Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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pagenum
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409
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in
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f,
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conveniant autem hæ tangentes in axe
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TQ
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ad
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Y
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; & ſi
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note438
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<
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ML
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deſignet ſpatium quod Luna in Circulo revolvens, interea
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dum deſcribit arcum
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PM,
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urgente & impellente vi prædicta
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3
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IT,
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motu tranſverſo deſcribere poſſet, &
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ml
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deſignet ſpatium
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quod Luna in Ellipſi revolvens eodem tempore, urgente etiam vi
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3
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emph
type
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IT,
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deſcribere poſſet; & producantur
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LP
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&
<
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lp
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donec occurrant
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plano Eclipticæ in
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G
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&
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g
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; & jungantur
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FG
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&
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fg,
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quarum
<
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FG
<
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type
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<
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producta ſecet
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pf, pg
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&
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TQ
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in
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c, e
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&
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R
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reſpective, &
<
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fg
<
emph.end
type
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pro
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ducta ſecet
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TQ
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in
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r
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: Quoniam vis 3
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IT
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ſeu 3
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PK
<
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type
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in Circulo
<
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eſt ad vim 3
<
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type
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IT
<
emph.end
type
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ſeu 3
<
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pK
<
emph.end
type
="
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"/>
in Ellipſi, ut
<
emph
type
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"/>
PK
<
emph.end
type
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italics
"/>
ad
<
emph
type
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pK,
<
emph.end
type
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ſeu
<
emph
type
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AT
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ad
<
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<
emph
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aT
<
emph.end
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; erit ſpatium
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ML
<
emph.end
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vi priore genitum, ad ſpatium
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ml
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emph.end
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vi po
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ſteriore genitum, ut
<
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PK
<
emph.end
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ad
<
emph
type
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pK,
<
emph.end
type
="
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id eſt, ob ſimiles figuras
<
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<
emph
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PYKp
<
emph.end
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&
<
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FYRc,
<
emph.end
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ut
<
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FR
<
emph.end
type
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ad
<
emph
type
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"/>
cR.
<
emph.end
type
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"/>
Eſt autem
<
emph
type
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ML
<
emph.end
type
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"/>
ad
<
emph
type
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FG
<
emph.end
type
="
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"/>
(ob
<
lb
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ſimilia triangula
<
emph
type
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"/>
PLM, PGF
<
emph.end
type
="
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) ut
<
emph
type
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PL
<
emph.end
type
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ad
<
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PG,
<
emph.end
type
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hoc eſt (ob
<
lb
/>
parallelas
<
emph
type
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"/>
Lk, PK, GR
<
emph.end
type
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"/>
) ut
<
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"/>
