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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 74, page id 797435492:0298
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L. E C X. IZ.
At Z T P:: REP. S P, _ CONNCCTaTUE SF; hac Curram
F B Frariset; id quod omnino limili discurtu demonstratur, quo ter-
tia hujus; cancum hic (non per P ad V D parallela ducitur, ar) con-
nectitur FT; _ loco sextimx allegarur octara seprim Lectionis.
quid plura ?.
ZIII AdnOTetT, Si linea E B F. SE recta, (rectxe nempe B R coin-
eidens) esse lineam F B P ex infinitis hyperbolis (vel hyperboliformi-
bus) aliquam; quarum isieur (una cum aliarum intinities diversi ge-
neris plurium) Fangentes dererminandi modum uno Theoremate com-
Plexi CUMIuIS.
XIV. Ouod Si puncta P, Rnon ad easdem partes puncti D (vel P)
cadane; CuIErX F B F tangens (B S) delignatur Faciendo NI X. R D-:
est
-LFD. MX TD:: RD. SD.
Simili plone discursu constat hoc, tantium (quartae loco) seprimae
Lectionis quincam adhibendo.
ZV. Fhinc autem nedum Ellipsoidum omnium. (polito nempe line-
atm F B E. rectam esse, linex B R coincidentem) alt aliarum alcerius
generis linearum innumerabilium Tansentes una opera determinan-
TUIE.
Exemplum. Si P F SIt e quatuor mediis quarta, Peu H =5; d H
=4; erit SD =STDX RD
+RD = TD.
Cocetur. Si conrigerit esse ND X RD =
MZ XFD, esse DS
intinitam; seu B S ip(i V D parallelam. Alia possene adnorari; sed
relinquo.
ZVI. Inter alias curras innumeras, etiam hâc methodo (issolse
Cissoidalium omne genus comprehenditur: Sir urique semirectus an-
Sulus DSB; curraeque dux SCB, SF F. sic ad se reterantUE, ut
ductâ libere recta C F ad BD parallelii, (quae lineas expositas, ut
conspicis, (CceF) (InE P G, P F, P F continue proxortionales; tangat
aurem recta C T curram SG B in G, reperietur qua ad E linea SFB
tansit, Faciendo 2TP-SP. TP:: SP. RP: utique COnNCZA
R F CuEram S P F tanget. Id quod e praemisses Facile colligime.
DuodEijam carra SCB sic ciiculus, ex applicationis ansulus SP
F18. 202.
Eig. 203.