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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 41, page id 797435492:0253
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LF C T.
punctum Z intra punctum M; erit tum recta P F majOF areU P Z;
unde arC P A. P F =  ArC P A. PZ :: PM. Z Z -- DM.: F18. 27.
PM. XZ - EHI:: P M. XF -= ZZ DPM. EI Z. _ vicissim
PA. PM SP F. TIZ. Verum ut priiis) est P A. PM :: PF. HK.
ergo PE. HIR  7 P F HIZ; PrOPtereaque HIKL IIZ; rartuS
ique liguer Punctum R exera curram exiltere. Pota proinde recta
MK Z exera curram verlatur; e ean rangit ad MI: CL. F. D.
Intranscursuhoc. 2d alias curra nostra passIOneS REVEKTAmUE.
VII. Si tangenci cuixiam (ut ip(I M T) Parallela ducatur quae-
piam E F. (a puncto nempe quoxiam P in recta intra punctum T ium-
PtO) hZC CUEYX OCCUTrEE.
Sienim intra punctum M in curra sumatur ponctum quodlibet, _ Fis. 2.8,
ab eo duci concipiatur curram tansens recta; huie Occurret rangens
TM intra ordinatam PM. ergo recta R F cidem occurret, ac curvam
priustranfiliar opoxter. erg o liquer Propolicum.
VIII. Fadem opera patet, si punctum assumprum F puncto T.
ee rertici A incerjiciacur, rectum E P currx bis occurturam, eam Cupra
quam intra contactum MI.
Operose connitus est Apollonins hxc de Sectionibus Conicis ostendereo con. Y. 27, 28.
Caeterum ad penitus determinandos occurtuum locos Specialis mo-
dus sen ratio moruum descendentis atqe transversi cognosci debet: runc
cos Analysis Ctatim prodet.
IX. Si dix reCt quaeris (AIM, R N) ad curram propOII
im aequalicex inclinentur Chocest xquales cum ejus ad occurtusran- FiB. 29
gentibus (puta cum ipsiSM T, N Z) angulos efficinnc) lix exrrortum
diveroent, Peu ad partes P P producta COnCUrreNE.
Nam ducatur subrensa NM; haec uriq; secundum antedicta cum
ipsa AZ conreniet, puta ad O. Fst ergo ang OMHI 2 (an8.
LMH = anB. Z N R = B) anB. ON R. ergOAnG. HMN -1
MNRC 2rect. ergOrectX HM, R N concurrunt ad partes F F.
Limitandum est hoc, intelligendo pares angulos HM A, RN A ad
ealdem partes velari; scu alrerum alteri lore externum interno. al ias
corrra crenier.
X. Si fuerit recta EM curva perpendicularis (hoc esuis lat. L19. 30
GenCI MZ) ec in hac sumatur quxpiam detinira HIM; eris H M mi-
nima rectarum omnium, juxe a puncto FI duei poNunE Ad CUrVaTI. Ab l. Y. 38 dic.
DucatMr