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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 336, page id 1066518432:0364
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336 DE VFRLBUS FF MIOTFBUS COREORUM. LFB. II.
Atqui areA AMNSB aequatur perpetuo rectangulo sub BB recta,
quae graritatem uniformem exponit, e abscissa BC CUIEVE ADB
descensu mobilis descripex, cum quodlibet elementum arexe NDd
aequetur rec. IO BB. FF, Scumomento graritatis centralis BB. Fodem
AEGUICNEO SEGUIEUITFOTC ATCaM CMNSBC = BB. BII, CTGOAMINSB
CMNSB, quod arCA ATRC A aequariostensum, aequabitur etiam
rec. lo BB. CTI. Ouod crat demonstrandum.
C OR OL L A R F U M I.
583. Si Relistentia aeris sint ut celeritates mobilis acquisitXe, erit
AMND =aTCX ATD +:TD. Nam TD (sccundum hypothesin)
est uc celeritas in D acquisita, adeoque, per praecedentem parasra-
Phum, crit momentum Colicitationis acceleratricis, (eu ND. Dd +
ID. Dd = elem. AMNVD + elem. ATD, aequale momento celerita-
tis, Ceu TD. +o, quod aequatur elem. ex : ID. Erso lummando, crit
OMNINO ArCA AMND = area ATD = :FD, atque adeo AMND =
ATD +: TD. Eodem argumento concludetur eACNECM = :FP
=OTF.
C O R OL L A R I U M II.
484. Sin vero relistentix aeris fuerint in duplicata ratione cele-
ritatum acquisitarum, quae rerior est hypothesis, CTIE arCA AMND =
AO. TD F ATD, _E arCA CMNE = AO. TE -OTE. Obi AO CA
maonitudo data leu constans.
Hoc enim casu celeritatis in D acquisitae quadratum erit = 2AO.
TD, cum resistentix sint ut quadrata celeritatum; et dimidium ce.
leritatis quadratum AO. TD, hujusque elementum, id est momen-
cum celeritatis acquisitae in D, reperietur AG. 1B; unde, quia momen-
tum Colicitationis acceleratricis ND - TD aequatur momento celc-
ritatis in D acquisiItX, ACE ND. Dd = FTD. Dd = AG. 1B, ec Cum
mando, omnia NVD. Da, sCu arCA AMIND = omn. TD. Dd, Ieu arca
ATD = omnibus A9. +B, id est, rec- lO AO. FD; ad COqUC AMND =
AFD + AO. TD. Eadtem terme ratione probatur CAO CMNF. =
AO. TBC.
no C