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# Title: [Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ (shelfmarks Leibn. Marg. 0; ZEN Leibn. Marg. 0)
# Folio 51, page id 797435492:0263
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V ECF. VI
CNus. DB. P. hoc est. DB. DC:: DC xDB. CNXP. hOC
eAtDBKDC. DCq:: DCX DB. C.NVXP. OUApFOPTeK est
DC9 = CN XP; erGO PateE curvam D N N esse parabolam, cu.
jusparameter P, Vertex D; diamerer ips B A Parallela.
Dedit hoc Cresorius à S. Vincentio sed operosa (A probe memini) in Lib. de
prolixitate, demonstratum.
Spiralio
XV. Adjicimus; Si reliquis iisdem potitis, ita Ferantur C X, _ F18. 48.
DY, ut jam semper habeane B L, B C rationem eandem (puta quam
BD ad R) erunc etiam intersectiones ad parabolam.
Nam bisecetur DB in C5, ducaturque GV ad B F parallela, se-
cans curram DN NI inV. _ quoniam est B C R:: BF. BD::
CH. CD, exIEB C X CD = R X CH. ergo (secundum benE
noram parabola proprietatem) eAt curra D AN parabola, cujus para-
meter H, diameter CV.
Pxolecaria sune Fortan ista; Ped non perinde notara occurunc hXC:
XVI. Si reliquis similirer politis, recta C. X non jam ad ipsam BA, Fi8. 49.
sed ad aliam politione datam (D HI) Feratur parallela; sirque per-
Detuo BF. DC:: DB. R; erun intersectiones N ad hyperbolam.
Nam ducta AIC ad B A Parallela, nuncupentur DB =- b. BH -
h; DO = x. OH = y. EAque v. y: : b. = = BF. item B.
b: : 7.  = G C. quare C D = ∞ -,. ERisitur (ex hyporte (i)
2. X - -:: b. r; underalis ordinabitur aequatio;
v
xx. Ponendoq;  = m; exit y xJ. my = x x; est ergo
curra D N N hyperbola,  quae supra haberur determinata.
ZVII. Duinetiam Si C reliquis, ut in praecedente, suppolitis) ita
jam Peratur C X, ur semper habear B P ad B C rarionem eandem, quam
BD ad R. erunt itidem intexsectiones H ad hyperbolam,
Nam ducta NVC ad A B parallela, nomineneur rectae, ut in prX
eunte; eAque jam BC = b - X ]
B
 Tu 20 hujen.