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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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PRINCIPTA MATHIEMATICA.
PROPOSITIOMI THEOREMA HI.
Vim qua Luna retinetur in Orbe suo respicere Terram, e esse re-
ciproce ut quadratum distantiee locorum ab ipsius centro.
Patet altertionis pars Prior per PhenOmenON sextuM, et PrOPO-
policionem secundam vel tertiam Libri primi: de pars posterior
per mocum cardissimum Lunaris Apogei. Nam motus ille, qui
lingulis revolutionibus eA graduum eantum trium ex minutorum
erium in consequentia, contemni potest. Patet enim (per Corol. I.
PFOP. XLV. Lib. I.) quod s dictantia LUINX a CeNErO PCFEX SIC ad
Lemidiametrum PCrEX UE D ad F; vis a qua motus talis oriatur lIE
rCCIPROCC VE D2, 4, id cA, reciproco ut ca ipsius D dignitas cu-
jus index est 224, hoc est, in ratione distancix paulo majore quam
duplicata inverse, scd quae partibus 593 propius ad duplicatam
quam ad criplicatam accedit. Oritur vero ab actione Solis (uri
Dotthac dicetur) et proprerea hic neglisendus eAt. Actio Solis
quatenus Lunam distrahie a Ferra, est ut distantia Lunxe a Terra
quamproxime; ideoque (per ca quae dicuntur in C Orol. 2. Prop.
ZLV. Lib. I.) es ad Lunae vim centripetam ut 2 2d 357,45 circi-
Ter, Peu L ad 17845. Et neslecta Solis vi cantilla, vis reliqua qua
Luna retinetur in Orbe erit reciproce ut D2. Id quod eriam
plenius constabir conterendo hanc vim cum vi Gravitatis, vE AC
in PropOCriOnE sEGUentE.
Corol. Si vis centripeta medioeris qua Luna retinetur in Orbe,
augeatur primo in racione 17745 ad 27825, deinde criam in rati-
one duplicata semidiameeri Perrae ad medioerem dictantiam centri
Lunae a centro Terrae: habebitur vis centripeta Lunaris ad super-
siciem Terrae, polito quod vis illa descendendo ad superticiem
TErrA Perpetuo auseatur in reciproca alcicudinis ratione du-
plicata.
PROPOSITIOIV. THEOREMA WV.
Lunam gravitare in Terram, e vi gravitatis retrahi semper a
motu rectilineo, es in Orbe suo retineri.
Liunae distantia medioeris a Ferra in Syzygiis est Pemidiameero-
rum cerrestrium, secundum plerosque AAtronomorum 59, secun-
dum Pendelinum 60. secundum Copernicum 603, et sccundum Ty-
A ad
ehonem
L IBEK
TRXTIVS.
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