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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 58, page id 1066518432:0086
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58 DE V ERIBDS EF MIOTIBVS CORPOROM. L. IB. L.
qualiter distantibus eadem solicitatione centrali BF urcentur, erit ubi-
que momentum solicitationis centralis seu rectaneulum BEC aequale Bo-
moloeo rectane ulo XTn. SF. vel NTn. NB, quod exponit momentum solici-
rationis tangentialis in curvae puncto quolibet N.
Aecus circuli epn centro D deleripti locet rectam DI, in pun-
eto p, ex triangulum Anp tanquam rectilincum ob suam infinitam
parricatem spectari porest rectangulum ad p, atque adeo simile trian-
sulo NaB. Idcirco erit Na vel BF: NB (SF) = Nn: BC (NP), e
BF. Fe = NTB. FC =SF. NTn = NTB. NTn. Ouod erat demonstrandum.
C OR OL L A R E U M I.
234. FTinc si scalae celeritatum AVF ad punctum F perpendicu-
laris FI ducatur axi occurrens in T, Tubnormalis PP dequalis ubi-
que erit respectirae BF, quae solicitationem centralem exponit in
distantiis ED, ND a centro D aequalibus; nam quia TFF rectus
est, triangula FTP ex Ffa similia erunt, atque adco FF: FI = P a
FC): af. ErGO PF. af = TB. Ce; atqui (5. 133.) SF. Nn =BF. PC
ec (5. 132.) SE. Nn =M. PF. aF, aut Cumta M instar unicatis, = LF.
af, erit TP. De = BF. Fe atque adeo TF =BF.
C O R OL L A R Y U M II.
135. In quibuslibet punctorum F, N distantiis aequalibus F. D
et NVI a CCnErO D, momenta celeritatum cadendo acquisitarum
erunc aequalia. NNam Sicut (5. 132.) ACr vel CHI celeritatem acqui-
litam mobilis M in curra MON descendentis, ec rectangulum IIg
triansulo IIAC inscriptum celeritatis momentum in N exponunt.
ita etiam 2A2C e rectangulum 2FI28 triangulo 2FI2A26 inscri-
Deum, exponent celeritatem ex descentu mobilis A per spatium
AE in puncto P. acquisitam, ejusque momentum. Verum (9. 132.)
CASF. NVn =MI. FF. af =MI. TICE, item BF. F C = A. 21T2C528. atque
(5. 233.) SF. Nn =BF. FC; PrOpFerCa Het MI. TIOB =A. 2L126128,
vel quia (secundum hrpothelim) iplae M et A aequales IIC8 =
21126528.
PROPOSTTTOZTZ. PHEOREMA.
15. 32. 736. Si mobilia M e A ex punctis M ex A in cur Da MOH e
recta AD a quiete cadere incipiant, celeritates ipsorum in punctis N