              ,BOOK ,,III
                   #A
  ,WE M/1 )A VIEW 6! SCI;E : WE >E
SEEK+1 F/ REC.T ! SUBJECTS T %D 2 F/
4CUSS$4 ,^! 9CLUDE BO? ! O!R OP9IONS T
"S H HELD ON ! F/ PR9CIPLES1 & ANY PO9T
2SS ^! T HAPP5S 6H BE5 OV]LOOK$4 ,= ^?
:O WI% 6GET CLE> ( DI6ICULTIES X IS
ADVANTAGE\S 64CUSS ! DI6ICULTIES WELL2 =
! SUBSEQU5T FREE PLAY ( ?"\ IMPLIES !
SOLU;N (! PREVI\S DI6ICULTIES1 & X IS N
POSSI# 6UNTIE A KNOT ( : "O DOES N "K4
,B ! DI6ICULTY ( \R ?9K+ PO9TS 6A
,8KNOT0' 9 ! OBJECT2 = 9 S F> Z \R ?"\
IS 9 DI6ICULTIES1 X IS 9 L CASE ) ^? :O
>E B.D2 = 9 EI CASE X IS IMPOSSI# 6G
=W>D4 ,H;E "O %D H SURVEY$ ALL !
DI6ICULTIES 2FH&1 BO? =! PURPOSES WE H
/AT$ & 2C P :O 9QUIRE )\T F/ /AT+ !
DI6ICULTIES >E L ^? :O D N "K ": !Y H
6G2 2SS1 A MAN DOES N O!RWISE "K EV5
:E!R HE HAS AT ANY GIV5 "T F.D :AT HE IS
LOOK+ = OR N2 =! 5D IS N CLE> 6S* A MAN1
:ILE 6HM :O HAS F/ 4CUSS$ ! DI6ICULTIES
X IS CLE>4 ,FUR!R1 HE :O HAS HE>D ALL !
3T5D+ >GU;TS1 Z IF !Y 7 ! "PIES 6A CASE1
M/ 2 9 A BETT] POSI;N = JUDG+4
  ,! F/ PRO#M 3C]NS ! SUBJECT : WE
4CUSS$ 9 \R PREFATORY REM>KS4 ,X IS ?-
7#A7 :E!R ! 9VE/IG,N (! CAUSES 2L;GS 6"O
OR 6M SCI;ES1 & 7#B7 :E!R S* A SCI;E %D
SURVEY ONLY ! F/ PR9CIPLES ( SUB/.E1 OR
AL ! PR9CIPLES ON : ALL M5 BASE _!
PRO(S1 E4G4 :E!R X IS POSSI# AT ! SAME
"T 6ASS]T & D5Y "O &! SAME ?+ OR N1 &
ALL O!R S* "QS2 & 7#C7 IF ! SCI;E 9 "Q
D1LS ) SUB/.E1 :E!R "O SCI;E D1LS ) ALL
SUB/.ES1 OR M ?AN "O1 & IF M1 :E!R ALL
>E AK91 OR "S ( !M M/ 2 CALL$ =MS (
,WISDOM &! O!RS "S?+ ELSE4 ,& 7#D7 ? XF
IS AL "O (! ?+S T M/ 2 4CUSS$-:E!R S5SI#
SUB/.ES AL"O %D 2 SD 6EXI/ OR O!RS AL
2SS !M1 & :E!R ^! O!RS >E ( "O K9D OR "!
>E S"EAL CLASSES ( SUB/.ES1 Z IS SUPPOS$
0^? :O 2LIEVE BO? 9 ,=MS & 9 MA!MATICAL
OBJECTS 9T]M$IATE 2T ^! & S5SI# ?+S4
,96^! "QS1 !N1 Z WE SAY1 WE M/ 9QUIRE1 &
AL 7#E7 :E!R \R 9VE/IG,N IS 3C]N$ ONLY )
SUB/.ES OR AL )! ESS5TIAL ATTRIBUTES (
SUB/.ES4 ,FUR!R1 ) REG>D 6! SAME & O!R &
L & UNLIKE & 3TR>IETY1 &) REG>D 6PRIOR &
PO/]IOR & ALL O!R S* T]MS AB : !
DIALECTICIANS TRY 69QUIRE1 />T+ _!
9VE/IG,N F PROBA# PREMISES ONLY1-^:
BUSI;S IS X 69QUIRE 96ALL ^!8 ,FUR!R1 WE
M/ 4CUSS ! ESS5TIAL ATTRIBUTES ( ^!
!MVS2 & WE M/ ASK N ONLY :AT EA* ( ^!
IS1 B AL :E!R "O ?+ ALW HAS "O 3TR>Y4
,AG 7#F71 >E ! PR9CIPLES & ELE;TS ( ?+S
! G5]A1 OR ! "PS PRES5T 9 EA* ?+1 96: X
IS DIVID$2 & 7#G7 IF !Y >E ! G5]A1 >E !Y
! G5]A T >E PR$ICAT$ PROXIMATELY (!
9DIVIDUALS1 OR ! HI<E/ G5]A1 E4G4 IS
ANIMAL OR MAN ! F/ PR9CIPLE &! M
9DEP5D5T (! 9DIVIDUAL 9/.E8 ,& 7#H7 WE
M/ 9QUIRE & 4CUSS ESPECI,Y :E!R "! IS1
2SS ! MATT]1 ANY ?+ T IS A CAUSE 9 XF OR
N1 & :E!R ? C EXI/ A"P OR N1 & :E!R X IS
"O OR M 9 NUMB]1 & :E!R "! IS "S?+ A"P F
! 3CRETE ?+ 70! 3CRETE ?+ ,I M1N ! MATT]
) "S?+ ALR PR$ICAT$ ( X71 OR "! IS NO?+
A"P1 OR "! IS "S?+ 9 "S CASES ?\< N 9
O!RS1 & :AT SORT ( CASES ^! >E4 ,AG 7#I7
WE ASK :E!R ! PR9CIPLES >E LIMIT$ 9
NUMB] OR 9 K9D1 BO? ^? 9 ! DEF9I;NS & ^?
9 ! SUB/RATUM2 & 7#AJ7 :E!R ! PR9CIPLES
( P]I%A# &( IMP]I%A# ?+S >E ! SAME OR
DI6]5T2 & :E!R !Y >E ALL IMP]I%A# OR ^?
( P]I%A# ?+S >E P]I%A#4 ,FUR!R 7#AA7 "!
IS ! "Q : IS H>DE/ ( ALL & MO/ P]PLEX+1
:E!R UN;Y & 2+1 Z ! ,PY?AGOR1NS & ,PLATO
SD1 >E N ATTRIBUTES ( "S?+ ELSE B !
SUB/.E ( EXI/+ ?+S1 OR ? IS N ! CASE1 B
! SUB/RATUM IS "S?+ ELSE1-Z ,EMP$OCLES
SAYS1 LOVE2 Z "S "O ELSE SAYS1 FIRE2
:ILE ANO!R SAYS WAT] OR AIR4 ,AG 7#AB7
WE ASK :E!R ! PR9CIPLES >E UNIV]SAL OR L
9DIVIDUAL ?+S1 & 7#AC7 :E!R !Y EXI/
POT5TI,Y OR ACTU,Y1 & FUR!R1 :E!R !Y >E
POT5TIAL OR ACTUAL 9 ANY O!R S5SE ?AN 9
REF];E 6MOVE;T2 = ^! "QS AL WD PRES5T M*
DI6ICULTY4 ,FUR!R 7#AD71 >E NUMB]S &
L9ES & FIGURES & PO9TS A K9D ( SUB/.E OR
N1 & IF !Y >E SUB/.ES >E !Y SEP>ATE F
S5SI# ?+S OR PRES5T 9 !M8 ,) REG>D 6ALL
^! MATT]S N ONLY IS X H>D 6GET POSSES.N
(! TRU?1 B X IS N EASY EV5 6?9K \ !
