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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 52, page id 797435492:0264
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18.
218. 53
L. E C Y. VI.
:: b. r. unde talis emerser aequatio: y a -) - B X  y-
X a x; hoc est (BosiTO = = m) y X ) B~ - my = X X; FA
isicur curra B HI NI hyperbola, qualem superius exhibuimus determi-
MaLaM.
ZVTII. Dacx posirione sint rectae DB, B A; (_ in DB detiene
cux punctum D) Cirque linea D N N calis, ne duct a utcunque CH
ad B A parallela; Sumpris vero determinaris e, r, vocatisque DC)
= ∞; dC OH = y, CiEr y - y x = 8 x; erir linea DNN hy-
perbola, lic determinanda.
CapiatuED F = r, _ BO = 8. _ per F duCatuF recta F R ad
BA, 2c per O recta O S ad BD parallelx; erunE ZR, ZS asym-
PFOtI.
Nam ducta N P ad D B parallela, esEZ P = 5 -- y; _PH =
r - X; quare L. Px P ( = Cr - C x =   ry = Y X. VerUT CX
typocheli eA -  ∞ . ) -. x y - y X = 0. erBOZ PXPN = Gr =
LF X F. D. unde liquido constat Provolicum.
Ouod Si fuerit aequatio x y = r y = C x; sumenda eAt D F = Y
e BO=  (intra rectam DB) ductisque, ceu prius, parallelis
SZR; eric hyperbola NVN N ansuloSZ R comprehenla; quod co-
dem facile comprobatur modo.
Z1Z. Datae positione sint recte D B, B A; ac ita serantur rectx
EZ ad DB parallela, ac D Y per punctum delignatum D transiens,
ut sic semper ratio iplius B P. ad ipsam BF aequalis altionatae D B ad
R; crunt rectarum DY, PX incerlectiones ad lineam rectam.
etam per N ducatur CR ad B A parallela; est que DB. DC::
B B. GH:: BF. BF:: BD. R. itaque semper est DC =R. Pa-
tet igitur Facta DC = R, _ ductâ C R ad B A parallela, incersecti-
ones omnes ad hanc exictere.
ZX. Ouod Sireliquis similiter posiris; sumpro aurem alio in B A
puncto O: ab hoc lumatur compurandi inicium; ut nimirin CIE
perpetuo BF, O F:: DB. R; crune intersectiones H ad hyper-
bolam.
Nam duct a N C, ad AB paralleta, si D B = b; OB = 5; DC