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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)
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P. E C T.
22.
cenErum C) dirique sine duo puncta A, X; reperiendum est si
circumterenria punctum aliquod; a quo ductx ad A, i recta, alrera sic
alrerius rerexa. I Hlocit2 perticimus:
18. 92,93. Conjurgantur rectae A C, X C; ee tiat (scortim) ans. S = = an8.
AC. X. e in Ed crure ansuli s sumpro libere puncto a ducacur e V
ad Es. perpendicularis alrerum erus sceans in V; _ in V a prorracta
CapinEuE ~V. = uV; cum dividatur z V in 8, ut (IC V P. DV:: XC. CA;
verque punctum e crajiciatur rE sic uc sicnE. XY:: CX. CH. denique
Har angulus C N xqualis angulo EuV; erir punctum N quale deli-
deramus. Nam ducantur Z 1V, EV; SAac ane. C NC == ang.
 vy. adlumaturque PO = PN; ex connectatur XC.. liquet jam
trarigula ZC. N, Er v Cimitia fore; nec non ipsa C NF, u ve;
ex ipla X. P F, E ~P; ipsaque demun X FHI, EoV altimilari. Quare
BF. XF :: ∞8. EP. _ XF. FN:: EP. PV. e ex Xquo PF.
F. N:: 8 P. oV. e antecedenres duplando 2 PF. FH:: 2 ~ 8. pV.
componendoque 2 P F -+ FN. FN :: 2 ∞ P + PV. PV. hoc est
GF. FN: : 7 8. oV (hoc CA):: XC. C A. ducatur jam NL ad
DC parallela; quare est ans. I. N C = an8. (1 = a18. XNC;
e XG (XN): NL:: GF. FN:: XC. CA. POrrO HaL anS
L. NEI = = ang. XC A, _ EIN protracta ip(I C. A Occurrat in M:
eAque propterea rriangulum LINI. simile criangulo HCM, idcir
coque HC. CM:: HI. N. N L. ducatur denio tangens NC; cA
que rum ans. PNO = rect - C NP = rect u N V _ == aBB.
= 2X C A; vel 2 ang. P NC == 2nG XC A = ar8 L. NH.
Veriim eFaL priuS 2 ang. X N F = aHg. X NLs erGO 2 anS ZN F
2 arBP NC
= anS XNL - ang. L NFI. HoC CA2 anG X N C
=ans. X NH. ergo cangens N O Disecat angulum XNH; indéque
consectatur fore rectam HI M iplius X N reRenam; ac ideo esse XC.
HC:: XHI. HIN. atquifuic prius HC. CM:: HN. NI quare
Jam exit ex xquo XC. CM:: XN. N L. (hoc eAt etiam e PEXmIOM
Atratis):: XC. C A. unde C M =C A. QuaPEOPTeEHM, ipsiuS.
XN rehera transir per A: Ouod propolirum erat efficere. I
VIII. Hujulee Problematis Ia generallus propolui. varis Guidemt
calus lune (erenim vel data puncta jacene aribo extra circulim re
Acctencem; vel ucrumque politum est intra circulum; vel unum incra:
jacet, alterum extra; quinetiam in horum catuum unoquoque pluries
conticitur negorium, alt ubique non ablimilis erit construetio, lane
nimius essem; meamque pariter ac vestram pacienciam macerarem
omnes intricai Problematis nodos erolvendo; suffecerit ejulce specir
men aliquod proculisse.
IX Adnora.
Fem. Prared.