pl
<
emph.end
type
="
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"/>
ad
<
emph
type
="
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"/>
pe,
<
emph.end
type
="
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"/>
id eſt, (ob ſimilia trian
<
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gula
<
emph
type
="
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"/>
plm, cpe
<
emph.end
type
="
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"/>
) ut
<
emph
type
="
italics
"/>
lm
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
ce
<
emph.end
type
="
italics
"/>
; & inverſe ut
<
emph
type
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italics
"/>
LM
<
emph.end
type
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"/>
eſt ad
<
emph
type
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lm,
<
emph.end
type
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ſeu
<
lb
/>
<
emph
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FR
<
emph.end
type
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ad
<
emph
type
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"/>
cR,
<
emph.end
type
="
italics
"/>
ita eſt
<
emph
type
="
italics
"/>
FG
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
ce.
<
emph.end
type
="
italics
"/>
Et propterea ſi
<
emph
type
="
italics
"/>
fg
<
emph.end
type
="
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"/>
eſſet ad
<
emph
type
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"/>
ce
<
emph.end
type
="
italics
"/>
ut
<
lb
/>
<
emph
type
="
italics
"/>
fY
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
cY,
<
emph.end
type
="
italics
"/>
id eſt, ut
<
emph
type
="
italics
"/>
fr
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
cR
<
emph.end
type
="
italics
"/>
(hoc eſt, ut
<
emph
type
="
italics
"/>
fr
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
FR
<
emph.end
type
="
italics
"/>
&
<
emph
type
="
italics
"/>
FR
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
cR
<
emph.end
type
="
italics
"/>
<
lb
/>
conjunctim, id eſt, ut
<
emph
type
="
italics
"/>
fT
<
emph.end
type
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italics
"/>
ad
<
emph
type
="
italics
"/>
FT
<
emph.end
type
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italics
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&
<
emph
type
="
italics
"/>
FG
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
ce
<
emph.end
type
="
italics
"/>
conjunctim,) quo
<
lb
/>
niam ratio
<
emph
type
="
italics
"/>
FG
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
ce
<
emph.end
type
="
italics
"/>
utrinque ablata relinquit rationes
<
emph
type
="
italics
"/>
fg
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
FG
<
emph.end
type
="
italics
"/>
<
lb
/>
&
<
emph
type
="
italics
"/>
fT
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
FT,
<
emph.end
type
="
italics
"/>
foret
<
emph
type
="
italics
"/>
fg
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
FG
<
emph.end
type
="
italics
"/>
ut
<
emph
type
="
italics
"/>
fT
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
FT
<
emph.end
type
="
italics
"/>
; atque adeo anguli,
<
lb
/>
quos
<
emph
type
="
italics
"/>
FG
<
emph.end
type
="
italics
"/>
&
<
emph
type
="
italics
"/>
fg
<
emph.end
type
="
italics
"/>
ſubtenderent ad Terram
<
emph
type
="
italics
"/>
T,
<
emph.end
type
="
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"/>
æquarentur inter ſe. </
s
>
<
s
>
<
lb
/>
Sed anguli illi (per ca quæ in præcedente Propoſitione expoſui
<
lb
/>
mus) ſunt motus Nodorum, quo tempore Luna in Circulo ar
<
lb
/>
cum
<
emph
type
="
italics
"/>
PM,
<
emph.end
type
="
italics
"/>
in Ellipſi arcum
<
emph
type
="
italics
"/>
pm
<
emph.end
type
="
italics
"/>
percurrit: & propterea motus
<
lb
/>
Nodorum in Circulo & Ellipſi æquarentur inter ſe. </
s
>
<
s
>Hæc ita ſe
<
lb
/>
haberent, ſi modo
<
emph
type
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fg
<
emph.end
type
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"/>
eſſet ad
<
emph
type
="
italics
"/>
ce
<
emph.end
type
="
italics
"/>
ut
<
emph
type
="
italics
"/>
fY
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
cY,
<
emph.end
type
="
italics
"/>
id eſt, ſi
<
emph
type
="
italics
"/>
fg
<
emph.end
type
="
italics
"/>
æqua
<
lb
/>
lis eſſet (
<
emph
type
="
italics
"/>
ceXfY/cY
<
emph.end
type
="
italics
"/>
). Verum ob ſimilia triangula
<
emph
type
="
italics
"/>
fgp, cep,
<
emph.end
type
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italics
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eſt
<
emph
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italics
"/>
fg
<
emph.end
type
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<
lb
/>
ad
<
emph
type
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italics
"/>
ce
<
emph.end
type
="
italics
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ut
<
emph
type
="
italics
"/>
fp
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
cp
<
emph.end
type
="
italics
"/>
; ideoque
<
emph
type
="
italics
"/>
fg
<
emph.end
type
="
italics
"/>
æqualis eſt (
<
emph
type
="
italics
"/>
ceXfp/cp
<
emph.end
type
="
italics
"/>
); & propterea
<
lb
/>
angulus, quem
<
emph
type
="
italics
"/>
fg
<
emph.end
type
="
italics
"/>
revera ſubtendit, eſt ad angulum priorem, quem
<
lb
/>
<
emph
type
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"/>
FG
<
emph.end
type
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ſubtendit, hoc eſt, motus Nodorum in Ellipſi ad motum
<
lb
/>
Nodorum in Circulo, ut hæc
<
emph
type
="
italics
"/>
fg
<
emph.end
type
="
italics
"/>
ſeu (
<
emph
type
="
italics
"/>
ceXfp/cp
<
emph.end
type
="
italics
"/>
) ad priorem
<
emph
type
="
italics
"/>
fg
<
emph.end
type
="
italics
"/>
ſeu
<
lb
/>
(
<
emph
type
="
italics
"/>
ceXfY/cY
<
emph.end
type
="
italics
"/>
), id eſt, ut
<
emph
type
="
italics
"/>
fpXcY
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
fYXcp,
<
emph.end
type
="
italics
"/>
ſeu
<
emph
type
="
italics
"/>
fp
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
fY
<
emph.end
type
="
italics
"/>
&
<
emph
type
="
italics
"/>
cY
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
cp,
<
emph.end
type
="
italics
"/>
<
lb
/>
hoc eſt, ſi
<
emph
type
="
italics
"/>
ph
<
emph.end
type
="
italics
"/>
ipſi
<
emph
type
="
italics
"/>
TN
<
emph.end
type
="
italics
"/>
parallela occurrat
<
emph
type
="
italics
"/>
FP
<
emph.end
type
="
italics
"/>
in
<
emph
type
="
italics
"/>
h,
<
emph.end
type
="
italics
"/>
ut
<
emph
type
="
italics
"/>
Fh
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
FY
<
emph.end
type
="
italics
"/>
<
lb
/>
&
<
emph
type
="
italics
"/>
FY
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
FP
<
emph.end
type
="
italics
"/>
; hoc eſt, ut
<
emph
type
="
italics
"/>
Fh
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
FP
<
emph.end
type
="
italics
"/>
ſeu
<
emph
type
="
italics
"/>
Dp
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
DP,
<
emph.end
type
="
italics
"/>
adeoque
<
lb
/>
ut area
<
emph
type
="
italics
"/>
Dpmd
<
emph.end
type
="
italics
"/>
ad aream
<
emph
type
="
italics
"/>
DPMd.
<
emph.end
type
="
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"/>
Et propterea, cum area po-</
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