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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 67, page id 797435492:0291
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E F CT. VTII.
Nam asymptoris E R, A B Per F descripra concipiatur hyperbola
OF O; cui occurrat à D projecta guxepiam DO, lineas expolitas (a) Convers. 9
secans, uti cernis. FAque QO (a) = DP; (b) quareMOC D P Lect. VI.
(0dE, DEI (b) =M NI. ergo hyperbola O FO CUrram YF N Lan- (6) Hyp.
BIt
(5) Fiter.
Verim (d) recta L. Shyperbolam O FO tansit; BXCItAQUC CUEVAM (d) 9. Buju.
YF N quoquetanzet.
NoL. Si X F M ponatur linea recta (vel ipsi P. R coincidar) erit
YF N Conchois prima vulsaris, Peu Nicomedea; hujus ipitur tangens
e generali ratione quidam habetur determinata.
ZIII. Sic recta L A, curraque quaepiam B F I; cum alia CuEVA
DF Ctalis, ut dueta libere recta P FF ad pelitione datam quandam
parallela, postic recta P E quadratum ex P P una cum quadrato ex da- Fis. 87.
Ea Z; item curram B C I tangac recta F T; tum Hac PF g. PF9::
P Z. P S; connexa SF curram D FC tanget.
NIAM CONCIPIAEUE CUEVA V F EI calis, ut libere ducta O R ad P Li
parallela (quae lincas expolitas secet ut vides) (IE DErPeTUO OR9 =
OHg.  L9; unde quoniam est QR (a) C Gl; exit OK9
Ca) Hyp.
L4c OI9 - Z q3hoc eAt OHgL GG9; ergO CUrra V FH (B) 22. Lett. 6.
curram D FCcanset ad F; (b) est aurem curra V FHI hyperbola, quam (C) Cor. 22.
(5) cansit recta SF. hxec itaque curram D FC quoque conrin- Lcct. L.
BCI.
ZIV. Cxrera ponantne eadem; at jam P P una cum quadrato ex
daTA Z POSSIE QuadIEaTUIM Ex P F; RarquE P F g. P F G:: PT. PS; FI∞. 88.
e connectatrur FS; haec rurtus iplam C F C continger.
Similis est demonstrario; sed adhibe 23am prime Lectionis.
ZV. Sint CUrVx duIX AE B, CCD, communem habenteS AXeM
A D, ac ita versus se relatxe, ut duetâ quacunque recta F F. C ad AD
perpendiculari (quae rectas expoticas secer nie vides) sic summa qua-
dratorum ex ipsis F F, P C. aequalis quadraro ex decerminata recta L; Fig. 89.
tansar autem recta F R ex his curris unam AFB; _ HaC F F 9.
FGq:: F R. FT; COnnexa C. T CurraM C GD quoque tanget.
Concipiatur enim curra OCO calis, ut ducta rectâ R QO (qua
rectas FR, PR secet punctiS R, C cueram OCO in O) (IIO K9
20 == 29; erit ideo OKg - + 209 = O19. -OL9;
_E Cu SEOK9 (4)C OI9, erir ideo OOg3 OL 9. itaque (a) Hy.
curra O GO curram C G D (inerortum) cansic. (b) Es auem (ex (6) 24. Loct.
E
Ostenlis)