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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 116, page id 1066518432:0144
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TI6 DE V FREBUS ET NIOTZBUS CORPORUM. LID. L.
in quadrata velocitatum collective sumta ante ex post conftictum a
quantur.
TIOc est A. AD L B. BD == A. Da = B. DB existentibus Da,
Do celeritatibus corporum A, B post collilionem, et AD ac BD re.
locitacibus ante contictum.
Demonstr. Posito A acquisirisse celeritatem Cuam AD casu ex al-
titudine F A, alterumque B ex altitudine FB, dirilaque recta R F
junsente puncta P, lin ratione reciproca ponderum A, B, linca
CC denotabit descensum centri graritatis mobilium A, B; dc ea,
fb denotent altitudines, quibus accelerato motu transmissis mobili.
bus acquiruntur celeritates Da, D, cum quibus deinceps in altum
terri incipientia iterum ad easdem altitudines ae, bf asturgere pol-
Tunt; quo motu alcentionali eorum centrum graritatis c’alcendet
Der altitudinem cs. Jam quia (5. 218.) eadem manet ris absoluta
COrporum A, B ante ec pest contictum corum, erit 6C = Ce, vel
DOSito C Significare A L B, erit C. 6C =C. C8; atqui (5. 4 4.) C.
C = A. F A + B. FB, X C. cg == A. ae F B. bf, ergoctiam A. l. A +
B. FB = A. ae + B. bf; VerUM (5, T5O.) rectIS F A, FB, ae, bf PFO.
Portionalia CunE AD, BD, Da, X DB, unde sufficiendo haec il.
larum loco in proxime antecedenti analosia, reperietur A. AD +
B. BD. = A. Da + B. DB. Ouod crat demonstrandum.
C O R OL L A R Y U M.
223. Tdcirco erit etiam A. AC. AB F C. CD = A. ac. ab + C. DC.
NNam A. AD = A. AC + 2. A. AC. CD + A. CD, _ B. BD = B
BC = 2. B. BC. CD + B. CD, ergOA. AD + B. BD. = A. AC + B.
BC + (A + B). OD, + 2. A. AC. CD = 2. B. BC. CD (vel quia cen-
trUm GravitaLIS C eHICIE A. AC =B. BC vel 2A. AC - 2B. BC =0,
et C = A F B, CrIt) = A. AC + B. BC + C. CD (Pcu quia B. BC
A. AC vel B. BC =A. AC. BC, etiam) = A. AC. AB + C. CD.
PAFIATGUIENEOINFCFCtE A. Da L B. DB== A. ac. ab + C. DCE. Adeo.
que cum habeamus A. AD: + B. BD = A. Da + B. Db; erit etiam
A. AC. AB i C. CD = A. ac. ab + C. DC.
lEoeue ae lCttk.
224. Centeu etadtalis corporum actabsorum inder se collisoramt
Eadem post occursum celeritate ac directione feretur, qua ante incedebat,
Ca