BODY 6T : IS NEXT )9 X IS T ( =M
6MATT]47 ,?US 6ASK :Y FIRE MOVES UPW>D &
E>? D[NW>D IS ! SAME Z 6ASK :Y ! H1LA#1
:5 MOV$ & *ANG$ QUA H1LA#1 ATTA9S H1L? &
N :ITE;S2 & SIMIL> "QS MI<T 2 ASK$ 3C]N+
ANY O!R SUBJECT ( ALE;N4 ,( C\RSE !
SUBJECT ( 9CR1SE1 :5 *ANG$ QUA 9CR1SA#1
ATTA9S N H1L? B A SUP]IOR SIZE4 ,! SAME
APPLIES 9 ! O!R CASES4 ,"O ?+ *ANGES 9
QUAL;Y1 ANO!R 9 QUANT;Y3 & S 9 PLACE1 A
LI<T ?+ GOES UPW>D1 A H1VY ?+ D[NW>D4 ,!
ONLY DI6];E IS T 9 ! LA/ CASE1 VIZ4 T (!
H1VY &! LI<T1 ! BODIES >E ?"\ 6H A SPR+
( *ANGE )9 !MVS1 :ILE ! SUBJECTS ( H1L+
& 9CR1SE >E ?"\ 6BE MOV$ PURELY F )\T4
,"S"TS1 H["E1 EV5 !Y *ANGE ( !MVS1 IE4 9
RESPONSE 6A SLI<T EXT]NAL MOVE;T R1*
H1L? OR 9CR1SE1 Z ! CASE MAY BE4 ,& S9CE
! SAME ?+ : IS H1LA# IS AL RECEPTIVE (
41SE1 X DEP5DS ON :E!R X IS MOV$ QUA
H1LA# OR QUA LIA# 641SE :E!R ! MO;N IS
T[>DS H1L? OR T[>DS 41SE4 ,B ! R1SON :Y
! H1VY &! LI<T APPE> M ?AN ^! ?+S 63TA9
)9 !MVS ! S\RCE ( _! MOVE;TS IS T _!
MATT] IS NE>E/ 62+4 ,? IS 9DICAT$ 0!
FACT T LOCOMO;N 2L;GS 6BODIES ONLY :5
ISOLAT$ F O!R BODIES1 & IS G5]AT$ LA/ (!
S"EAL K9DS ( MOVE;T2 9 ORD] ( 2+ !N X W
2 F/4 ,N[ :5"E AIR -ES 962+ \ ( WAT]1
LI<T \ ( H1VY1 X GOES 6! UPP] PLACE4 ,X
IS =?) LI<T3 2COM+ IS AT AN 5D1 & 9 T
PLACE X HAS 2+4 ,OBVI\SLY1 !N1 X IS A
POT5TIAL;Y1 :1 9 XS PASSAGE 6ACTUAL;Y1
-ES 96T PLACE & QUANT;Y & QUAL;Y : 2L;G
6XS ACTUAL;Y4 ,&! SAME FACT EXPLA9S :Y
:AT IS ALR ACTU,Y FIRE OR E>? MOVES1 :5
NO?+ OB/RUCTS X1 T[>DS XS [N PLACE4 ,=
MO;N IS EQU,Y IMM 9 ! CASE ( NUTRI;T1 :5
NO?+ H9D]S1 & 9 ! CASE (! ?+ H1L$1 :5
NO?+ /AYS ! H1L+4 ,B ! MOVE;T IS AL DUE
6! ORIG9AL CR1TIVE =CE & 6T : REMOVES !
H9DR.E OR (F : ! MOV+ ?+ REB.D$1 Z 0
EXPLA9$ 9 \R OP5+ 4CUS.NS1 ": WE TRI$
6%[ H[ N"O ( ^! ?+S MOVES XF4 ,! R1SON (
! V>I\S MO;NS (! V>I\S BODIES1 &! M1N+ (
! MO;N (A BODY 6XS [N PLACE1 H N[ BE5
EXPLA9$4

                   #D
  ,WE H N[ 6SP1K (! 4T9CTIVE PROP]TIES (
^! BODIES &(! V>I\S PH5OM5A 3NECT$ ) !M4
,9 A3ORD.E ) G5]AL 3VIC;N WE MAY 4T+UI%
! ABSOLUTELY H1VY1 Z T : S9KS 6! BOTTOM
( ALL ?+S1 F ! ABSOLUTELY LI<T1 : IS T :
RISES 6! SURFACE ( ALL ?+S4 ,I USE ! T]M
,8ABSOLUTELY0'1 9 VIEW (! G5]IC "* (
,8LI<T0' & ,8H1VY0'1 9 ORD] 63F9E !
