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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 98, page id 797435492:0334
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L C C Y. XI.
mulciplicando) 2Fn ) - sn =- m F - . m s. vel transponendo 2 n t.
M F == M S -- 1 5. WHde M = n a 2 B - M : : t, 5:: C A o A D. Cx.
50 patet ex antecedente.
ZIV. Srance duodecima hypochesi, paraboliformis A F B enera ty-
perbolam A F: B tota cadet.
Nam utcunque ducatur P F C ad B D parallela; _ recta F R By
(a)2 Bujus ap. perbolam, recta FS paraboliformem tansant. F. Aque SC. A C:: (a)
M. B:: TD. AD (b) =RC. AC. unde RGC SC,. (6) unde
curra A F. B exrra curram A F B tota cadet.
XV. Friam, Si reliquis perstantibus, ad basin G F, axin AC COn
Scicutam imagineris ejusdem ordinis paraboliformem; haec ad partes
ipsa C P. Superiores intra byperbolam tora cadet.
Nam si in curva hyperbolica A E. sumatur ubicunque punctum M, 
Ordinetur M P, ducaturque hyperbolam tansens MV; exIE V P.
APC m. n. adeoque rursus c tertia liquet Proposirum.
XVI. Oninetiam Si hac altera coordinata paraboliformis, ad basin
EC constituta, ad D B protracta concipiatur, ejus ipsis PC, BI in-
tercepta pars extra hyperbolam tota cadet.
Nam quod exrra hyperbolam infra FC cadit, exinde patet, quod
ipla cum iplius cangente recta F S angulum efficie minorem eo, quem
eadem recta P Setticit cum recta R P. hyperbolam tansente. quod au-
tem eadem alibi, velut ad N, hyperbolae non occurric, patet; quoniam
Cs. hoc polito, (a) ipla intra hyperbolam A N cota contisteret, contra
quam mox oltentum est.
XVII. EIabCanE CircHluS AEB, _ Parabola AE B communem
axem AD, ec balin DB; parabola ad partes supra BD intra C iren-
Tum; at intra BD extra circulum cadet.
Sit enim Circuli Diameter AZ, _ ci xqualis A EI ad BD paralle.
la, ec connectaturZII; _ huic B D producta ad l; ergo DI est
Parameter parabolae A F B. Quod (i supra B D utcunque ducatur recta
EF O R ad B D parallela circulum secans in F, parabolam in F, rectas
AZ, IIZ, InC, _ R, patet esse O E9 = AG XOR= AOXDI
G F 9. unde OF L GF. Trem, B intra BD utcunque ducatuF
recta M ATOL ad BD parallela parabolam secans In M, ciron-
cum in NI, rectas AZ, IIZ in O, _ L, iridem patet eAC NO9
= AOX D IE AO x O L = HO4. e ideo MO
F19. 2420
f636. Bujus al.
Shujus a
FiB. 14T.
F18. 142.
F18. 242