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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 50, page id 797435492:0262
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F18. 46.
P. C
d =m. vel dy-xy = xx. Aliaquae dam hic (nonnulla FOrtan i a 5lp 3Co5)
inseremus.
ZIII. Sic positione data recta YD, sit item curra DN NI calis
ut in ID Cumpro puncto quopiam C, duct aque rectâ C N ad politio
nem datam lK parallelâ; sumpeisque determinaris lineis e, m, r
Potirisque DC = x, _G N = y; Cir perpetim y x g x - m y=
XX; linea D N N erit hyperbola, sic determinabilis: SumatuE
DM = m;  Pe MI duCaTYM L ad LK paralleta; _ in hac acci-
Piatur MC.
2Z =
M n
de
: _ TIL OY =M Q; _ ab M Y auteratur
S; connexaque O D, ducatur Z P ad OD parallela; CxUNE
ZM, L T asimptoci.
Nam ducatur Z S ad AI D parallela; cui occurrat C N producta in
R (sed _C R iplam Z T Cecet in P). FAque jam PN = R C-
RP  GN=
m m
e
M X
= y. adeoque PH X MC =
M s ) y ∞ -) 8X - m y
M
M
∞ X = M _ 0. =
= DM X Z O. unde PN. ZO:: (DM. MC::) OD.
ZP, erGOPNX ZP =ZOX OD. Liquerigitur curram D. IN
esse hyperbolam, cujus asymptoti Z M, Z. I.
Sixequario sit = 7 2 -)  g x. J. my = - X x; eadem erit Byper-
bola. Sed puncta C inter B, M tunc accipiuneur; e ita prout aliis
ac aliis locis puncta C delignantur, xquarionis signa variantur; at
non est ea jam exponendi locus.
ZIV. Potitione datae sint rectae DB, BA; perque rectam D B
Feratur recta C X ad B A Parallela; item per punctum D rorando
transeat recta DY, sic iplam B A secanS in P, ut lic intex rectas B F.
DC eadem semper proportio (puta quae cujusdam assignatX R ad DB)
rectae vero D F, C. X se incerlecent punctis H; erir linca D NN Pa-
rabola.
PTam (ER, DB:: DB. P. Fst ergd BE. DC:: DB. P. Item
eAtDB. BEE: D C. C. HI. ergODB. BF ] BB. DC =DC..
 P