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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 35, page id 797435492:0063
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I B C F. IV
terrallum LR minuS IpSORL; seu generalius efferendo, libere sum.
peis ipsis M N, NO erit IR. RL = QMN. N O. hoc vero non
aliter, opinor, elesantius quam ex adjunctis uno, vel alrero Theore fii8. 43.
mate constabit.
XVI. In primOCatu; SIE (uE antehaC) ZB. AB: : L. R; super
que diametro Z B constiruatur semicirculus; cui a puncto B adapte-
tur BD = BA; e per puncta L, D ducta recta retringenti occur-
ratIn Y; cum ad semiaxes BZ, BY (centronempe B, vertice L) de
Tcribatur Hyperbole HIZC; in hac aurem sumpro quolibet punctoS
ducantur S N ad A B, _ SR ad P F parallelx. Denique ducancur F18. 44.
AN, KNa; eriE R M a incidentis A N refractus.
Nam ex yperbolae natura est RB9 = ZBg. BNG:: BZ9.
BYg:: ZD g. BD9 (hoc est):: ZB9 - ABg. ABg. quare
componenco HB9 -L B g  BNg. BNg:: Z B9. ABq hOc
eAtRN9 -ZB9. BNg:: ZBg. ABg. permutandôque R H9
Z B9. ZB9:: BNg. A B g rursulque componendo RI9.
ZBg:: ANg. ABg. denuoque permutando RN9. AN9::
ZB9. AB9:: Ig. Rg. quarEKN. AN:: l. R. ergO RN ip.
siuS A N retractus exic: . F. D.
ZVII. Elinc retractorum cum axe ConcursuS (puTa L, R, L) à sC
distant incerrallis ordinatim applicatarum ad Pyperbolam, puta recta-
rUI, BZ, MR, NS, OT; vel iplaruM O, ZI, ZR, ZL. IIX re-
ro (ceupaltim notum, ex a nobis aliquando generatim circa cunctas
hujusmodi curras ostensum est) in majori ratione crescune, quam ip (x
BM, BN, BO; nempCZL. QRL LI. RS. _EQR. ZIE RS.
PR. quare Paris liquet propolitum. Fnimrero prope verricem L.
ordinatarum difterentix perquam exisux sunt; ue bene multorum
perpendiculari A B adjacentium radiorum retracti relur e puncto
Lmanare videantur; utcunque circa ipsum praecipue constipantur.
XVIII. Flaud absimiliter, in secundo casu, super ipsa AB describa.
tur semicirculus; _ huic accommodetur BD = BZ; _ COnneKA
procractaque AD retringenti occurrat ad Y; tum centro B semiaxi-
bus BZ, BT describatur ellipsISHIZ C3; Cc in hac accepto quocunque P18. 45.
puncto S ducantur S AI ad Z B, _S R ad FF parallela; connectan-
tur denique rectae ANI, KN; eric R N incidentis A N retractus.
Frenim ex ellipsis natura eAtRS9. Z B4--SNg:: BYg. BZ9
i: BF9. BDg::B A9. ADG:: BAG. BAg- B29. _ per COn
vexsam