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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 66, page id 1066518432:0094
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F18. 33.
66 DE VERIBUS EY MOTTBUS CORPORUM. L. IB. I.
IXPOTHES1S. L.
24.8. Si solicitationes eravitatis sint ut distantiae a centro gravium
D, earum (cala erit linea recta CD per centrum D ducta cum asse
AD anculum quemlibet DA continens; e scala celeritatum linea et
liptica ASR, cujus semiaxis transversus est AD, e semissis axis conju-
eati Da par mediae proportionali inter DA vel aequalem. A0, e OA.
Nam deleripeo circa centrum D quadrante circuli AV L, ductis-
que aL, X BFF parollela DL vel a A; quia DR (conAtr.) media
est proportionalis inter DI vel oA e OA, crit propter CIlipsin
ASH; L F~: FS= (= a A: OA) = 2. traDCZII aBF A ad 2. FraP. OC L A;
acqui duplum trapezii. a BE. A est excestus quadrati AD vel DF CN-
pra quadratum DE, atque adeo sequatur PF=; ergo requantur etiam
duplum trapezii OCF A, quod est duplum arexe in scala Colicitatio
num centralium OCD, ec quadratum ES, atque adco (5. 136.)
ES exponit celeritatem acquilitam in P ex descentu per AE; cr8O
ellipsis ASR eA scala celeriratum acquilitarum. Quod erat demon-
Strandum.
249. Si fiat ansulus X ad anculum ADF, in ratione DL ad DR,
ipse anculus Z exponet tempus descensus mobilis per AF, hOC CA X =
TAF. Sit enim X elementum ipsius X homologum elemento anguli
ADF, quod est angulus FDF, ducta scilicat bf alteri BF indetinite
ViCIHA. EFIE CEGO Z: FDF=DL: DR =E E: R, S, CrOO Z. RS =F F.
anG. FAF, vel X. F S. DF = RF. DF. anG. FDF, atqui (5. T29.) DF
in aNG. FDE exprimie arCUIUM FF, CrOO Z. RS. DF = RF. FF, aC
VerO FF: FF = DF. RC, quod ex similitudine triangulorum PFa et
EDE Facile collisitur, igitur X. ES. DE = DF. BC, vel deleta DF,
exit Z. BS = RC, eE X = LC: PS. VeruM (5. F28.) EC: FS = tEC, CF -
50X = tFC, atque adco omnes X hoc cst X = omnibus tEe, hoc
est CAE. Ouod crat demonstrandum.
Hlinc ducto quolibet radio DV, qui quadrantes concentricos
AVL _E ETK sCceE in V _ T, ductisque arCUUM AV _E FY S-
nibus VW ec Te (per accidens cAt, quod Te cadat super bf, sC5
utcunque aliter. Ce habere potest) spatia AW ex Fe eodem tempo-
re a mobilibus aequalibus A ex P. simul cadere incipientibus, descri-
ventur; eodemque rempore ambo ad centrum D perrenient.