APPLIC,N 6BODIES : D N -B9E LI<T;S &
H1VI;S4 ,X IS APP>5T1 ,I M1N1 T FIRE1 9
:AT"E QUANT;Y1 S L;G Z "! IS NO EXT]NAL
OB/ACLE MOVES UPW>D1 & E>? D[NW>D2 &1 IF
! QUANT;Y IS 9CR1S$1 ! MOVE;T IS ! SAME1
?\< SWIFT]4 ,B ! H1VI;S & LI<T;S (
BODIES : -B9E ^! QUALITIES IS DI6]5T F
?1 S9CE :ILE !Y RISE 6! SURFACE ( "S
BODIES !Y S9K 6! BOTTOM ( O!RS4 ,S* >E
AIR & WAT]4 ,NEI ( !M IS ABSOLUTELY EI
LI<T OR H1VY4 ,BO? >E LI<T] ?AN E>?-=
ANY POR;N ( EI RISES 6! SURFACE ( X-B
H1VI] ?AN FIRE1 S9CE A POR;N ( EI1 :AT"E
XS QUANT;Y1 S9KS 6! BOTTOM ( FIRE2 -P>$
TGR1 H["E1 ! "O HAS ABSOLUTE WEI<T1 !
O!R ABSOLUTE LI<T;S1 S9CE AIR 9 ANY
QUANT;Y RISES 6! SURFACE ( WAT]1 :ILE
WAT] 9 ANY QUANT;Y S9KS 6! BOTTOM ( AIR4
,N[ O!R BODIES >E S"E,Y LI<T & H1VY1 &
EVID5TLY 9 !M ! ATTRIBUTES >E DUE 6!
DI6];E ( _! UNCOMP.D$ "PS3 T IS 6SAY1 AC
Z ! "O OR ! O!R HAPP5S 6PREPOND]ATE !
BODIES W 2 H1VY & LI<T RESPECTIVELY4
,"!=E WE NE$ ONLY SP1K ( ^! "PS1 S9CE !Y
>E PRIM>Y & ALL ELSE 3SEQU5TIAL3 & 9 S
DO+ WE % 2 FOLL[+ ! ADVICE : WE GAVE 6^?
^: ATTRIBUTE H1VI;S 6! PRES;E ( PL5UM &
LI<T;S 6T ( VOID4 ,X IS DUE 6! PROP]TIES
(! ELE;T>Y BODIES T A BODY : IS REG>D$ Z
LI<T 9 "O PLACE IS REG>D$ Z H1VY 9
ANO!R1 & VICE V]SA4 ,9 AIR1 = 9/.E1 A
TAL5T'S WEI<T ( WOOD IS H1VI] ?AN A M9A
( L1D1 B 9 WAT] ! WOOD IS ! LI<T]4 ,!
