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# Title: [Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa (shelfmark Leibn. Marg. 124)
# Folio 382, page id 1040780814:0400
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382
AST RONOMTE PHZSTCA
liD. 11.
quatore Luna ad consimilem Vim in squatore lerra: Sed datus (pes
Prop. EII. Lib. III.) ratio inter Vim centritusam in Aiquatore Terra
e Graritatem in Terrae Superticie, _ ex PrOD. LNH. datur ratio
Graritatis in Terrae superticie ad Graritatem in superticie Luna;
e isitur data erit ratio ex tribus hisce composita, nempe ratio VIS
centritusa in Lquatore Lunx ad Graritatem versus Lunx cen
trum qua in ejus superticie obtinet, qua (in dicta PrOP. LIT. Lib.
III.) oltensa est eadem cum ratione ex cessis Diametri Lunx secun-
dum ejus A quatorem ad LunX AXem. Ideoque (per 6. D at.) da-
bitur ratio inter Lunae Axem ec ejus Diametrum quamris Axi nOr
malem; hoc est, inter axes FMlipIS CujuS FOTatIONO CIrCa aXeM
minorem Ac Sphaerois prolata Lunae similis.
Ratio praedicta rationem aequalitatis adeo appropinquat, ut Luna
Fixura sphaeroides prolata, hinc oriunda, parum admodum dit
Terat à Sphaerica.
PROPOSITIO LXIV.
LTelluris Clobus ubique prosundo Mari opertus esdet, inauer
Dhic Fixuram sphaeroidem obloneam fere, cujus avis productus
per Lunam transiret.
DesIOneE CircuIUS CeNErO Y Fellurem, cireuluS CONFrO F Lunam:
Patet, quod si nulla esset actio Luna nec alterius cujulris extranet
corporis in Tellurem, hanc cum undique Auido operta st sphae
ricam ese, nisi quatenus ab hac deriat propter rationes PFOD. XXXI.
Lib. J. indicatas, de qua deriatione hic non asitur. Verum, quon
am Telluris partes singula grares sunt in Lunam, de gravitas ver
Lus Lunam (sieut versus corpus aliud quodris) est rociproce ut qua
dratum distantia ab illius centro; si (ut in PrOp. L X. L Ib. T. C PFOP. I.
Lib. IV. Fuse explicatum est) recta L r exponat Craritatem accelera
tricem corporis in Perra Cen
tro locati versus Lunam, Sit.
que (in (8. T.) X qualibet Fluidi
marini particula, s porro in re-
Eta L F (CaVO pTOdUETA) TUmatUE
LK aqualis LY, QET F qua TiF ad
F. K in duplicata ratione LK ad
L. F; exponet LF Graritatem
corporis ad P locati versuS L,
quae (uc rulgo notum) diridi-
cur in Vires ut EG _ GL. 8
cum iis directionibus: Si au-
tem a Vi illa qua corpus ad P.
Potitum urSCtE, qua CAt ut
GL, auteratur ViS UIE YF. qud Ferra centrum unaque intesra l’el
Ius versus Lunam ursetur: relinguentur Vires ut FC _E CT d cum
directionibus FC _ Cr, quibus COrpUS ad F POSILIM UrSETUE, PTX
er Vim proxria Coraricatis qud P versus Zerra centrum rendit.