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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 401, page id 1041163592:0435
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PRTNCTPTA MATHEMATICA.
anguli CTp ad angulum CTP. Oux quidem rationes ex SInu. Eiven
bus angulorum contactus ac difterenciarum ansulorum Facile colli- Pexriv.
suntur. Ilis autem inter se collatis, prodit curratura Pigurae C’p a
in a ad ipsius curraturam in C, ut AT cub + 100 CFgX AL
2
2d CTcub + 200000 TgXCT. Obi numerus 1000 delignaE
difterentiam quadratorum angulorum CF~ dc C F p applI
cacam 2d quadratum anguli minoris CFP, seu (quod Per.
inde CA) differentiam quadratorum temporum 278. 76. 43, e
298. 121. 443 applicatam ad quadracum temporis 27 d. 7n. 4.3.
gitur cum a delionet Srrsiam Lunxe, et C. iplius Ouadratu-
ram, proportio jam inventa eadem ese debet cum proportione
curvaturE Orbis Lunxe in Syzygiis ad ejusdem curvacuram in
Duadraturis, quam supra invenimus. Proinde uc inveniatur pro.
portio CT ad AT, duco extrema ex media in se invicem. EC
cermini prodeuntes ad ATX C.I applicatis AunE 2062,79CF99
2151969N XCT cub + 368676I Z ATXCF9 + 36342 A4
XCT9 = 362047 N X ATgX CF + 219137FN X AY cub +
4051, 4 ATgg =0. Hlic pro terminorum AY e CF Temilum
ma  Ccribo I, ec pro corundem lemidisterentia ponendo x, AC
CT = T + x, e AT = 1 = x: quibus in aequatione lcripeis, et
aequatione prodeunce resoluta, obcinctur x aequalis 0,00719, de
inde lemidiameter C. F fc 2,00719. e Cemidiameter AY 0,9928T,
qui numeri lunE ut 7054 ec 6924 quam proxime. FA isitur di-
Stancia Lunae a Terra in Syzy eiis ad ipsius distantiam in Guadra-
curis (sepolica scilicet Eccentricicatis consideratione). ut 6974 2d
7024 vel numeris rocundis ut 69 ad 70.
PROPOSITIO ZXIZ. PROBLEMA Z.
Invenire Variationem Lunae.
Oritur haec inaequalitas partim ex Forma Flliprica orbis Luna-
ris, parrim ex inaequalitate momentorum arcae, quam Luna radio
ad Terram ducto describit. Si Luna P in EIlipA D BC A circa
Terram in centro Fllipleos quiescentem moveretur, et radio TF
ad Terram ducto describeret aream C T F tempori proportiona-
lem; eNec aurem Fllipleos semidiameter maxima C. T ad semi-
diametrum minimam Y  ut 70 2d 69: Foret tangens anguli
E F ad tangentem anguli motus medii a Guadratura C compu-
cacis ut Lllipseos Cemidiameter T A ad ejusdem semidiamecrum
i