R1SON IS T ALL ! ELE;TS EXCEPT FIRE H
WEI<T & ALL B E>? LI<T;S4 ,E>?1 !N1 &
BODIES 9 : E>? PREPOND]ATES1 M/ NE$S H
WEI<T "EY":1 :ILE WAT] IS H1VY ANY": B 9
E>?1 & AIR IS H1VY :5 N 9 WAT] OR E>?4
,9 XS [N PLACE EA* ( ^! BODIES HAS WEI<T
EXCEPT FIRE1 EV5 AIR4 ,( ? WE H EVID;E 9
! FACT T A BLA4] :5 9FLAT$ WEI<S M ?AN
:5 EMPTY4 ,A BODY1 !N1 9 : AIR
PREPOND]ATES OV] E>? & WAT]1 MAY WELL 2
LI<T] ?AN "S?+ 9 WAT] & YET H1VI] ?AN X
9 AIR1 S9CE S* A BODY DOES N RISE 9 AIR
B RISES 6! SURFACE 9 WAT]4
  ,! FOLL[+ A3.T W MAKE X PLA9 T "! IS
AN ABSOLUTELY LI<T & AN ABSOLUTELY H1VY
BODY4 ,& 0ABSOLUTELY LI<T ,I M1N "O : (
XS [N NATURE ALW MOVES UPW>D1
0ABSOLUTELY H1VY "O : ( XS [N NATURE ALW
MOVES D[NW>D1 IF NO OB/ACLE IS 9 ! WAY4
,"! >E1 ,I SAY1 ^! TWO K9DS ( BODY1 & X
IS N ! CASE1 Z "S MA9TA91 T ALL BODIES H
WEI<T4 ,DI6]5T VIEWS >E 9 FACT AGRE$ T
"! IS A H1VY BODY1 : MOVES UNI=MLY T[>DS
! C5TRE4 ,B IS AL SIMIL>LY A LI<T BODY4
,= WE SEE ) \R EYES1 Z WE SD 2F1 T E>?Y
?+S S9K 6! BOTTOM ( ALL ?+S & MOVE T[>DS
! C5TRE4 ,B ! C5TRE IS A FIX$ PO9T4 ,IF
"!=E "! IS "S BODY : RISES 6! SURFACE (
ALL ?+S-& WE OBS]VE FIRE 6MOVE UPW>D EV5
9 AIR XF1 :ILE ! AIR REMA9S AT RE/-
CLE>LY ? BODY IS MOV+ T[>DS ! EXTREM;Y4
,X _C !N H ANY WEI<T4 ,IF X _H1 "! WD 2
ANO!R BODY 9 : X SANK3 & IF T _H WEI<T1
"! WD 2 YET ANO!R : MOV$ 6! EXTREM;Y &
?US ROSE 6! SURFACE ( ALL MOV+ ?+S4 ,9
FACT1 H["E1 WE H NO EVID;E ( S* A BODY4
,FIRE1 !N1 HAS NO WEI<T4 ,NEI HAS E>?
ANY LI<T;S1 S9CE X S9KS 6! BOTTOM ( ALL
?+S1 & T : S9KS MOVES 6! C5TRE4 ,T "! IS
A C5TRE T[>DS : ! MO;N ( H1VY ?+S1 &
AWAY F : T ( LI<T ?+S IS DIRECT$1 IS
MANIFE/ 9 _M WAYS4 ,F/1 2C NO MOVE;T C
3T9UE 69F9;Y4 ,= :AT _C 2 C NO M -E-TO-
BE ?AN BE1 & MOVE;T IS A -+ TO-BE 9 "O
PLACE F ANO!R4 ,SECONDLY1 L ! UPW>D
MOVE;T ( FIRE1 ! D[NW>D MOVE;T ( E>? &
ALL H1VY ?+S MAKES EQUAL ANGLES ON E
SIDE )! E>?'S SURFACE3 X M/ "!=E 2
DIRECT$ T[>DS ! C5TRE4 ,:E!R X IS RE,Y !
C5TRE (! E>? & N R T (! :OLE 6: X MOVES1
MAY 2 LEFT 6ANO!R 9QUIRY1 S9CE ^! >E
CO9CID5T4 ,B S9CE T : S9KS 6! BOTTOM (
ALL ?+S MOVES 6! C5TRE1 NECESS>ILY T :
RISES 6! SURFACE MOVES 6! EXTREM;Y (!
REGION 9 : ! MOVE;T ( ^! BODIES TAKES
PLACE4 ,=! C5TRE IS OPPOS$ Z 3TR>Y 6!
EXTREM;Y1 Z T : S9KS IS OPPOS$ 6T :
RISES 6! SURFACE4 ,? AL GIVES A R1SONA#
GR.D =! DUAL;Y ( H1VY & LI<T 9 ! SPATIAL
DUAL;Y C5TRE & EXTREM;Y4 ,N[ "! IS AL !
9T]M$IATE REGION 6: EA* "N IS GIV5 9
OPPOSI;N 6! O!R EXTREME4 ,= T : IS
9T]M$IATE 2T ! TWO IS 9 A S5SE BO?