DI6ICULTIES WELL4
                   #B
  7#A7 ,F/ !N ) REG>D 6:AT WE M5;N$ F/1
DOES X 2L;G 6"O OR 6M SCI;ES 69VE/IGATE
ALL ! K9DS ( CAUSES8 ,H[ CD X 2L;G 6"O
SCI;E 6RECOGNIZE ! PR9CIPLES IF ^! >E N
3TR>Y8
  ,FUR!R1 "! >E _M ?+S 6: N ALL !
PR9CIPLES P]TA94 ,= H[ C A PR9CIPLE (
*ANGE OR ! NATURE (! GD EXI/ = UN*ANGEA#
?+S1 S9CE "EY?+ T 9 XF & 0XS [N NATURE
IS GD IS AN 5D1 &A CAUSE 9 ! S5SE T = XS
SAKE ! O!R ?+S BO? -E 6BE & >E1 & S9CE
AN 5D OR PURPOSE IS ! 5D ( "S AC;N1 &
ALL AC;NS IMPLY *ANGE8 ,S 9 ! CASE (
UN*ANGEA# ?+S ? PR9CIPLE CD N EXI/1 NOR
CD "! 2 A GD XF4 ,? IS :Y 9 MA!MATICS
NO?+ IS PROV$ 0M1NS ( ? K9D ( CAUSE1 NOR
IS "! ANY DEMON/R,N ( ? K9D-,82C X IS
BETT]1 OR WORSE0'2 9DE$ NO "O EV5 M5;NS
ANY?+ (! K9D4 ,& S = ? R1SON "S (!
,SOPHI/S1 E4G4 ,>I/IPPUS1 US$ 6RIDICULE
MA!MATICS2 = 9 ! >TS 7HE MA9TA9$71 EV5 9
! 9DU/RIAL >TS1 E4G4 9 C>P5TRY & CO2L+1
! R1SON ALW GIV5 IS ,82C X IS BETT]1 OR
WORSE10' B ! MA!MATICAL SCI;ES TAKE NO
A3.T ( GDS & EVILS4
  ,B IF "! >E S"EAL SCI;ES (! CAUSES1 &A
DI6]5T SCI;E = EA* DI6]5T PR9CIPLE1 : (
^! SCI;ES %D 2 SD 6BE T : WE SEEK1 OR :
(! P :O POSSESS !M HAS ! MO/ SCI5TIFIC K
(! OBJECT 9 "Q8 ,! SAME ?+ MAY H ALL !
K9DS ( CAUSES1 E4G4 ! MOV+ CAUSE (A H\SE
IS ! >T OR ! BUILD]1 ! F9AL CAUSE IS !
FUNC;N X FULFILS1 ! MATT] IS E>? & /"OS1
&! =M IS ! DEF9I;N4 ,6JUDGE F \R PREVI\S
4CUS.N (! "Q : (! SCI;ES %D 2 CALL$
,WISDOM1 "! IS R1SON = APPLY+ ! "N 6EA*
( !M4 ,= 9ASM* Z X IS MO/ >*ITECTONIC &
AU?ORITATIVE &! O!R SCI;ES1 L SLAVEWOM51
MAY N EV5 3TRADICT X1 ! SCI;E (! 5D &(!
GD IS (! NATURE ( ,WISDOM 7=! O!R ?+S >E
=! SAKE (! 5D74 ,B 9ASM* Z X 0
DESCRIB$0' Z D1L+ )! F/ CAUSES & T : IS
9 ! HI<E/ S5SE OBJECT ( K1 ! SCI;E (
SUB/.E M/ 2 (! NATURE ( ,WISDOM4 ,= S9CE
M5 MAY "K ! SAME ?+ 9 _M WAYS1 WE SAY T
HE :O RECOGNIZES :AT A ?+ IS 0XS 2+ S &
S "KS M FULLY ?AN HE :O RECOGNIZES X 0XS
N 2+ S & S1 & 9 ! =M] CLASS XF "O "KS M
FULLY ?AN ANO!R1 & HE "KS MO/ FULLY :O
"KS :AT A ?+ IS1 N HE :O "KS XS QUANT;Y
OR QUAL;Y OR :AT X C 0NATURE D OR H D"O
6X4 ,& FUR!R 9 ALL CASES AL WE ?9K T ! K
( EA* EV5 (! ?+S ( : DEMON/R,N IS POSSI#
IS PRES5T ONLY :5 WE "K :AT ! ?+ IS1
E4G4 :AT SQU>+ A RECTANGLE IS1 VIZ4 T X
IS ! F9D+ (A M1N2 & SIMIL>LY 9 ALL O!R
CASES4 ,& WE "K AB 2COM+S & AC;NS & AB E
*ANGE :5 WE "K ! S\RCE (! MOVE;T2 & ? IS
O!R ?AN & OPPOS$ 6! 5D4 ,"!=E X WD SEEM
62L;G 6DI6]5T SCI;ES 69VE/IGATE ^!
CAUSES S"E,Y4
  ,B 7#B71 TAK+ ! />T+-PO9TS ( DEMON/R,N
Z WELL Z ! CAUSES1 X IS A 4PUTA# "Q :E!R
!Y >E ! OBJECT ( "O SCI;E OR ( M 70!
/>T+-PO9TS ( DEMON/R,N ,I M1N ! -MON
2LIEFS1 ON : ALL M5 BASE _! PRO(S72 E4G4
T "EY?+ M/ 2 EI A6IRM$ OR D5I$1 & T A ?+
_C AT ! SAME "T 2 & N BE1 & ALL O!R S*
PREMISSES3-! "Q IS :E!R ! SAME SCI;E
D1LS ) !M Z ) SUB/.E1 OR A DI6]5T SCI;E1
& IF X IS N "O SCI;E1 : (! TWO M/ 2
ID5TIFI$ ) T : WE N[ SEEK4-,X IS N
R1SONA# T ^! TOPICS %D 2 ! OBJECT ( "O
SCI;E2 = :Y %D X 2 PECULI>LY APPROPRIATE
6GEOMETRY OR 6ANY O!R SCI;E 6"U/& ^!
MATT]S8 ,IF !N X 2L;GS 6E SCI;E ALIKE1 &
_C 2L;G 6ALL1 X IS N PECULI> 6! SCI;E :
9VE/IGATES SUB/.ES1 ANY M ?AN 6ANY O!R
SCI;E1 6"K AB ^! TOPICS4-,&1 AT ! SAME
"T1 9 :AT WAY C "! 2 A SCI;E (! F/
PR9CIPLES8 ,= WE >E AW>E EV5 N[ :AT EA*
( !M 9 FACT IS 7AT L1/ EV5 O!R SCI;ES
USE !M Z FAMILI>72 B IF "! IS A
DEMON/RATIVE SCI;E : D1LS ) !M1 "! W H
6BE AN "ULY+ K9D1 & "S ( !M M/ 2
DEMON/RA# ATTRIBUTES & O!RS M/ 2 AXIOMS
7= X IS IMPOSSI# T "! %D 2 DEMON/R,N AB
ALL ( !M72 =! DEMON/R,N M/ />T F C]TA9
PREMISSES & 2 AB A C]TA9 SUBJECT & PROVE
C]TA9 ATTRIBUTES4 ,"!=E X FOLL[S T ALL
ATTRIBUTES T >E PROV$ M/ 2L;G 6A S+LE
CLASS2 = ALL DEMON/RATIVE SCI;ES USE !
