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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 68, page id 797435492:0292
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# Lines: 44 recognised, mean confidence 0.88
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L. E C F. VIIK
Octensis) curra OOO Ellipsis, quam recta C P tangit. ergo recta
C T curram C. C, D quoque TanSCF.
ZVI Sit curra guxepiam A F B (cujus axis AD, _ ad hunc ap.
plicata D B) sic etiam alia curra VC C ad iltam lic relara, ut a desig.
nato quodam in axe AD punito Z ad curram A F B utcunque ducta
recta LF, _ per F ducta recta F F C ad DBC parallela, sIE LC7
aequalis ip(I Z F; SIF autem P O perpendicularis CurVX A FB. SU
maturque R aequalis ipsi Y F; connexa recta C, R ipli currXVGC
perpendicularis crit.
Nam ducatur F T ad ipsam FO perpendicularis, Peu curram AEB
tangens; _ concipiatur curra OC: Ocalis, ut dueti quicunq; rectâ
HIRO ad E FC parallela (gux rectas T F, T F, _ curram OG
secet punctis H, K, O) connexaque Z K, SEHIO -=ZK; tum du-
(6)25 Fec. VF Cta Z. I, quoniam HK (a) = HI, CFIEZ RE Z I, velHOC HL.
quare curra OC O curram V C,C cansit. (b) F.st aurem OC
(ex oltensis) Hyperbola cui perpendicularis cst recta GR; eadem
itaque CR CUrYX V C C quoque perpendicularis erir: Quod E. D.
ZVII. Sint recta DO. duxque CUEVX D R S, D Y X ita relatX.
ne ductâ urcunque rect a R P Z ad positione datam D B parallela (quae
dictas lineas secet, ut perspicis) connexaque recta D Y, sit Cemper
RX. DY:: DY. PY; tangat autem recta R F CUrraM D R S ad R;
OPOrTCE CUTVX D P X cansentem ad P rectam delignare.
Concipiatur linea D Y Ocalis, ut duetâ urcunque CO ad DB pa-
rallela (guxe lineas F R, PP, DY O secet punctis C, P, O) connexd
que DO s semperCiO. DO:: DO. PO; tanset Curra DYO
curram D Y Z ad Y; Nam secet recta C1O CurVAS DR Si, D Y X
punctisS, X; _ connectantur recta DC, DS, DZ; patet (e cur-
varum nacura) angulos XDP, DSP; nec non angulosODP, DCP
requari; quare rum angulusD S P major siransuloD CP; exit an-
sulus X D P angulo ODP major, adeoque PX major erit quam P O.
hinC CUrVa D YO CUrraM D Y X tanget ad Y. eAt autem curra DYO
hyperbola (a) superius determinata; Hanc cansat XS; taec igitur
suxram B Y X quoquetanget.
NoF. Si Curra D R S sit circulus, et angulus 2 D Brectus, erit cur-
ra D Y Xcissois vulgario, hujus icaque (cum innumeris aliis limilirer
peniris) cansens hic detinirmr.
AVdal. L. aa Clalai husC xect D L B3 uqe C aD L A
talis:
F18. 90.
(a) Hyp.
B
4) XZ Lec
NiB. 920