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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 67, page id 1066518432:0095
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DE VTRFBUS ET MIOTEDUS CORDORUM. LIB. I. 67
IIY POY H F STS II.
250. Si Cravitas corporum ubique uniformis est, ut in Cralilei hypo-
thesi, scala Celeritatum erit Parabola conica, cujus abscissae axis spa-
tia mobilipercurrenda, e ordinatae celeritates acquisitas exponunt: Prunt-
que propterea celeritates in sub duplicata ratione spatiorum confectorum. Fi8. 34.
Nam Scala Colicicarionum gravitatis erit, hoc casu, recta BC 2xi
AC parallela, atque adco (5. 244.) 2. AB. AE: M = P. F2, ubi M de
nocat massam mobilis, AB ejus pondus, et AE spatium cadendo
confectum, at que P F celeritatem acquisitam. Inde ob constantem AB
scala celeritatum est parabola conica, atque adeo spatia mobili de
seripta sunt ut quadrata celeritatum acquisitarum, et hae relocita-
ces in subduplicata ratione spatiorum. Parameter rero Parabolae CA
2. AB: NI.
15T. Tempus vero quo spatium quodlibet AF. cadendo conficitur est
P. ut duplum spatium AV. applicatum ad celeritatem F. L hoc tempore
acquisitam. 2. Et radix ex facto massa corporis in duplum spatium
applicato ad mobilis pondus seu eravitatem. Pt denique 3. ut factum
ex Massa corporis in celeritatem acquisitam applicatum ad sravitatem
ejusdem corporis. SignetUT, UEANECA, COMPUS PeF AH, Per TAH.
Jam (8. 13F.) eke =M. at: AB, ergO summandO FAF =MI. R. F:
AB, quod est tertium. POrrO quIa FAH =M. P F: AB, erit etiam
=MI. H, FE: R F. AB (5. 750.) = 2. AB. AF: AB. F F = 2. AF,: H. F. K, F
hoc est primum. Denique, quia ordinata parabolae est ad dimidium
parametrum in subduplicata ratione dupli abscise ad semissem pa-
rametri, erie CAP. (= M. P. F: AB) =Y (M. 2AP: AB). Duod exat se
cundum.
152. Idcirco, rocando duorum mobilium malas MI, m; Gravita
tes scu pondera Cr, s; spatia cadendo descripta S, s; ec denique
tempora descensuum T, t. Frit T = V (2NIS: C) e TI =2NIS:
G, Vel C. T2 = 2. MI. S; X ett =2ms. Adeoque, li spatia ab ambobus
mobilibus dirertis temporibus confecta sunt in duplicata ratione tem
Porum, corporum pondera massis eorum proportionalia crunt; nam
AFF: H = 5:s exic Y. S= HS; adeoque 6.
s= 2. MS, vel CH = 2. NS, Peu 8tt = 2 81
Gm, vel G: G = MI: M.
2= 2. Nd fet 1t. 65:
=2Ms, adeoque sM =
Propterea hujus paragraphi ope sccunda Propolitio Der experi
menta contirmari porelt. Videatur 5. 30.