AXIOMS4
  ,B IF ! SCI;E ( SUB/.E &! SCI;E : D1LS
)! AXIOMS >E DI6]5T1 : ( !M IS 0NATURE M
AU?ORITATIVE & PRIOR8 ,! AXIOMS >E MO/
UNIV]SAL & >E PR9CIPLES ( ALL ?+S4 ,& IF
X IS N ! BUSI;S (! PHILOSOPH]1 6:OM ELSE
W X 2L;G 69QUIRE :AT IS TRUE & :AT IS
UNTRUE AB !M8
  7#C7 ,9 G5]AL1 D ALL SUB/.ES FALL "U
"O SCI;E OR "U M ?AN "O8 ,IF ! LATT]1
6:AT SORT ( SUB/.E IS ! PRES5T SCI;E 6BE
ASSIGN$8-,ON ! O!R H&1 X IS N R1SONA# T
"O SCI;E %D D1L ) ALL4 ,= !N "! WD 2 "O
DEMON/RATIVE SCI;E D1L+ ) ALL
ATTRIBUTES4 ,= "E DEMON/RATIVE SCI;E
9VE/IGATES ) REG>D 6"S SUBJECT XS
ESS5TIAL ATTRIBUTES1 />T+ F ! -MON
2LIEFS4 ,"!=E 69VE/IGATE ! ESS5TIAL
ATTRIBUTES ( "O CLASS ( ?+S1 />T+ F "O
SET ( 2LIEFS1 IS ! BUSI;S ( "O SCI;E4
,=! SUBJECT 2L;GS 6"O SCI;E1 &!
PREMISSES 2L;G 6"O1 :E!R 6! SAME OR
6ANO!R2 S T ! ATTRIBUTES D S TOO1 :E!R
!Y >E 9VE/IGAT$ 0^! SCI;ES OR 0"O -P.D$
\ ( !M4
  7#E7 ,FUR!R1 DOES \R 9VE/IG,N D1L )
SUB/.ES AL"O OR AL ) _! ATTRIBUTES8 ,I
M1N = 9/.E1 IF ! SOLID IS A SUB/.E & S
>E L9ES & PLANES1 IS X ! BUSI;S (! SAME
SCI;E 6"K ^! & 6"K ! ATTRIBUTES ( EA* (
^! CLASSES 7! ATTRIBUTES AB : !
MA!MATICAL SCI;ES (F] PRO(S71 OR (A
DI6]5T SCI;E8 ,IF (! SAME1 ! SCI;E (
SUB/.E AL M/ 2 A DEMON/RATIVE SCI;E1 B X
IS ?"\ T "! IS NO DEMON/R,N (! ESS;E (
?+S4 ,& IF ( ANO!R1 :AT W 2 ! SCI;E T
9VE/IGATES ! ATTRIBUTES ( SUB/.E8 ,? IS
A V DI6ICULT "Q4
  7#D7 ,FUR!R1 M/ WE SAY T S5SI# SUB/.ES
AL"O EXI/1 OR T "! >E O!RS 2SS ^!8 ,& >E
SUB/.ES ( "O K9D OR >E "! 9 FACT S"EAL
K9DS ( SUB/.ES1 Z ^? SAY :O ASS]T !
EXI/;E BO? (! ,=MS &(! 9T]M$IATES1 ) :
!Y SAY ! MA!MATICAL SCI;ES D1L8-,! S5SE
9 : WE SAY ! ,=MS >E BO? CAUSES & SELF-
DEP5D5T SUB/.ES HAS BE5 EXPLA9$ 9 \R F/
REM>KS AB !M2 :ILE ! !ORY PRES5TS
DI6ICULTIES 9 _M WAYS1 ! MO/ P>ADOXICAL
?+ ( ALL IS ! /ATE;T T "! >E C]TA9 ?+S
2SS ^? 9 ! MAT]IAL UNIV]SE1 & T ^! >E !
SAME Z S5SI# ?+S EXCEPT T !Y >E ET]NAL
:ILE ! LATT] >E P]I%A#4 ,= !Y SAY "! IS
A MAN-HMF &A HORSE-XF & H1L?-XF1 ) NO
FUR!R QUALIFIC,N1-A PROC$URE L T (! P :O
SD "! >E GODS1 B 9 HUMAN =M4 ,= !Y 7
POSIT+ NO?+ B ET]NAL M51 NOR >E !
,PLATONI/S MAK+ ! ,=MS ANY?+ O!R ?AN
ET]NAL S5SI# ?+S4
  ,FUR!R1 IF WE >E 6POSIT 2SS ! ,=MS &!
S5SI#S ! 9T]M$IATES 2T !M1 WE % H _M
DI6ICULTIES4 ,= CLE>LY ON ! SAME
PR9CIPLE "! W 2 L9ES 2SS ! L9ES-!MVS &!
S5SI# L9ES1 & S ) EA* (! O!R CLASSES (
?+S2 S T S9CE A/RONOMY IS "O ( ^!
MA!MATICAL SCI;ES "! W AL 2 A H1V5 2SS !
S5SI# H1V51 &A SUN &A MOON 7& S )! O!R
H1V5LY BODIES7 2SS ! S5SI#4 ,YET H[ >E
WE 62LIEVE 9 ^! ?+S8 ,X IS N R1SONA# EV5
6SUPPOSE S* A BODY IMMOVA#1 B 6SUPPOSE X
MOV+ IS Q IMPOSSI#4-,& SIMIL>LY )! ?+S (
: OPTICS & MA!MATICAL H>MONICS TR1T2 =
^! AL _C EXI/ A"P F ! S5SI# ?+S1 =! SAME
R1SONS4 ,= IF "! >E S5SI# ?+S & S5S,NS
9T]M$IATE 2T ,=M & 9DIVIDUAL1 EVID5TLY
"! W AL 2 ANIMALS 9T]M$IATE 2T ANIMALS-
!MVS &! P]I%A# ANIMALS4-,WE MI<T AL
RAISE ! "Q1 ) REF];E 6: K9D ( EXI/+ ?+S
WE M/ LOOK = ^! SCI;ES ( 9T]M$IATES4 ,IF
GEOMETRY IS 6DI6] F M5SUR,N ONLY 9 ?1 T
! LATT] D1LS ) ?+S T WE P]CV1 &! =M] )
?+S T >E N P]CEPTI#1 EVID5TLY "! W AL 2
A SCI;E O!R ?AN M$IC9E1 9T]M$IATE 2T
M$ICAL-SCI;E-XF & ? 9DIVIDUAL M$ICAL
SCI;E1 & S ) EA* (! O!R SCI;ES4 ,YET H[
IS ? POSSI#8 ,"! WD H 6BE AL H1L?Y ?+S
2SS ! P]CEPTI# H1L?Y ?+S &! H1L?Y-XF4--
,& AT ! SAME "T N EV5 ? IS TRUE1 T
M5SUR,N D1LS ) P]CEPTI# & P]I%A#
MAGNITUDES2 = !N X WD H P]I%$ :5 !Y
P]I%$4
  ,B ON ! O!R H& A/RONOMY _C 2 D1L+ )
P]CEPTI# MAGNITUDES NOR ) ? H1V5 ABV U4
,= NEI >E P]CEPTI# L9ES S* L9ES Z !