EXTREM;Y & C5TRE4 ,= ? R1SON "! IS ANO!R
H1VY & LI<T2 "NLY1 WAT] & AIR4 ,B 9 \R
VIEW ! 3T95T P]TA9S 6=M &! 3TA9$ 6MATT]3
& ? 4T9C;N IS PRES5T 9 E G5US4 ,ALIKE 9
! SPH]E ( QUAL;Y & 9 T ( QUANT;Y "! IS T
: CORRESPONDS R 6=M & T : CORRESPONDS
6MATT]4 ,9 ! SAME WAY1 AM;G SPATIAL
4T9C;NS1 ! ABV 2L;GS 6! DET]M9ATE1 ! 2L
6MATT]4 ,! SAME HOLDS1 3SEQU5TLY1 AL (!
MATT] XF ( T : IS H1VY & LI<T3 Z
POT5TI,Y POSSESS+ ! "O "*1 X IS MATT] =!
H1VY1 & Z POT5TI,Y POSSESS+ ! O!R1 =!
LI<T4 ,X IS ! SAME MATT]1 B XS 2+ IS
DI6]5T1 Z T : IS RECEPTIVE ( 41SE IS !
SAME Z T : IS RECEPTIVE ( H1L?1 ?\< 9 2+
DI6]5T F X1 & "!=E 41S$;S IS DI6]5T F
H1L?I;S4

                   #E
  ,A ?+ !N : HAS ! "O K9D ( MATT] IS
LI<T & ALW MOVES UPW>D1 :ILE A ?+ : HAS
! OPPOSITE MATT] IS H1VY & ALW MOVES
D[NW>D4 ,BODIES -POS$ ( K9DS ( MATT]
DI6]5T F ^! B HAV+ RELATIVELY 6EA* O!R !
"* : ^! H ABSOLUTELY1 POSSESS BO? !
UPW>D &! D[NW>D MO;N4 ,H;E AIR & WAT]
EA* H BO? LI<T;S & WEI<T1 & WAT] S9KS 6!
BOTTOM ( ALL ?+S EXCEPT E>?1 :ILE AIR
RISES 6! SURFACE ( ALL ?+S EXCEPT FIRE4
,B S9CE "! IS "O BODY ONLY : RISES 6!
SURFACE ( ALL ?+S & "O ONLY : S9KS 6!
BOTTOM ( ALL ?+S1 "! M/ NE$S 2 TWO O!R
BODIES : S9K 9 "S BODIES & RISE 6!
SURFACE ( O!RS4 ,! K9DS ( MATT]1 !N1 M/
2 Z NUM]\S Z ^! BODIES1 I4E4 F\R1 B ?\<
!Y >E F\R "! M/ 2 A -MON MATT] ( ALL-
"PICUL>LY IF !Y PASS 96"O ANO!R-: 9 EA*
IS 9 2+ DI6]5T4 ,"! IS NO R1SON :Y "! %D
N 2 "O OR M 9T]M$IATES 2T ! 3TR>IES1 Z 9
! CASE ( COL\R2 = ,89T]M$IATE0' &
,8M1N0' >E CAPA# ( M ?AN "O APPLIC,N4
  ,N[ 9 XS [N PLACE E BODY 5D[$ ) BO?
WEI<T & LI<T;S HAS WEI<T":AS E>? HAS
WEI<T "EY":-B !Y ONLY H LI<T;S AM;G
BODIES 6^: SURFACE !Y RISE4 ,H;E :5 A
SUPPORT IS )DRAWN S* A BODY MOVES D[NW>D
UNTIL X R1*ES ! BODY NEXT 2L X1 AIR 6!
PLACE ( WAT] & WAT] 6T ( E>?4 ,B IF !
FIRE ABV AIR IS REMOV$1 X W N MOVE UPW>D
6! PLACE ( FIRE1 EXCEPT 03/RA9T2 & 9 T
WAY WAT] AL MAY 2 DRAWN UP1 :5 ! UPW>D
MOVE;T ( AIR : HAS _H A -MON SURFACE ) X
IS SWIFT 5 6OV]P[] ! D[NW>D IMPULSE (!
WAT]4 ,NOR DOES WAT] MOVE UPW>D 6! PLACE
( AIR1 EXCEPT 9 ! MANN] J DESCRIB$4 ,E>?
