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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 395, page id 1041163592:0429
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1II
PRTNCIDTA MATHEMATIOA.
Solem. Fa componitur ex partibus SM, L. HI, quarum L. M d LIvE
ipsus SM ParS L M percurbac motum Lunae, uc in Libri primi FcarI
PrOP. FXVI. e ejus Corollariis expotirum cst. OUaFENUS Perr2
ec Luna circum commune graritatis centrum revolvuntur, Pertur-
babitur etiam motus Terrae circa cenerum illud a riribus consimi
libus; sed summas tam virium quam moruum reterre licet ad Lu-
nam, ex Cummas virium per lineas ipsis anal0925 FM ec ML
delignare. Vis ML (in medioeri lua quantitate) eA ad vim
centripetum, qua Luna in Orbe suo circa Lerram quiescentem ad
dittantiam PT revolvi posset, in duplicata ratione temporum
periodicorum Luux circa Terram a Terrae circa Solem, (per
Corol. 17. PFOD. LXVr. Lib. l.) hoc eA, in duplicata ratione die
rum 27. Bor. 7. min. 4.3. 2d dics 365. Bor. 6. min. 9. id est, uE 1000
24 178725, Teu F 2d 17826. Invenimus autem in Propositione
quarca quod, A Terra ee Luna circa commune gravitatis centrum
revolvancur, carum distantia mediocris ab invicem cric 60= Temi-
diametrorum mediocrium Terrae quamproxime. Ec vis qua Luna
in Orbe circa Terram quiescentem, ad distantiam P Y Cemidiame-
erorum cerrestrium 602 revolri porset, est ad vim, qua codem
cempore ad distantiam lemidiameerorum 60 revolvi poset, uE
602 2d 60; _ haec vis ad vim graritatis apud nos ut L ad
60760 quamproxime. Ideoque ris mediocris ML eA ad vim
graritaris in superticie Terrae, UE XZ 607 ad 60X60X60X 178+07
seu 1 2d638092,6. Vnde ex proportione linearum Y M, M L.
datur etiam vis YMI: et hxe Pune vires Solis quibus Lunx mOtus
percurbantur. d. F. I.
PROPOSITIO ZXVI. PROBLEMA VII
Invenire incrementum horarium areae quam Luna, radio ad Ter
ram ducto, in Orbe circulari describit.
Diximus aream, quam Luna radio ad Ferram ducto describie,
esse cempori proporcionalem, nisi quatenus motus Lunaris ab
actione Solis curbatur. Inaequalicatem momenti (vel incremenei
horarii) hic inveltisandam proxonimus. Ot compuratio Facilior
reddatur, Ensamus orbem Lunae circularem esse, e inaequalitates
omnes neslisamus, ca sola excepta, de qua hic asitur. Ob in-
gentem vero Solis distantiam, ponamus criam lineas SP, S7 Sbi
inricem parallelas esse. Hoc pacto vis L. M reduCCtuE TEPCF
FCC.
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