GEOMET] SP1KS ( 7= NO P]CEPTI# ?+ IS
/RAI<T OR R.D 9 ! WAY 9 : HE DEF9ES
,8/RAI<T0' & ,8R.D0'2 =A HOOP T\*ES A
/RAI<T $GE N AT A PO9T1 B Z ,PROTAGORAS
US$ 6SAY X DID1 9 8 REFUT,N (!
GEOMET]S71 NOR >E ! MOVE;TS & SPIRAL
ORBITS 9 ! H1V5S L ^? ( : A/RONOMY
TR1TS1 NOR H GEOMETRICAL PO9TS ! SAME
NATURE Z ! ACTUAL />S4-,N[ "! >E "S :O
SAY T ^! S-CALL$ 9T]M$IATES 2T ! ,=MS &!
P]CEPTI# ?+S EXI/1 N A"P F ! P]CEPTI#
?+S1 H["E1 B 9 ^!2 ! IMPOSSI# RESULTS (
? VIEW WD TAKE TOO L;G 6ENUM]ATE1 B X IS
5 63SID] EV5 S* PO9TS Z ! FOLL[+3-,X IS
N R1SONA# T ? %D 2 S ONLY 9 ! CASE ( ^!
9T]M$IATES1 B CLE>LY ! ,=MS AL MI<T 2 9
! P]CEPTI# ?+S2 = BO? /ATE;TS >E "PS (!
SAME !ORY4 ,FUR!R1 X FOLL[S F ? !ORY T
"! >E TWO SOLIDS 9 ! SAME PLACE1 & T !
9T]M$IATES >E N IMMOVA#1 S9CE !Y >E 9 !
MOV+ P]CEPTI# ?+S4 ,& 9 G5]AL 6:AT
PURPOSE WD "O SUPPOSE !M 6EXI/ 9DE$1 B
6EXI/ 9 P]CEPTI# ?+S8 ,=! SAME
P>ADOXICAL RESULTS W FOLL[ : WE H ALR
M5;N$2 "! W 2 A H1V5 2SS ! H1V51 ONLY X
W 2 N A"P B 9 ! SAME PLACE2 : IS / M
IMPOSSI#4
                   #C
  7#F7 ,A"P F ! GRT DI6ICULTY ( /AT+ !
CASE TRULY ) REG>D 6^! MATT]S1 X IS V
H>D 6SAY1 ) REG>D 6! F/ PR9CIPLES1 :E!R
X IS ! G5]A T %D 2 TAK5 Z ELE;TS &
PR9CIPLES1 OR R ! PRIM>Y 3/ITU5TS (A ?+2
E4G4 X IS ! PRIM>Y "PS ( : >TICULATE
S.DS 3SI/ T >E ?"\ 6BE ELE;TS &
PR9CIPLES ( >TICULATE S.D1 N ! -MON
G5US->TICULATE S.D2 & WE GIVE ! "N (
,8ELE;TS0' 6^? GEOMETRICAL PROPOSI;NS1 !
PRO(S ( : >E IMPLI$ 9 ! PRO(S (! O!RS1
EI ( ALL OR ( MO/4 ,FUR!R1 BO? ^? :O SAY
"! >E S"EAL ELE;TS ( CORPOR1L ?+S & ^?
:O SAY "! IS "O1 SAY ! "PS ( : BODIES >E
-P.D$ & 3SI/ >E PR9CIPLES2 E4G4
,EMP$OCLES SAYS FIRE & WAT] &! RE/ >E !
3/ITU5T ELE;TS ( ?+S1 B DOES N DESCRIBE
^! Z G5]A ( EXI/+ ?+S4 ,2SS ?1 IF WE
WANT 6EXAM9E ! NATURE ( ANY?+ ELSE1 WE
EXAM9E ! "PS ( :1 E4G4 A B$ 3SI/S & H[
!Y >E PUT TGR1 & !N WE "K XS NATURE4
  ,6JUDGE F ^! >GU;TS1 !N1 ! PR9CIPLES (
?+S WD N 2 ! G5]A2 B IF WE "K EA* ?+ 0XS
DEF9I;N1 &! G5]A >E ! PR9CIPLES OR />T+-
PO9TS ( DEF9I;NS1 ! G5]A M/ AL 2 !
PR9CIPLES ( DEF9A# ?+S4 ,& IF 6GET ! K (
! SPECIES AC 6: ?+S >E "ND IS 6GET ! K (
?+S1 ! G5]A >E AT L1/ />T+-PO9TS (!
SPECIES4 ,& "S AL ( ^? :O SAY UN;Y OR
2+1 OR ! GRT &! SMALL1 >E ELE;TS ( ?+S1
SEEM 6TR1T !M Z G5]A4
  ,B1 AG1 X IS N POSSI# 6DESCRIBE !
PR9CIPLES 9 BO? WAYS4 ,=! =MULA (! ESS;E
IS "O2 B DEF9I;N 0G5]A W 2 DI6]5T F T :
/ATES ! 3/ITU5T "PS (A ?+4
  7#G7 ,2SS ?1 EV5 IF ! G5]A >E 9 !
HI<E/ DEGREE PR9CIPLES1 %D "O REG>D ! F/
(! G5]A Z PR9CIPLES1 OR ^? : >E PR$ICAT$
DIRECTLY (! 9DIVIDUALS8 ,? AL ADMITS (
4PUTE4 ,= IF ! UNIV]SALS >E ALW M (!
NATURE ( PR9CIPLES1 EVID5TLY ! UPP]MO/ (
! G5]A >E ! PR9CIPLES2 = ^! >E PR$ICAT$
( ALL ?+S4 ,"! W1 !N1 2 Z _M PR9CIPLES (
?+S Z "! >E PRIM>Y G5]A1 S T BO? 2+ &
UN;Y W 2 PR9CIPLES & SUB/.ES2 = ^! >E
MO/ ( ALL PR$ICAT$ ( ALL EXI/+ ?+S4 ,B X
IS N POSSI# T EI UN;Y OR 2+ %D 2 A S+LE
G5US ( ?+S2 =! DI6]5TIAE ( ANY G5US M/
EA* ( !M BO? H 2+ & 2 "O1 B X IS N
POSSI# =! G5US TAK5 A"P F XS SPECIES
7ANY M ?AN =! SPECIES (! G5US7 6BE
PR$ICAT$ ( XS PROP] DI6]5TIAE2 S T IF
UN;Y OR 2+ IS A G5US1 NO DI6]5TIA W EI H
2+ OR 2 "O4 ,B IF UN;Y & 2+ >E N G5]A1
NEI W !Y 2 PR9CIPLES1 IF ! G5]A >E !
PR9CIPLES4 ,AG1 ! 9T]M$IATE K9DS1 9 ^:
NATURE ! DI6]5TIAE >E 9CLUD$1 W ON ?
