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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 309, page id 1066518432:0337
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DE VFRTBUS ET MIOTFBUS CORPORUM. LIB. II. 309
ubique FIF. FP = F C. bC. Ad id, ductis CL, LN atque NTO pa-
rallelis rectis MI _E MA respectire, Hat ME = MO, et sic ubique,
dabunturque tot puncta in Curra C2CM, quot libuerit, ex qua dein-
ceps alteram IIM construere non erit difficile. Ducantur cl, In, no
prioribus CL, L.N e NO aequidistantes ex indefinice ricinx, su-
maturque in qualibet ON major OV, quae sic ad homologam ON,
uE haec NO ad MI; quae MI simul etiam log-micxe IN fubtangen-
tem sionificat, e hrac ratione relultabit nora log.mica IV, cujus Tub.
tansens erit semissis IMI Subtangentis log-micx IVV.
Demonstr. I. Ouia rectae FG, LC ∞ LFI (secundum hyPOFhCHIN)
TUINE In CONFINUA FaTIONC, CFIE EO: FHI =PC: FC, rei invertendo
et componendo ITG: FC =TS2: TMI = LSE: INI = NO2: IMI (Vel
ob continue proportionales VO, NO eE IM) =VO: IM vel FG,
ergO HIO =VO; _ quia OMI = FM, ac oM = eM, et proinde
O0 = Ee; erit HIC. G2, Vel HIG. De = VO. O0 (5. 49T. nUm. ZII.) =
NO. Np = LS. Lm (5. 493.) MS. Ss =FC. Cb. Id est momentum ce-
Peritatis decrescentis F. C aequatur momento resistentiae totalis FIG. Jam
ME vel MO est log-us rationis NO ad IM, scu IS ad IMI, id cAt,
l0g. us rationis secancis anguli MIIS, Cujus tangens MIS = FC celeri-
tarem inicialem exponit, ad radium (M vel MA. Quod erat pri
MUM.
II. Ouia VO: IMI =NOE: INT =LSE: INI =MR2: NN (8. 165.)
=Rr: RR, atque adeo, quia Rr = Cb, Crit RK: IMI = Cb: VO = Cb:
HO (5, 132, 485.) = tRC, _ RB: MR vel IM (5. 129.) =angulo
RMe, adeoque FFe=angulo RMK, ac proindetempus totius alcen-
Cus per spatium E.M exponi debet angulo KMI, cujus tangens eAt
IR vel E.C. Quod erat alcerum.
C OK OL L A R Y U M I.
33. Cune. sete Ccera. Feliltentiarum tocalium. ML e
10g. mica similis ec aequalis l0g- micx IV. Atque adeo s relictentix
totales lumantur in progressione geometrica descendente, spatia
alcendendo confecta erunt in proorestione arithmetica descendente,
scilicet spatia toto ascentu deseripta. TTorum demonstratio cadem
terme eAt cum ea corolI. II. ProD. PEaced. 8. 527.
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