Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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1anguli CTpad angulum CTP.Quæ quidem rationes ex ſinu­
bus angulorum contactus ac differentiarum angulorum facile colli­
guntur.
His autem inter ſe collatis, prodit curvatura Figuræ Cpa
in aad ipſius curvaturam in C,ut AT cub+(16824/100000)CTqXAT
ad CT cub+(16824/100000) ATqXCT.Ubi numerus (16824/100000) deſignat
differentiam quadratorum angulorum CTP& CTpappli­
catam ad quadratum anguli minoris CTP,ſeu (quod per­
inde eſt) differentiam quadratorum temporum 27d. 7h. 43′, &
29d. 12h. 44′, applicatam ad quadratum temporis 27d. 7h. 43′,
LIBER
TERTIUS.
Igitur cum adeſignet Syzygiam Lunæ, & Cipſius Quadratu­
ram, proportio jam inventa eadem eſſe debet cum proportione
curvaturæ Orbis Lunæ in Syzygiis ad ejuſdem curvaturam in
Quadraturis, quam ſupra invenimus.
Proinde ut inveniatur pro­
portio CTad AT,duco extrema & media in ſe invicem. Et
termini prodeuntes ad ATXCTapplicati, fiunt 2062, 79 CTqq
-2151969 NXCTcub+368676 NXATXCTq+36342 ATq
XCTq-362047 NXATqXCT+2191371 NXAT cub+
4051, 4 ATqq=0. Hic pro terminorum AT& CTſemiſum­
ma N ſcribo 1, & pro eorundem ſemidifferentia ponendo x,fit
CT=1+x,& AT=1-x: quibus in æquatione ſcriptis, &
æquatione prodeunte reſoluta, obtinetur xæqualis 0,00719, &
inde ſemidiameter CTfit 1,00719, & ſemidiameter AT0,99281,
qui numeri ſunt ut (70 1/24) & (69 1/24) quam proxime.
Eſt igitur di­
ſtantia Lunæ a Terra in Syzygiis ad ipſius diſtantiam in Quadra­
turis (ſepoſita ſcilicet Eccentricitatis conſideratione) ut (69 1/24) ad
(70 1/24), vel numeris rotundis ut 69 ad 70.
PROPOSITIO XXIX. PROBLEMA X.
Invenire Variationem Lunæ.
Oritur hæc inæqualitas partim ex forma Elliptica orbis Luna­
ris, partim ex inæqualitate momentorum areæ, quam Luna radio
ad Terram ducto deſcribit.
Si Luna Pin Ellipſi DBCAcirca
Terram in centro Ellipſeos quieſcentem moveretur, & radio TP
ad Terram ducto deſcriberet aream CTPtempori proportiona­
lem; eſſet autem Ellipſeos ſemidiameter maxima CTad ſemi­
diametrum minimam TAut 70 ad 69: foret tangens anguli
CTPad tangentem anguli motus medii a Quadratura Ccompu­
tati, ut Ellipſeos ſemidiameter TAad ejuſdem ſemidiametrum

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