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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 430, page id 1041163592:0464
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430
PHITLOSOPMITA NATVRALIS
DEMONBE Corol. 2. Cum vis Lunae ad Mare movendum, sc 2d rim gravi-
SYSTENATELaTIS UF F 2d 2871400, perspicuum cA quod vis illa (It lonse
minor quam quae rel in experimentis Pendulorum, vel in Scaticis
auE FIydroctaticis quibuscunque senciri possit. In Acu (ol0 ma-
rino hec vis sensibilem edic efectum.
Crrol. 3. Duoniam vis Luux ad Mare movendum, est ad Solis
vim consimilem ut 4,4815 2d 2, e vires illae (per Corol. 14.
PEOP. LXVT. Lib. l.) Tunc ut densitates corporum Lunxe de Solis
ec cubi diametrorum apparentium conjunctim; denficas L unx crit
2d denlitarem Solis, uc 4,4815 ad i directe e cubus diametri
Luux 2d cubum diamerri Solis inverse: id est (cum diametri me-
dioeres apparentes Lunxe e Solis (InE 31. 162 _ 32. 12) ue
489F 2d 1000. Densicas aurem Solis Crat ad densIFALeM TCFTX,
UC 100 2d 296; _ propeerea densitas Lunx est ad densitatem
Terrae, ut 4891 2d 3900 Teu 2Y 2d 17. Fct isitur corpus Lunx
densius e magis terrestre quam Terra nostra.
Corol. q. tE cum vera diameter Lunae (ex Obserrationibus
Astronomicis) sic ad veram diametrum PerrX, UF 100 2d 365;
erie massa Lunae ad massam Terrae, uF 1 2d 39, 371.
Corol. 5. EF graricas acceleraerix in superticie Luna, erit quali
triplo minor quam gravitas acceleratrix in (uperheie Terrae.
Corol. 6. FE distantia Centri LUnX a CenErO FerrXs erit ad di-
Santiam centri Lunxe a communi graritatis centro Terra ee Lunx,
UC 40,371 2d 39, 37T.
Corol. 7. Fe medioeris distantia ceneri Lunx a Centro Terrae, erit
Semidiametrorum maximarum Perrx 60+ quamproxime. Nam
semidiameter maxima Terrae Fuic pedum Parisiensium 19767630,
e medioeris distantia centrorum Perrae ec Lunae ex hujusmodi
Lemidiametris 60 constans, aequalis es pedibus 1790999707. RF
haec distantia (per Corollarium superius) est ad distantiam cencri
Lunae a communi sravitatis Centro Terra _ Lunae, uE 40, 37F 2d
39, 37r, qua proinde cA pedum 1161498340. FF cum Luna rC-
volratur respectu Fixarum, diebus 27, horis7 ec minutis primis 4353
linus versus anguli quem Luna, cempore minuci unius primi motu
suo medio, circa commune gravitatis centrum Perrxe de Lunxe de-
fcribie, cs 1275235, existente radio 100,000000, 000000. lC ut
radius cs ad hunc sinum versum, ica (unc pedes 1162498340 ad
pedes 14, 8r1833. Luna igitur ri illa qua retinctur in Orbes ca-
dendo in Terram, tempore minuti unius primi describet pedes
24,812833. E.F A haec vis augeatur in ratione 17746 2d 17845, ha-
bebitur