!ORY 2 G5]A1 D[N 6! 9DIVISI# SPECIES2 B
Z X IS1 "S >E ?"\ 6BE G5]A & O!RS >E N
?"\ 6BE S4 ,2SS ?1 ! DI6]5TIAE >E
PR9CIPLES EV5 M ?AN ! G5]A2 & IF ^! AL
>E PR9CIPLES1 "! -ES 6BE PRACTIC,Y AN
9F9ITE NUMB] ( PR9CIPLES1 ESPECI,Y IF WE
SUPPOSE ! HI<E/ G5US 6BE A PR9CIPLE4-,B
AG1 IF UN;Y IS M (! NATURE (A PR9CIPLE1
&! 9DIVISI# IS "O1 & "EY?+ 9DIVISI# IS S
EI 9 QUANT;Y OR 9 SPECIES1 & T : IS S 9
SPECIES IS ! PRIOR1 & G5]A >E DIVISI#
96SPECIES = MAN IS N ! G5US ( 9DIVIDUAL
M571 T : IS PR$ICAT$ DIRECTLY (!
9DIVIDUALS W H M UN;Y4-,FUR!R1 9 ! CASE
( ?+S 9 : ! 4T9C;N ( PRIOR & PO/]IOR IS
PRES5T1 T : IS PR$ICA# ( ^! ?+S _C 2
"S?+ A"P F !M 7E4G4 IF TWO IS ! F/ (
NUMB]S1 "! W N 2 A ,NUMB] A"P F ! K9DS (
NUMB]S2 & SIMIL>LY "! W N 2 A ,FIGURE
A"P F ! K9DS ( FIGURES2 & IF ! G5]A ( ^!
?+S D N EXI/ A"P F ! SPECIES1 ! G5]A (
O!R ?+S W SC>CELY D S2 = G5]A ( ^! ?+S
>E ?"\ 6EXI/ IF ANY D74 ,B AM;G !
9DIVIDUALS "O IS N PRIOR & ANO!R
PO/]IOR4 ,FUR!R1 ": "O ?+ IS BETT] &
ANO!R WORSE1 ! BETT] IS ALW PRIOR2 S T (
^! AL NO G5US C EXI/4 ,F ^! 3SID],NS1
!N1 ! SPECIES PR$ICAT$ ( 9DIVIDUALS SEEM
6BE PR9CIPLES R ?AN ! G5]A4 ,B AG1 X IS
N EASY 6SAY 9 :AT S5SE ^! >E 6BE TAK5 Z
PR9CIPLES4 ,=! PR9CIPLE OR CAUSE M/ EXI/
AL;GSIDE (! ?+S ( : X IS ! PR9CIPLE1 &
M/ 2 CAPA# ( EXI/+ 9 SEP>,N F !M2 B =
:AT R1SON %D WE SUPPOSE ANY S* ?+ 6EXI/
AL;GSIDE (! 9DIVIDUAL1 EXCEPT T X IS
PR$ICAT$ UNIV]S,Y &( ALL8 ,B IF ? IS !
R1SON1 ! ?+S T >E M UNIV]SAL M/ 2
SUPPOS$ 6BE M (! NATURE ( PR9CIPLES2 S T
! HI<E/ G5]A WD 2 ! PR9CIPLES4
                   #D
  7#H7 ,"! IS A DI6ICULTY 3NECT$ ) ^!1 !
H>DE/ ( ALL &! MO/ NEC 6EXAM9E1 &( ? !
4CUS.N N[ AWAITS U4 ,IF1 ON ! "O H&1 "!
IS NO?+ A"P F 9DIVIDUAL ?+S1 &!
9DIVIDUALS >E 9F9ITE 9 NUMB]1 H[ !N IS X
POSSI# 6GET K (! 9F9ITE 9DIVIDUALS8 ,=
ALL ?+S T WE -E 6"K1 WE -E 6"K 9 S F> Z
!Y H "S UN;Y & ID5T;Y1 & 9 S F> Z "S
ATTRIBUTE 2L;GS 6!M UNIV]S,Y4
  ,B IF ? IS NEC1 & "! M/ 2 "S?+ A"P F !
9DIVIDUALS1 X W 2 NEC T ! G5]A EXI/ A"P
F ! 9DIVIDUALS1 EI ! L[E/ OR ! HI<E/
G5]A2 B WE F.D 04CUS.N J N[ T ? IS
IMPOSSI#4
  ,FUR!R1 IF WE ADMIT 9 ! FULLE/ S5SE T
"S?+ EXI/S A"P F ! 3CRETE ?+1 :5"E "S?+
IS PR$ICAT$ (! MATT]1 M/ "!1 IF "! IS
"S?+ A"P1 2 "S?+ A"P F EA* SET (
9DIVIDUALS1 OR F "S & N F O!RS1 OR F
N"O8 7,A7 ,IF "! IS NO?+ A"P F
9DIVIDUALS1 "! W 2 NO OBJECT ( ?"\1 B
ALL ?+S W 2 OBJECTS ( S5SE1 & "! W N 2 K
( ANY?+1 UN.S WE SAY T S5S,N IS K4
,FUR!R1 NO?+ W 2 ET]NAL OR UNMOVA#2 =
ALL P]CEPTI# ?+S P]I% & >E 9 MOVE;T4 ,B
IF "! IS NO?+ ET]NAL1 NEI C "! 2 A
PROCESS ( -+ 6BE2 = "! M/ 2 "S?+ T -ES
6BE1 I4E4 F : "S?+ -ES 6BE1 &! ULTIMATE
T]M 9 ? S]IES _C H -E 6BE1 S9CE ! S]IES
HAS A LIMIT & S9CE NO?+ C -E 6BE \ ( T :
IS N4 ,FUR!R1 IF G5],N & MOVE;T EXI/ "!
M/ AL 2 A LIMIT2 = NO MOVE;T IS 9F9ITE1
B E MOVE;T HAS AN 5D1 & T : IS 9CAPA# (
-PLET+ XS -+ 6BE _C 2 9 PROCESS ( -+
6BE2 & T : HAS -PLET$ XS -+ 6BE M/ HE Z
SOON Z X HAS -E 6BE4 ,FUR!R1 S9CE !
MATT] EXI/S1 2C X IS UNG5]AT$1 X IS A
=TIORI R1SONA# T ! SUB/.E OR ESS;E1 T :
! MATT] IS AT ANY "T -+ 6BE1 %D EXI/2 =
IF NEI ESS;E NOR MATT] IS 6BE1 NO?+ W 2
AT ALL1 & S9CE ? IS IMPOSSI# "! M/ 2
"S?+ 2SS ! 3CRETE ?+1 VIZ4 ! %APE OR =M4
  ,B AG 7,B7 IF WE >E 6SUPPOSE ?1 X IS
H>D 6SAY 9 : CASES WE >E 6SUPPOSE X & 9
: N4 ,= EVID5TLY X IS N POSSI# 6SUPPOSE
X 9 ALL CASES2 WE CD N SUPPOSE T "! IS A
H\SE 2SS ! "PICUL> H\SES4-,2SS ?1 W !
SUB/.E ( ALL ! 9DIVIDUALS1 E4G4 ( ALL
M51 2 "O8 ,? IS P>ADOXICAL1 = ALL ! ?+S
^: SUB/.E IS "O >E "O4 ,B >E ! SUB/.ES
_M & DI6]5T8 ,? AL IS UNR1SONA#4-,AT !
SAME "T1 H[ DOES ! MATT] 2COME EA* (!
