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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)
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guadrando)
De Sectionibus Conicis.
c
5
1-
DROP. 39.
1H a2  2 aN = - 1. EC (eran(-
Donendo, acq; reducendo) 2ac - -- a 2 + - l. BC (qua
drando)
44 e c2 l = a 4 + = + 5 + 1 2 + 2 a  52 I1
44 2 1
(dividendo per
) erit c2
Adeoque
a12 +5 + 12 + 2 a 2 52 I
4
5
1
Habetur ergo quancicas c2, (cujus radix c =C HI,) adcogi
punctum H, cui (i OrdliMaEIM- DONATUIE COM, eriE OM =a3
Cquod, h opus se lynchetice demonstrari postie, repecicis Ana-
LyCeosrelisiis,) adeoqi minor quam distancia allignaca 34.
Tdeogi distancia continuata rectae CMM, ab Hyperbola con
rinvaca AO, tandem minor eradet dictancia queris alignarL.
Ouod erac cercio demonstrandum, Adeoq; conttat propoll.
Eur
Posset _ hic octendi, ad eandem Eyperbolam, nonnist duas A
sympioras (urrinque unam) duei posse; se muiuo incentro secantes. Alia
enim quaecunqe in eodem plano recta, rel yperbolam lecabits
rel ad requilicam axproxinquacionem non accedet. Ictacile
es demonstracu.
Icem, asimptoras unius IsyPerbolae esse etiam (I) perbolae eppositae A.
simpiotas. Duod simili Fere progressu demonstrabicur ei quov
lus Cum ad Ciorollarium prop. 37.
Neque illis tantum binis Cyperbolis Opposiris, sed es binis aliis hisce
conjusaris (de gnibus pose dicetur) ea dem conveniunt asympiolae, es qui-
dem solae.
PacCCIcem, quod C si ab eodem puncto FI, ordinatim- applicata
TIO, EO, urinque continuentur ut asemproris occurrant in NI,) crunt
OM, OM. Cutring sumpia) aequales. Cum enim eam HN, HM.
1) quam HV, HO, CV- 1- VE
_ OM, OM, CHIM L 1O) eguales.
1) erunE
Icem; Si Cadeandem gnamvis Diametrum) Ordinatim ponantu
rectae quorlibet AOFIM, C.Asymptoris occurrenes in MZ FBy perbolae in O,
diametro in FI, omnia rectanenta NOM (seementis comprehensa) vel
etiam rectaneula OMO Csumpris O, O, in utroque crure Hyperbola) erunt
ta1B