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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 264, page id 1066518432:0292
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264 DE V FRTBUS ET MOTTBUS CORPORUM. L IB. II.
Peractis, praebebune bblt -aalt -aaht; + 2. (aa + bb) 2. bet: 30 = -
26b2D; + 2. (aa + bb) . bed: 35. Atqui (secundum hrpothesin) cAt b L
B = k, _ (5. 454.) cC = aa + bb, erso hi ralores, in postrema xequa-
tione suffecti, praebebunt bblt -aant + 3bcet = - 26bl0 + 3bc ed. TTinc
etiam 2bb1t + 6bbeD = 3aakt = 2bcet = 2bcet, et quadrando 9b.IIH +
36bhtB = TBaabblet + 36b22B - 36aabbkKHF + 9a kH = (4bbeedo -
8bbeeto + Abbeett) in cc. Unde substituendo aa F bb loco CC, fet
aabbeedo =Saabbeeto = qaabbeett + 4b eedo -8b eetB + 4b cet t = 9b. IlHF
=366to = =8aabbIKHF. + 36bteBB = 36aabbkktL + 9artetHt. Vel Positis
loco bec a proportionalibusr. X B, in hac postrema aequatione, Prore.
MICE Arreed =Srreeto + ArreettOB + 4r eedo - 8r eetB + 4r eett =Or IEt
+ 36r+ RrB = 28r= IR++DD, + 36r 4kkBD -ZCrrkkHIBO + OkKHHO. F. X qua li-
quet problema esse Colidum, nam radices hujus aequationis biqua-
draticae exhibent ralorem tansentis quaesitxe o, seu tansentis ansuli
TAW, seu anguli declinationis bilinei 2BAC.
C OR O. E L A R Y U II V.
46T. Si CUIrrA AB. e A2B sunt aequales, adeo ut communem
abscintam AFI habeant e ordlinatas aequales BII e 2B2TI, uc in A-
SUTa TI3. CTUNE AT = A2 eF A3 =0; BF =B2, _ CF =C2; DI =
D2, lingula rero B3, C3 e D3 Perinde ac A3 _quales O; era-
nelcet pariter linca, quae in AGUta LTS. TCPERTenEatur DeT DEI vel
D2TI, altoraque, quae crat in hac cadem Agura IA, in priore scili-
cet A8. 213. erit BII. Hoc eroo calu Formula generalis paragraphi
459. mutabitur in aat. BII + (bbF = aat). B2 = 2660. C2. In exemplo
proinde superiore (5. 457.) currae parabolicae, retentis Eymbolis il-
lic positis, erunt BIL, =Y; B2 = W ∞ C2 =7 = 0 = C, atque adcox-
quatio aat. BII + (bbF =aat). B2 = 2668. C.2, abibit in aaty + bbto -
aatio = 2bbDC, vel aate + bbt0 = 26b08; atque adeo lubrogatis loco a
ec b proportionalibus d et r, erit teB + rrto = 2rreo, ac proinde
dd =
2rr0
rrao
; quae est eadem aequatio, quam citato locoreperimus.
Ac sciendum hanc solutionem imperfectam esse, quoniam aequatio
amplius non inserrie, si ratiotangentis y ad arcum a minor fuerit du-
Plicata ratione secantis anguli SAW ad radium in Ag. 114. SCd c0
in calu ipla B, ne quidem suxposita arcuum circularium rectiticatione,
nulla aequatione alsebraica exhiberi potest.
SCH