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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 117, page id 1066518432:0145
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DE VERTBOS ET MIOTTBOS CORDORUM. LIB. I. Z77
eadem que erit post impulsum a se mutuo recedentium corporum celeritas
relativa, quae ante constictum erat accedentibus.
Politis quae in praecedenti propolitione, probandum est Fore Fis. 50.
DC =CD ex ab = AB, nam AB eAt celeritas relatira ante, et ab cc.
leritas relatira corundem corporum A, B, post occurtum, puncta-
que C, c centra graritatis indicant in ueroque catu.
Demonstr. Finsatur lineam rectam, in qua COrpOramOVentuT, in- F18. 5I.
finire lonsam esse, atque moreri rertus m relocitare infinite parra
AM, HUINCGLE MOEUI COMMUNCI CEIaM COFPOTA A, B in linea in-
finita incedentia participabunt; unde Factis lingulis Dd, au, cn,
bB aequalibus Am, slobus A morebitur tantum celeritate absoluta
Ad locO ipliuS AD ante occurlum; quandoquidem ex motu ejus
proprio AD communis Dd utpote contrarius est auterendus: B ve-
1o incedet relocitate Bd ante conflictum, accedente ejus motui pEo-
prio BD communi Dd alteri BD conspirante. Pos consictum au-
tem celeritates Da, DB, mutabuntur in Da X DB; rerum quia
omnes bB, cn, au Dd (secundum hypochesin) aequales, crunt
en = ac, _ aB = ab; atque adco velOcitatES AC, aC, nCC HOM AB
ee ab inalterata manent in aequalitate superiore (5. 223.) Solis CD
et De variationem Cubeuntibus. Idcirco Ei in ea aegualitate A. AC.
AB + C. CD. = A. ac. ab L C. DC lOCOCD _ DCTuBSIELANEuE Cd et
Dn, HCt A. AC. AB + C. Cd = A. ac. ab + C. Dn, quae Cx altera
ubdueta relinquet C. CD -C. C8 = C. DC-C. Dn, vet CD-
Cd = DC: = Dr, auE etiam 2CD. Dd =Dd = 21C. Cn = ex, hOc eA
quia Dd = Cn, erit 2CD. Dd = 2DC. Cn, acque adeo CD =DC.
POrTO CX aequalitatE A. AC. AB F C. CD = A. ac. ab + C. DC. 2b-
jectis aequalibus C. CD et C. DC, restabIE A. AC. AB = A. ac. ab,
vel AC. AB = ac. ab. Verum CA AB: AC = ab: ac, vel AB: AC.
AB = ab: ac. ab, ISItUE DFOPFeT AC. AB = ac. ab, exit AB = ab at-
que adeo AB = ab. Ouxe crant demonstranda.
PROPOSTTTOZLI PROBEEMA.
225. Datis corporibus A, B utcunque inaqualibus sibi directe occur- FiB. 52.
rentibus cum datis celeritatibus, invenire velocitates eorumdem corpo-
rum post constictum.
Ex praecedenti propositione hujus Problematis solutio Facillima
est. Nam Factis DC=CD, item Ca = CA, _ cb = C B, ubi obler-
randum punctum B, quo recta relocitatum ante occursum rCPEE
(et.