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# Title: Qua Continentur De Angulo Contactus & Semicirculi, Disquisitio Geometrica. De Sectionibus Conicis Tractatus. Arithmetica Infinitorum: sive de Curvilineorum quadraturâ, &c. Eclipseos Solaris Observatio (shelfmark Leibn. Marg. 84:2)
# Folio 48, page id 824573315:0068
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De Angulo contactns.
C AF. 14
ric, adeoq; peripheria B Aeranclcat e nullius eradac magni-
cudinis, limal eciam angulus BAP cranelcet d nullaS ACC, H
venullius maxnieudinis. Es aucem, hoc in catu, angulus ille
B A P, rel iple ansulus conractus, rel Calcem non iplo minoii
trgo angulus contactus nullius et magnicudinis, sire non. an-
sulus. Ouoderas demonstrandum.
C A P. XI
Rreumentum sexrum, Fx Opricis petitum, es
Sectionibus Conicis.
Onechic tandem Clarius, de quidem recte, Id quod de an-
V gulo conractus, qui fir incirculis, docetur; verum etiam esse de an-
sulo contactus, qui inconieis sectionibus efficitur: Vi enim demonstrat
pollonins Pereaeus lib. X. Prop 32. In lecum, qui inter coni sectionem
e rectam lixeam tanoentem interjicitur altera recta linea non eadir: A. q
aceo angulus ille comactus minor etiam est omni acuto rectilineo,  rels
quus anculus ex recto (snimirum ex pancto contactus ad lineam ran-
eentem excitatur perpondicularis; omni acuo rectilineomajor. Tloc c90
quidem canquam rerissimum aenolco, non modo de lectioni-
bus conicis, sed B aliis qnibulris curris: nempe angulum con-
caccus, qui ad illasesticicur, minorem esse omni angulo acuco,
mpote quilinonansulus; reliquum vero ad rectum, majorem
esse omni acuto rectilineo, efenim reccus, et recto rectilinco 
qualis: cR enim hic eadem racio qua in circulo. AC hic, IN-
quie, major absurditas apparet, quead sensum, in ea FIlips quae perexi
duom habet laricedirem, e in ea Fs) Perbola quae fere linea recta esse vi-
deatur: valdesenim inaquales cernuntur anguli ad verricem illius Fllipsis
e Fyperbola constitnti. Verum cgo neque majorem absirdicacem
neqi omninocllam hic conspicio. Duamris enim crurum di-
raricatio exera punctum contactus raria ridencur; in iplocam
contactus puncto non est varia linearum inclinacio, nec quidem
omninoella. FC, si nihil absurdi sir, lineas conciguas in iplo
contaccus puncto, requaliter omnes distare, (hoc est, non omni-
nO,) licec exera illud punctum carum distancia (pro varia ip.
Carum diraricacione) verix sinc; cur masis ab lurdum cset, ca.
rum omnium inclinariones, in pancto contactiis, rquales esse
hoc ek, nullas) licec alibi Ene adm ocium inaquales ? AUC e.
Eda_