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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 123, page id 1066518432:0151
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DE V ERTBDS ET NIOTTBDS CORPORDM. LIB. I. 123
ad unitatem proxime. Tlugenius in postrema propolitione tractatus
lupra (5. 233.) Laudati numeros pro hisce casibus nottris minores
exhibet, transseriptorum forre aut calculi laptu.
PROPOSITIOZLIII YHEOREMA.
237. Centrum gravitatis duorum corporum sphaericorum elasticorum
sibi invicem oblique occurrentium; eadem directione ex celeritate feretur Fi8. 55.
post constictum, quibus ferebatur ante concursum.
Globi elastici P, O Sibi mutuo occurrant in D celeritatibus pro-
priis PD, VD, e post occursum resiliant celeritatibus propriis
Op, Dg, ita ut hae lineae eodem tempore aquabili motu absolvan-
tuT, quo rectae PD, OD ante synodum; sintque puncta M et m
centra graritatis globorum in P et L, item in p, q existentium; pro-
bandum eA rectaS ND ex Om tum aequales, tum etiam in directum
Politas esse; quandoquidem MD exponit relocitatem et directio-
nem centri graritatis M ante conflictum, Dm vero relocitatem et
directionem centri communis graritatis post collisionem. Sic D
punctum contactus globorum, et BA recta jungens centra corun-
dem, quae, ubi globi se mutuo contingunt, per punctum contactus
transibunt; ex centris Globorum P,  demissie sint ad AB perpen-
diculares PA, OB, _ ex MI recta MC reliquis OB, AP paralle.
la, quibus politis, manifectum est CX arF. 29, MOTuI juXta PD X-
quipollere laterales PA e AD, e motui OD laterales 9B ec BD.
Jam quia MOTUS juxta P A ex OB paralleli sune, slobi quatenUS MO-
cibus hisce asitantur, in se mucuo agere non poltune, led Coli mo.
TUS juxta AD e BD, utpore directe contrarii, in casu confictus con-
siderandi veniunt reliquis tantisper sepotitis et postea iterum relu-
mendis. Porro quia M est centrum graritatis globorum in P X 
existentium, etiam C corundem globorum in A e B politorum eric
centrum graritatis; adeoque factis DC =CD, nec nOn Ca = C A XC
cb = CB, erit (5. 225.) Da celeritas propria slobi A, ec Db celc
ritas alterius B, post collitionem in indetinita linca ab. POrrO Per
a e b ductae sInE rectX ap = AP, et bg = BC ipsi AB normales, quo
Dolito ex quia in ipso contlictu motus juxta PA et OB, utpote Pa-
ralleli, nullam mutationem Cubire potuerunt, hi motus post impul-
Cum illibati Cunt conserrandi; at que adeo post consrectum corpus P
2 puncto D recedet motu Dp relultante ex lateralibus Da et ap, al-
rerumque  motu Dq nalcente ex lateralibus D3 de b9. Verum
quin