9DIVIDUALS1 & H[ IS ! 3CRETE ?+ ^! TWO
ELE;TS8
  7#I7 ,AG1 "O MI<T ASK ! FOLL[+ "Q AL
AB ! F/ PR9CIPLES4 ,IF !Y >E "O 9 K9D
ONLY1 NO?+ W 2 NUM]IC,Y "O1 N EV5 UN;Y-
XF & 2+-XF2 & H[ W "K+ EXI/1 IF "! IS N
6BE "S?+ -MON 6A :OLE SET ( 9DIVIDUALS8
  ,B IF "! IS A -MON ELE;T : IS NUM]IC,Y
"O1 & EA* (! PR9CIPLES IS "O1 &!
PR9CIPLES >E N Z 9 ! CASE ( P]CEPTI# ?+S
DI6]5T = DI6]5T ?+S 7E4G4 S9CE ? "PICUL>
SYLLA# IS ! SAME 9 K9D :5"E X O3URS1 !
ELE;TS X >E AL ! SAME 9 K9D2 ONLY 9 K9D1
= ^! AL1 L ! SYLLA#1 >E NUM]IC,Y DI6]5T
9 DI6]5T 3TEXTS71-IF X IS N L ? B !
PR9CIPLES ( ?+S >E NUM]IC,Y "O1 "! W 2
NO?+ ELSE 2SS ! ELE;TS 7= "! IS NO
DI6];E ( M1N+ 2T ,8NUM]IC,Y "O0' &
,89DIVIDUAL0'2 = ? IS J :AT WE M1N 0!
9DIVIDUAL-! NUM]IC,Y "O1 & 0! UNIV]SAL
WE M1N T : IS PR$ICA# (! 9DIVIDUALS74
,"!=E X W 2 J Z IF ! ELE;TS ( >TICULATE
S.D 7 LIMIT$ 9 NUMB]2 ALL ! LANGUAGE 9 !
_W WD 2 3F9$ 6! ,,ABC1 S9CE "! CD N 2
TWO OR M LRS (! SAME K9D4
  7#AJ7 ,"O DI6ICULTY : IS Z GRT Z ANY
HAS BE5 NEGLECT$ BO? 0MOD]N PHILOSOPH]S
& 0_! PR$ECESSORS-:E!R ! PR9CIPLES (
P]I%A# & ^? ( IMP]I%A# ?+S >E ! SAME OR
DI6]5T4 ,IF !Y >E ! SAME1 H[ >E "S ?+S
P]I%A# & O!RS IMP]I%A#1 &= :AT R1SON8 ,!
S*OOL ( ,HESIOD & ALL ! !OLOGIANS ?"\
ONLY ( :AT 0 PLAUSI# 6!MVS1 & _H NO
REG>D 6U4 ,=1 ASS]T+ ! F/ PR9CIPLES 6BE
GODS & BORN ( GODS1 !Y SAY T ! 2+S : DID
N TA/E ( NECT> & AMBROSIA 2CAME MORTAL2
& CLE>LY !Y >E US+ ^WS : >E FAMILI>
6!MVS1 YET :AT !Y H SD AB ! V APPLIC,N (
^! CAUSES IS ABV \R -PREH5.N4 ,= IF !
GODS TA/E ( NECT> & AMBROSIA = _!
PL1SURE1 ^! >E 9 NO WISE ! CAUSES ( _!
EXI/;E2 & IF !Y TA/E !M 6MA9TA9 _!
EXI/;E1 H[ C GODS :O NE$ FOOD 2 ET]NAL8-
,B 96! SUBTLETIES (! MY?OLOGI/S X IS N
WOR? \R :ILE 69QUIRE S]I\SLY2 ^?1 H["E1
:O USE ! LANGUAGE ( PRO( WE M/ CROSS-
EXAM9E & ASK :Y1 AF ALL1 ?+S : 3SI/ (!
SAME ELE;TS >E1 "S ( !M1 ET]NAL 9
NATURE1 :ILE O!RS P]I%4 ,S9CE ^!
PHILOSOPH]S M5;N NO CAUSE1 & X IS
UNR1SONA# T ?+S %D 2 Z !Y SAY1 EVID5TLY
! PR9CIPLES OR CAUSES ( ?+S _C 2 ! SAME4
,EV5 ! MAN :OM "O MI<T SUPPOSE 6SP1K MO/
3SI/5TLY-,EMP$OCLES1 EV5 HE HAS MADE !
SAME MISTAKE2 = HE MA9TA9S T /RIFE IS A
PR9CIPLE T CAUSES DE/RUC;N1 B EV5 /RIFE
WD SEEM NO LESS 6PRODUCE "EY?+1 EXCEPT !
,"O2 = ALL ?+S EXCEPT+ ,GOD PROCE$ F
/RIFE4 ,AT L1/ HE SAYS3-
  ,F : ALL T 0 & IS & W 2 "HAF- ,TREES1
& M5 & WOM51 TOOK _! GR[?1
  ,& B1/S & BIRDS & WAT]-N\RI%$ FI%1
  ,& L;G-AG$ GODS4
  ,! IMPLIC,N IS EVID5T EV5 A"P F ^!
^WS2 = IF /RIFE _H N BE5 PRES5T 9 ?+S1
ALL ?+S WD H BE5 "O1 AC 6HM2 = :5 !Y H
-E TGR1 ,8!N /RIFE /OOD \T]MO/40' ,H;E X
AL FOLL[S ON 8 !ORY T ,GOD MO/ B.S$ IS
LESS WISE ?AN ALL O!RS2 = HE DOES N "K
ALL ! ELE;TS2 = HE HAS 9 HM NO /RIFE1 &
K IS (! L 0! L4 ,8,= 0E>?10' HE SAYS1
  WE SEE E>?1 0WAT] WAT]1
  ,0E!R GODLIKE E!R1 0FIRE WA/+ FIRE1
  ,LOVE 0LOVE1 & /RIFE 0GLOOMY /RIFE4
  ,B-& ? IS ! PO9T WE />T$ F ? AT L1/ IS
EVID5T1 T ON 8 !ORY X FOLL[S T /RIFE IS
Z M* ! CAUSE ( EXI/;E Z ( DE/RUC;N4 ,&
SIMIL>LY LOVE IS N SPECI,Y ! CAUSE (
EXI/;E2 = 9 COLLECT+ ?+S 96! ,"O X
DE/ROYS ALL O!R ?+S4 ,& AT ! SAME "T
,EMP$OCLES M5;NS NO CAUSE (! *ANGE XF1
EXCEPT T ?+S >E S 0NATURE4
  ,B :5 /RIFE AT LA/ WAX$ GRT 9 ! LIMBS
(! ,SPH]E1
  ,& SPRANG 6ASS]T XS "RS Z ! "T 0
FULFILL$
  ,: IS FIX$ = !M 9 TURN 0A MI<TY OA?4
  ,? IMPLIES T *ANGE 0 NEC2 B HE %[S NO
CAUSE (! NECESS;Y4 ,B YET S F> AT L1/ HE
AL"O SP1KS 3SI/5TLY2 = HE DOES N MAKE "S
?+S P]I%A# & O!RS IMP]I%A#1 B MAKES ALL
P]I%A# EXCEPT ! ELE;TS4 ,! DI6ICULTY WE
>E SP1K+ ( N[ IS1 :Y "S ?+S >E P]I%A# &
O!RS >E N1 IF !Y 3SI/ (! SAME PR9CIPLES4
  ,LET ? SU6ICE Z PRO( (! FACT T !