IS N S A6ECT$ AT ALL1 2C A -MON SURFACE
IS N POSSI# 6X4 ,H;E WAT] IS DRAWN UP
96! VESSEL 6: FIRE IS APPLI$1 B N E>?4
,Z E>? FAILS 6MOVE UPW>D1 S FIRE FAILS
6MOVE D[NW>D :5 AIR IS )DRAWN F 2N X3 =
FIRE HAS NO WEI<T EV5 9 XS [N PLACE1 Z
E>? HAS NO LI<T;S4 ,! O!R TWO MOVE
D[NW>D :5 ! BODY 2N IS )DRAWN 2C1 :ILE !
ABSOLUTELY H1VY IS T : S9KS 6! BOTTOM (
ALL ?+S1 ! RELATIVELY H1VY S9KS 6XS [N
PLACE OR 6! SURFACE (! BODY 9 : X RISES1
S9CE X IS SIMIL> 9 MATT] 6X4
  ,X IS PLA9 T "O M/ SUPPOSE Z _M 4T9CT
SPECIES ( MATT] Z "! >E BODIES4 ,= IF1
F/1 "! IS A S+LE MATT] ( ALL ?+S1 Z1 =
9/.E1 ! VOID OR ! PL5UM OR EXT5.N OR !
TRIANGLES1 EI ALL ?+S W MOVE UPW>D OR
ALL ?+S W MOVE D[NW>D1 &! SECOND MO;N W
2 ABOLI%$4 ,& S1 EI "! W 2 NO ABSOLUTELY
LI<T BODY1 IF SUP]IOR;Y ( WEI<T IS DUE
6SUP]IOR SIZE OR NUMB] (! 3/ITU5T BODIES
OR 6! FULL;S (! BODY3 B ! 3TR>Y IS A
MATT] ( OBS]V,N1 & X HAS BE5 %[N T !
D[NW>D & UPW>D MOVE;TS >E EQU,Y 3/ANT &
UNIV]SAL3 OR1 IF ! MATT] 9 "Q IS ! VOID
OR "S?+ SIMIL>1 : MOVES UNI=MLY UPW>D1
"! W 2 NO?+ 6MOVE UNI=MLY D[NW>D4
,FUR!R1 X W FOLL[ T ! 9T]M$IATE BODIES
MOVE D[NW>D 9 "S CASES QK] ?AN E>?3 =
AIR 9 SU6ICI5TLY L>GE QUANT;Y W 3TA9 A
L>G] NUMB] ( TRIANGLES OR SOLIDS OR
"PICLES4 ,X IS1 H["E1 MANIFE/ T NO POR;N
( AIR :AT"E MOVES D[NW>D4 ,&! SAME
R1SON+ APPLIES 6LI<T;S1 IF T IS SUPPOS$
6DEP5D ON SUP]IOR;Y ( QUANT;Y ( MATT]4
,B IF1 SECONDLY1 ! K9DS ( MATT] >E TWO1
X W 2 DI6ICULT 6MAKE ! 9T]M$IATE BODIES
2HAVE Z AIR & WAT] 2HAVE4 ,SUPPOSE1 =
EXAMPLE1 T ! TWO ASS]T$ >E VOID & PL5UM4
,FIRE1 !N1 Z MOV+ UPW>D1 W 2 VOID1 E>?1
Z MOV+ D[NW>D1 PL5UM2 & 9 AIR1 X W 2 SD1
FIRE PREPOND]ATES1 9 WAT]1 E>?4 ,"! W !N
2 A QUANT;Y ( WAT] 3TA9+ M FIRE ?AN A LL
AIR1 &A L>GE AM.T ( AIR W 3TA9 M E>? ?AN
A LL WAT]3 3SEQU5TLY WE % H 6SAY T AIR 9
A C]TA9 QUANT;Y MOVES D[NW>D M QKLY ?AN
A LL WAT]4 ,B S* A ?+ HAS N"E BE5 OBS]V$
ANY":4 ,NECESS>ILY1 !N1 Z FIRE GOES UP
2C X HAS "S?+1 E4G4 VOID1 : O!R ?+S D N
H1 & E>? GOES D[NW>D 2C X HAS PL5UM1 S
AIR GOES 6XS [N PLACE ABV WAT] 2C X HAS
