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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 824573315:0132
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De Sectionibus Conicis.
P ROD. 2Y.
rabola terminantur,) Ced alias qualvis ipsis parallelas
(quantaeris lonsicudinis) Diametro Cimiliter aDpoli-
tas, ex propterea eoldem cum diametro angulosta-
CIEnTCS.
Acq: hinc quidem E Fuisset res integra, neq. Conicx Section
DES, UE roCancur. Originem a Cono craxisse rulsO reputaren
EUT, (quare e mihi necesse ecac eas, sccundum illam eci. m hy-
Pothelin exponere, ne videar novas qualdam Aguras commin
nilcis pocius quam ab aliis receptas explicare:) licuisset corius
hujulce cractationis inicium poluisse, omiltis eis omnibus que
Tuperius in parce prima exhibuimus; auc ca tolcem (si libuil
set adjungere) hine qualia re ofonce demonttralle. (Adcog3
noras cerminorum aliquot detinitiones necesse ek e hic et de-
inceps aliquocies adjungere, omitta C’onimeneione, ne opus sit
ad praecedencia recurrere, aut Coni auxilium in detinicionibus
Pottulare.)
Non enim est Parabolae magis essenciale, uE Rac Sectione Cont
Plano lareri parallelo; quam Circulo, We Hae Sectione Ceni plano base
Parallelo; auc Prianvulo, uc trac Sectione Coni per Verricem. Neq3 il-
lud voluncalii: Onamris enim Parabolam (quod e de aliis
Coni. Sectionibus similicer incelligendum cM) Cecto Conosc.
merari dehniane; non camen Colas illas, qua Cectione Coni fune,
pro Parabolishabenc, (nam ec alios aenoscune P’arabolam in
plano delcribendi modos;) Ccd cales esse volune (sive fguras
sive lineas curraS) quales ejulmodi sectione Coni heripol
TUInE.
Parabolam aurem a nobis definitam eandem esse cum Parabola Apot
loniiu ee aliorum; calemnempe, qualis sectione C oni effici pOtIE
ic demonstro.
Fko Parabola quaelibet a nobis detinica aa (ejuisq; Oedina-
eim applicaca qua libet roo, cum diametro ax angulum ara
quemcunq. Faciens; (irg; ex lacus rectum.) Dicohanc Parabo-
lam calem ette qualis sectione Coni efici pollet,
FiaNE eNIM reCtX AD -- PB = Er: (IC9: aBGNlUS APB rectus
_ (Continara BP) HaC PS =an; e jungacur recta BA, quX
(CONCINVATA) CONCUERAE cum recta SV (ipsi PA DaraIICla) in
uc compleatur eriangulum VBS; super quod erigatur cir-
culur