PR9CIPLES _C 2 ! SAME4 ,B IF "! >E
DI6]5T PR9CIPLES1 "O DI6ICULTY IS :E!R
^! AL W 2 IMP]I%A# OR P]I%A#4 ,= IF !Y
>E P]I%A#1 EVID5TLY ^! AL M/ 3SI/ (
C]TA9 ELE;TS 7= ALL ?+S T P]I%1 P]I% 02+
RESOLV$ 96! ELE;TS ( : !Y 3SI/72 S T X
FOLL[S T PRIOR 6! PR9CIPLES "! >E O!R
PR9CIPLES4 ,B ? IS IMPOSSI#1 :E!R !
PROCESS HAS A LIMIT OR PROCE$S 69F9;Y4
,FUR!R1 H[ W P]I%A# ?+S EXI/1 IF _!
PR9CIPLES >E 6BE ANNULL$8 ,B IF !
PR9CIPLES >E IMP]I%A#1 :Y W ?+S -POS$ (
"S IMP]I%A# PR9CIPLES 2 P]I%A#1 :ILE ^?
-POS$ (! O!RS >E IMP]I%A#8 ,? IS N
PROBA#1 B IS EI IMPOSSI# OR NE$S M*
PRO(4 ,FUR!R1 NO "O HAS EV5 TRI$ 6MA9TA9
DI6]5T PR9CIPLES2 !Y MA9TA9 ! SAME
PR9CIPLES = ALL ?+S4 ,B !Y SWALL[ !
DI6ICULTY WE /AT$ F/ Z IF !Y TOOK X 6BE
"S?+ TRIFL+4
  7#AA7 ,! 9QUIRY T IS BO? ! H>DE/ ( ALL
&! MO/ NEC = K (! TRU? IS :E!R 2+ & UN;Y
>E ! SUB/.ES ( ?+S1 & :E!R EA* ( !M1 )\T
2+ ANY?+ ELSE1 IS 2+ OR UN;Y
RESPECTIVELY1 OR WE M/ 9QUIRE :AT 2+ &
UN;Y >E1 )! IMPLIC,N T !Y H "S O!R "ULY+
NATURE4 ,= "S P ?9K !Y >E (! =M]1 O!RS
?9K !Y >E (! LATT] "*4 ,PLATO &!
,PY?AGOR1NS ?"\ 2+ & UN;Y 7 NO?+ ELSE1 B
? 0 _! NATURE1 _! ESS;E 2+ J UN;Y & 2+4
,B ! NATURAL PHILOSOPH]S TAKE A DI6]5T
L9E2 E4G4 ,EMP$OCLES-Z ?\< REDUC+ 6"S?+
M 9TELLIGI#-SAYS :AT UN;Y IS2 = HE WD
SEEM 6SAY X IS LOVE3 AT L1/1 ? IS = ALL
?+S ! CAUSE ( _! 2+ "O4 ,O!RS SAY ? UN;Y
& 2+1 ( : ?+S 3SI/ & H BE5 MADE1 IS
FIRE1 & O!RS SAY X IS AIR4 ,A SIMIL>
VIEW IS EXPRESS$ 0^? :O MAKE ! ELE;TS M
?AN "O2 = ^! AL M/ SAY T UN;Y & 2+ >E
PRECISELY ALL ! ?+S : !Y SAY >E
PR9CIPLES4
  7,A7 ,IF WE D N SUPPOSE UN;Y & 2+ 6BE
SUB/.ES1 X FOLL[S T N"O (! O!R UNIV]SALS
IS A SUB/.E2 = ^! >E MO/ UNIV]SAL ( ALL1
& IF "! IS NO UN;Y XF OR 2+-XF1 "! W
SC>CELY 2 9 ANY O!R CASE ANY?+ A"P F :AT
>E CALL$ ! 9DIVIDUALS4 ,FUR!R1 IF UN;Y
IS N A SUB/.E1 EVID5TLY NUMB] AL W N
EXI/ Z AN 5T;Y SEP>ATE F ! 9DIVIDUAL
?+S2 = NUMB] IS UNITS1 &! UNIT IS
PRECISELY A C]TA9 K9D ( "O4
  ,B 7,B7 IF "! IS A UN;Y-XF &A 2+ XF1
UN;Y & 2+ M/ 2 _! SUB/.E2 = X IS N "S?+
ELSE T IS PR$ICAT$ UNIV]S,Y (! ?+S T >E
& >E "O1 B J UN;Y & 2+4 ,B IF "! IS 6BE
A 2+-XF &A UN;Y-XF1 "! IS M* DI6ICULTY 9
SEE+ H[ "! W 2 ANY?+ ELSE 2SS ^!1-,I
M1N1 H[ ?+S W 2 M ?AN "O 9 NUMB]4 ,= :AT
IS DI6]5T F 2+ DOES N EXI/1 S T X
NECESS>ILY FOLL[S1 AC 6! >GU;T (
,P>M5IDES1 T ALL ?+S T >E >E "O & ? IS
2+4
  ,"! >E OBJEC;NS 6BO? VIEWS4 ,= :E!R
UN;Y IS N A SUB/.E OR "! IS A UN;Y-XF1
NUMB] _C 2 A SUB/.E4 ,WE H ALR SD :Y ?
RESULT FOLL[S IF UN;Y IS N A SUB/.E2 &
IF X IS1 ! SAME DI6ICULTY >ISES Z >OSE )
REG>D 62+4 ,= :;E IS "! 6BE ANO!R "O 2SS
UN;Y-XF8 ,X M/ 2 N-"O2 B ALL ?+S >E EI
"O OR _M1 &(! _M EA* IS "O4
  ,FUR!R1 IF UN;Y-XF IS 9DIVISI#1 AC
6,Z5O'S PO/ULATE X W 2 NO?+4 ,= T : NEI
:5 A4$ MAKES A ?+ GRT] NOR :5 SUBTRACT$
MAKES X LESS1 HE ASS]TS 6H NO 2+1
EVID5TLY ASSUM+ T :AT"E HAS 2+ IS A
SPATIAL MAGNITUDE4 ,& IF X IS A
MAGNITUDE1 X IS CORPOR1L2 =! CORPOR1L
HAS 2+ 9 E DIM5.N1 :ILE ! O!R OBJECTS (
MA!MATICS1 E4G4 A PLANE OR A L9E1 A4$ 9
"O WAY W 9CR1SE :AT !Y >E A4$ TO1 B 9
ANO!R WAY W N D S1 &A PO9T OR A UNIT
DOES S 9 NO WAY4 ,B1 S9CE 8 !ORY IS (A
L[ ORD]1 & AN 9DIVISI# ?+ C EXI/ 9 S* A
WAY Z 6H A DEF;E EV5 AG/ HM 7=! 9DIVISI#
:5 A4$ W MAKE ! NUMB]1 ?\< N ! SIZE1
GRT]71-YET H[ C A MAGNITUDE PROCE$ F "O
S* 9DIVISI# OR F _M8 ,X IS L SAY+ T !
