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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 59, page id 797435492:0099
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I E C Y. VTII.
uHK. CHI. = AC. KC - AK. RC = RK. K C. verum est
HP. C. N. I AN. C.N = NP X AN. CN9. ergO CNIEAR.
RC:: NP XAN. CN9. componendoque A C. KC :: NP (5. 79, 80.
x AH + CN9. C N g. Cum CIE igituE NP X AN == AP K AN
 ANG. _ AP X AH = AC9- CN9; adeoque NYP
X AN F C N9 = AC9- CN9- AN9 + CN9;= AC9
ANg. erit AC. R C:: ACg. AN9. CN9: OuodF. D.
Corolb. AR. K C:: ANTXNP. CN9.
VI. Ftiam hoc Theorema subdemus: Si AaL 2 C A. CH::
CN. F. _2CR. CH:: C N. F; _ lumatur C 9 = F 1 F
erit ducta NO ad C A perpendicularis. vel reciproce; posito quod
sIFNO ad C A perpendicularis; erit C9 = F = I F. 1I Nam (ut
hoc posterius oltendamus) guoniam est 2 C A. CNI:: CHI. F.
_CHI. 2 CR:: F. C.H. Cxir Cx aquo perturbate 2C A. 2 C.K
3:F. F. vel C A. C. R:: F. F. componendoque C A + CK. C. K
3: F- + F. B. Porro quoniam est AN g = AC g + CN9 2AC
XC; erit 2 A C X CO - CN9 = A C 9-- AN 9. itaque
(juxta praecedentem) erit 2 AC X C( - CNg. CNO:: AC.
CK. hoc est (ob C N g = 2 AC X F) 2ACX CO = 2 AC
RF. 2AC XF:: AC. CK. hoc est CO-- F. B:: AC. CK.
vel componendo C 9. F:: AC L CK. CK. erac autem AC
L CR. CR:: F + B. F. erBoC = F. + F: OuodF. D.
VII. Fix ictis porro deducetur, si dividatur Semidiameter BC in
Z, UE(IEAC. AB:: CZ. BZ; punctum Z limes erit cirra quem
(respectu centri C) nullus hujusmodi rehexus axem decussabit. Cu
jutris, inguam, radii a N estoreAexus CN. ari occurrens in K.
dico Tore CRL CZ. INam ob hypochelin (permurando que) est AC;
CL:: AB. BZ. isitur Canrecedentes, _ consequentes copulan-
40) AC. CZ:: AC + AB. C B. quare (posterioris hujusce
rarionis urrum que terminum in aequales A C - AB, d BC ducen
40) erit AC. CZ:: AC 9 = ABg. C B 9. est autem AC 9
ABGC AC9 -- AN93 adeoque AC9 - AB9. C B9.
C AC9 ANg. C Bg:: AC. CR (emox ostenlis hoc) qua-
prOPtET erit AC. CZC, AC. CR. indéque CR C: C2: FiB. 81, 82.
D. E.D.
vIUI salicer hoc sdere; ut quibuldata tortalle ridebitur, minus
inrolure: per Nducarur V Y circulum contingens. e quoniam NI
bilecar