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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 262, page id 1041163592:0296
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HIIIIIII
262
PTITLOSODMT MATDRALIS
Corol. Inde nec motus partium Auidi incer se, per prestionem.
copponon Ruido ubiris in externa superticie illatam, mutari portune, nil qua-
tenuS aut fgura Superticiei alicubi mutatur, aut omnes Auidi parres
incensius vel remissius selc premendo difficilius vel facilius labun-
tur inter sc.
PROPOSITIO XX. THFOREMA XV.
Si Fluidi Sphaerici, e in aequalibus a centro distantiis homogenei,
fundo Sphaerico concentrico incumbentis partes singulae versus
centrum totius cravitent; sustinet fundum pondus Cylindri, cu-
jus basis aequalis est supersiciei fundi, e altitudo eadem qua
Fluidi incumbentis.
Sit D HM superticies Fundis et A F. L
Superticies superior Auidi. Superticiebus
Sphaericis innumeris BF R, CCL distin-
suatur Ruidum in Orbes concentricos ae
qualicer cracos; ec concipe vim grarita
eis agere Colummodo in Cuperticiem supe
riorem Orbis cujusque, et aequales esse a
ctiones in aequales partes superticierum om
nium. Premitur ergo superticies suprema
AF. vi simplici graritatis proprix, qua ee
omnes Orbis supremi partes de superticies
secunda BfR (DeT PrOP. XIX.) pro mentura sua equaliter pre-
unEuT. Premitur praeterea superticies secunda B S R vi proprix
Graritatis, quae addica vi priori facie prectionem duplam. FIac
prestione, pro mentura lua, ec insuper vi propriae gravitacis, id cAt
prectione cripla, ursetur superticies cerria C. EL. lc similirer prel.
sione quadrupla ursetur superficies quarta, quincupla quinta, et
sic deinceps. Prestio isitur qua superticies unaquaeque urgetuE,
non est ut quantitas solida Auidi incumbentis, (e d uc numerus Or-
bium ad usque summitarem Auidi; ec aequatur gravitari Orbis insi-
mi mulciplicacae per numerum Orbium: hoc est, graritati solidi cu-
jus ultima racio ad Cplindrum praetinitum, (si modo Orbium au-
reatur numerus ec minuatur crasitudo in intinicum, sic ue actio
graritatis a superticie intima ad supremam continua reddatur) fict
ratio aequalitatis. Sustinet ergo superticies intima pondus Cylindri
Praet
1II
DE MOTD