L9E IS MADE \ ( PO9TS4
  ,B EV5 IF ORE SUPPOSES ! CASE 6BE S*
T1 Z "S SAY1 NUMB] PROCE$S F UN;Y-XF &
"S?+ ELSE : IS N "O1 N"O ! LESS WE M/
9QUIRE :Y & H[ ! PRODUCT W 2 "S"TS A
NUMB] & "S"TS A MAGNITUDE1 IF ! N-"O 0
9EQUAL;Y & 0 ! SAME PR9CIPLE 9 EI CASE4
,= X IS N EVID5T H[ MAGNITUDES CD PROCE$
EI F ! "O & ? PR9CIPLE1 OR F "S NUMB] &
? PR9CIPLE4
                   #E
  7#AD7 ,A "Q 3NECT$ ) ^! IS :E!R NUMB]S
& BODIES & PLANES & PO9TS >E SUB/.ES (A
K9D1 OR N4 ,IF !Y >E N1 X BA6LES U 6SAY
:AT 2+ IS & :AT ! SUB/.ES ( ?+S >E4 ,=
MODIFIC,NS & MOVE;TS & REL,NS & 4POSI;NS
& RATIOS D N SEEM 69DICATE ! SUB/.E (
ANY?+2 = ALL >E PR$ICAT$ (A SUBJECT1 &
N"O IS A ,8?0'4 ,& Z 6! ?+S : MI<T SEEM
MO/ ( ALL 69DICATE SUB/.E1 WAT] & E>? &
FIRE & AIR1 ( : -POSITE BODIES 3SI/1 H1T
& COLD &! L >E MODIFIC,NS ( ^!1 N
SUB/.ES1 &! BODY : IS ?US MODIFI$ AL"O
P]SI/S Z "S?+ R1L & Z A SUB/.E4 ,B1 ON !
O!R H&1 ! BODY IS SURELY LESS (A SUB/.E
?AN ! SURFACE1 &! SURFACE ?AN ! L9E1 &!
L9E ?AN ! UNIT &! PO9T4 ,=! BODY IS B.D$
0^!2 & !Y >E ?"\ 6BE CAPA# ( EXI/+ )\T
BODY1 B BODY 9CAPA# ( EXI/+ )\T ^!4 ,?
IS :Y1 :ILE MO/ (! PHILOSOPH]S &! E>LI]
AM;G !M ?"\ T SUB/.E & 2+ 7 ID5TICAL )
BODY1 & T ALL O!R ?+S 7 MODIFIC,NS ( ?1
S T ! F/ PR9CIPLES (! BODIES 7 ! F/
PR9CIPLES ( 2+1 ! M REC5T & ^? :O 7 HELD
6BE WIS] ?"\ NUMB]S 7 ! F/ PR9CIPLES4 ,Z
WE SD1 !N1 IF ^! >E N SUB/.E1 "! IS NO
SUB/.E & NO 2+ AT ALL2 =! A3ID5TS ( ^! X
_C 2 "R 6CALL 2+S4
  ,B IF ? IS ADMITT$1 T L9ES & PO9TS >E
SUB/.E M ?AN BODIES1 B WE D N SEE 6:AT
SORT ( BODIES ^! CD 2L;G 7= !Y _C 2 9
P]CEPTI# BODIES71 "! C 2 NO SUB/.E4-
,FUR!R1 ^! >E ALL EVID5TLY DIVI.NS (
BODY1-"O 9 BR1D?1 ANO!R 9 DEP?1 ANO!R 9
L5G?4 ,2SS ?1 NO SORT ( %APE IS PRES5T 9
! SOLID M ?AN ANY O!R2 S T IF ! ,H]MES
IS N 9 ! /"O1 NEI IS ! HALF (! CUBE 9 !
CUBE Z "S?+ DET]M9ATE2 "!=E ! SURFACE IS
N 9 X EI2 = IF ANY SORT ( SURFACE 7 9 X1
! SURFACE : M>KS (F ! HALF (! CUBE WD 2
9 X TOO4 ,&! SAME A3.T APPLIES 6! L9E &
6! PO9T &! UNIT4 ,"!=E1 IF ON ! "O H&
BODY IS 9 ! HI<E/ DEGREE SUB/.E1 & ON !
O!R H& ^! ?+S >E S M ?AN BODY1 B ^! >E N
EV5 9/.ES ( SUB/.E1 X BA6LES U 6SAY :AT
2+ IS & :AT ! SUB/.E ( ?+S IS4-,= 2SS
:AT HAS BE5 SD1 ! "QS ( G5],N & 9/RUC;N
3FRONT U ) FUR!R P>ADOXES4 ,= IF SUB/.E1
N HAV+ EXI/$ 2F1 N[ EXI/S1 OR HAV+ EXI/$
2F1 AFWS DOES N EXI/1 ? *ANGE IS ?"\ 6BE
A3OMPANI$ 0A PROCESS ( 2COM+ OR P]I%+2 B
PO9TS & L9ES & SURFACES _C 2 9 PROCESS
EI ( 2COM+ OR ( P]I%+1 :5 !Y AT "O "T
EXI/ & AT ANO!R D N4 ,= :5 BODIES -E
963TACT OR >E DIVID$1 _! B.D>IES
SIMULTANE\SLY 2COME "O 9 ! "O CASE :5 !Y
T\*1 & TWO 9 ! O!R-:5 !Y >E DIVID$2 S T
:5 !Y H BE5 PUT TGR "O B.D>Y DOES N EXI/
B HAS P]I%$1 & :5 !Y H BE5 DIVID$ !
B.D>IES EXI/ : 2F DID N EXI/ 7= X _C 2
SD T ! PO9T1 : IS 9DIVISI#1 0 DIVID$
96TWO74 ,& IF ! B.D>IES -E 962+ & C1SE
6BE1 F :AT D !Y -E 962+8 ,A SIMIL> A3.T
MAY AL 2 GIV5 (! ,8N[0' 9 "T2 = ? AL _C
2 9 PROCESS ( -+ 962+ OR ( C1S+ 6BE1 B
YET SEEMS 6BE ALW DI6]5T1 : %[S T X IS N
A SUB/.E4 ,& EVID5TLY ! SAME IS TRUE (
PO9TS & L9ES & PLANES2 =! SAME >GU;T
APPLIES1 S9CE !Y >E ALL ALIKE EI LIMITS
OR DIVI.NS4
                   #F
  ,9 G5]AL "O MI<T RAISE ! "Q :Y AF ALL1
2SS P]CEPTI# ?+S &! 9T]M$IATES1 WE H
6LOOK = ANO!R CLASS ( ?+S1 I4E4 ! ,=MS :
WE POSIT4 ,IF X IS = ? R1SON1 2C !
OBJECTS ( MA!MATICS1 :ILE !Y DI6] F !
?+S 9 ? _W 9 "S O!R RESPECT1 DI6] N AT
ALL 9 T "! >E _M (! SAME K9D1 S T _! F/
PR9CIPLES _C 2 LIMIT$ 9 NUMB] 7J Z !
ELE;TS ( ALL ! LANGUAGE 9 ? S5SI# _W >E
N LIMIT$ 9 NUMB]1 B 9 K9D1 UN.S "O TAKES
! ELE;TS ( ? 9DIVIDUAL SYLLA# OR ( ?
9DIVIDUAL >TICULATE S.D-^: ELE;TS W 2
LIMIT$ EV5 9 NUMB]2 S IS X AL 9 ! CASE (
! 9T]M$IATES2 = "! AL ! MEMB]S (! SAME
K9D >E 9F9ITE 9 NUMB]71 S T IF "! >E N-
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