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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 207, page id 1066518432:0235
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DE VERTBOS ET MOTIBOS CORPORUM. LIB. II. 207
arithmeticam proeressionem ascendentem constituentes, et per singula-
rum terminos transeant ordinatae AB, CD, TCTD, 2C2V, exc. jua-
ta proeressionem arithmeticam decrescentes, definire curvam BDFDZI)
per sincularum ordinatarum terminos B, D, AD, ZD, transeuntem.
Per puncta D agantur parallelae ipsi AHI, ec in prima DE prO-
duCta LUatUE PF =DE, ac per F ducta FP parallela AB, in linca
TFTO a linea FP deortum ponatur xOeF aequalis excessui, quo se
cunda divisio CFC primam AC, vel tertia secundam, Peu quarta
tertiam, atque ita deinceps, excedunt, ducaturque per puncta L et
EF, recta FO; CTUNEque AC =DF = EV, item CTC = TRTV, d
XC2C = 2F 2F, atquO SIC POFTO. AdCOquC A2C = 2F 2F L TRTF L FF.
Veruim 2E, 2F = rec- IO 2E 2F. 2R FR : 2E FB, _E TL PF = RCC-IO TPPF.
TEE: AEB; ergo quia 2R TR = FHE = F B ex hypocheli quandoqui-
dem AB, CD, TCFD, 2C2D (secundum hypochelin) Cunt in PrO.
Gressione arithmetica, erit 2F2F F TE TF = (xCc- lum H ER + rec- 10
ITF): BF; haec vero rectangula simul Cumpta quotcunque corum
FUICFINE, XGUANtUT trapCZIO LFZF2F Simul cum triangulis TPXF,
IETFZF, quX TUNE eXtra trapeZIUM LFZFZB, e dicta triangula
simul aequantur rec- 10 sub dimidia 202F, ex 2F 1F vel BF: ergo
2EZF L TEFF = (EF2F2H + 5. 2OZF. BF ): BR =FF2F2F: BB
= 5. 2O2F; ac proinde A2C =F F2FEF: BF, + 3. 2O2F L R F -
2FQF + TEEF + FF; eodem aroumento probatur esse indefinite AC
vel od =EF fe: BF, + i. pf + PF vel ep, vel bisecta ps ing ductaque
Per g recta FgQ, crit ed = F F fe: BF, + p9 + ep = LL fe: BF, + eg;
adeoque ed. BF =FF fe + eg. BE; atqui trapezium P. P fe = rec- 10
eg. et; ergo ed. BF = eg. F C F eg. BP = BC. eq; hinc CuEVX QuX (IEX
haec est proprietas, ut de vel cA ubique siE ad homologam eq ut
Be ad BF, quae proprietas parabolae communi competit.
TT. Nam si quaedam T AIaE ad RB, SICUE RM (quXe reTUIEaE a COn-
cursu MI rectae OF productae cum recta AB itidem protenta) ad
EF; hinc erit etiam eg: CM (= FF: FM) =BF: YI, CUIEVX VerO
modo recensitae proprietas exhibet de: eg = Be: BF, ergO CX Xquo
de: eNt = Be: T, et de. T = MIe. Be = NTe =NB, bisecta scilicet
BM in N; hinc de. Y + NVB: = Ne =raE; eE SIV sIE FCREIa PFOPOE-
tionalis ad T ex BN erit T. V = BN., atque adeo de. T + P. V
(=de. T + NB) =rd, idcirco, si inrN perpendiculari ad AB prO-
auCta VerSUS S, SLatE NR =V, erit T. Rr =rd, acque adeo
CUrrA GUIXSITa RBDFD eAt parabola, cujus parameter eA L, e ver
tex in R; in qua I est quarta proporcionalis act datas EF, E. M