"S?+ ELSE1 & WAT] GOES D[NW>D 2C ( "S
SPECIAL K9D ( BODY4 ,B IF ! TWO BODIES
>E "O MATT]1 OR TWO MATT]S BO? PRES5T 9
EA*1 "! W 2 A C]TA9 QUANT;Y ( EA* AT :
WAT] W EXCEL A LL AIR 9 ! UPW>D MOVE;T &
AIR EXCEL WAT] 9 ! D[NW>D MOVE;T1 Z WE H
ALR (T5 SD4

                   #F
  ,! %APE ( BODIES W N A3.T = _! MOV+
UPW>D OR D[NW>D 9 G5]AL1 ?\< X W A3.T =
_! MOV+ FA/] OR SL[]4 ,! R1SONS = ? >E N
DI6ICULT 6SEE4 ,=! PRO#M ?US RAIS$ IS :Y
A FLAT PIECE ( IRON OR L1D FLOATS ^U
WAT]1 :ILE SMALL] & LESS H1VY ?+S1 S L;G
Z !Y >E R.D OR L;G-A NE$LE1 = 9/.E-S9K
D[N2 & "S"TS A ?+ FLOATS 2C X IS SMALL1
Z ) GOLD DU/ &! V>I\S E>?Y & DU/Y
MAT]IALS : ?R;G ! AIR4 ,) REG>D 6^! "QS1
X IS WR;G 6A3EPT ! EXPLAN,N (F]$
0,DEMOCRITUS4 ,HE SAYS T ! W>M BODIES
MOV+ UP \ (! WAT] HOLD UP H1VY BODIES :
>E BROAD1 :ILE ! N>R[ "OS FALL "?1 2C !
BODIES : (F] ? RESI/.E >E N NUM]\S4 ,B ?
WD 2 EV5 M LIKELY 6HAPP5 9 AIR-AN
OBJEC;N : HE HMF RAISES4 ,8 REPLY 6!
OBJEC;N IS FEE#4 ,9 ! AIR1 HE SAYS1 !
,8DRIVE0' 7M1N+ 0DRIVE ! MOVE;T (! UPW>D
MOV+ BODIES7 IS N UNI=M 9 DIREC;N4 ,B
S9CE "S 3T9UA >E EASILY DIVID$ & O!RS
LESS EASILY1 & ?+S : PRODUCE DIVI.N DI6]
SIMIL>LY 9 ! CASE ) : !Y PRODUCE X1 !
EXPLAN,N M/ 2 F.D 9 ? FACT4 ,X IS !
EASILY B.D$1 9 PROPOR;N Z X IS EASILY
B.D$1 : IS EASILY DIVID$2 & AIR IS M S
?AN WAT]1 WAT] ?AN E>?4 ,FUR!R1 ! SMALL]
! QUANT;Y 9 EA* K9D1 ! M EASILY X IS
DIVID$ & 4RUPT$4 ,?US ! R1SON :Y BROAD
?+S KEEP _! PLACE IS 2C !Y COV] S WIDE A
SURFACE &! GRT] QUANT;Y IS LESS EASILY
4RUPT$4 ,BODIES (! OPPOSITE %APE S9K D[N
2C !Y O3UPY S LL (! SURFACE1 : IS "!=E
EASILY "P$4 ,& ^! 3SID],NS APPLY ) F>
GRT] =CE 6AIR1 S9CE X IS S M* M EASILY
DIVID$ ?AN WAT]4 ,B S9CE "! >E TWO
FACTORS1 ! =CE RESPONSI# =! D[NW>D MO;N
(! H1VY BODY &! 4RUP;N-RESI/+ =CE (!
3T9U\S SURFACE1 "! M/ 2 "S RATIO 2T !
TWO4 ,= 9 PROPOR;N Z ! =CE APPLI$ 0!
H1VY ?+ T[>DS 4RUP;N & DIVI.N EXCE$S T :
RESIDES 9 ! 3T9UUM1 ! QK] W X =CE XS WAY
D[N2 ONLY IF ! =CE (! H1VY ?+ IS ! W1K]1
W X RIDE ^U ! SURFACE4
  ,WE H N[ F9I%$ \R EXAM9,N (! H1VY &!
LI<T &(! PH5OM5A 3NECT$ ) !M4