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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 304, page id 1066518432:0332
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304 DE VFRTBUS ET NIOTTDUS CORBORUM. LIB. II.
ratione, quam habet celeritatis initialis AMI pars hOC teMPOTC ex-
tincta DE ad reliduam BD. Ouod crat secundum.
C OR OL L A R E U M T.
523. Adeoque, tempora fuerint in progresione geometrica alcen-
dente, atque adeo relocitates mobili post haec tempora relidux
etiam in progressione geometrica, sed descendente, et quidem reci-
Proca progrettionis temporum, spatia transmissa crunt in progres-
sione arichmetica. Nam, si AT, AI snt in progressione seometrica,
ditterentix TI. quae lunt ut tempora, erunt in eadem progressio-
ne alcendente; iplae vero HII, scu celeritates mobili relidux ipsis
AI reciproce proportionales, erunt in progrestione geometrica de-
Ecendente, Spatia vero, Peu CC, existent in progrestione arithmetica.
Atque cum hoc corollario penitus consentit Prop. V. Lib. II. Princ.
Phil. Nat. Math. Celeberr. Nertoni.
C OR OL L A R Fu m TI.
524. circo  ista resistentixe hrpochesi mobile in infnitum ex
CUIrreNS, tempore infinito ut CTI, ubi infinite accesserit ad a(rmpEo-
Eam TR, PerCUEret etiam Spatium infinitum CC; nam, (I CC COn-
Funditur Cum aFYMPEOTa TK, AC infinita. In hrpoches vero capitis
Draecedentis, mobile tempore infinito ne quidem spatium Ainiex
magnitudinis, quod per rectam celeritatem initialem indicantem
exponitur, absolrere Dotest, ut lupra (5. 497.) octensum. Ouod
Flugenio notatu dignum merito rilum cst in Practatu De la C’ause
de la Pesanteur Pa5. 175. Circa finem.
PROPOSTTIO LZIV. YHFOREMA.
525. Si grave vi cravitatis uniformis in aere juxta duplicatam ra-
tionem celeritatum mobilis resistente verticaliter descendat a quiete motum
suum incipiendo,
Spatium descensu confectum exponetur log- mo rationis sinus totius ad
sinum complementi illius anculi, cujus sinus rectus celeritatem mobili ac-
quisitam repraesentat;
Tempus vero, quo spatium illud pertransitur, aut praedicta velocitas
mobili acquiritur, exponetur los morationis sinus totius ad tansentem