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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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De Sectionibus Conicis.
DROP. 17.
Hoc est (Tobsicutisidoneis symbolis, nemper =
Aa, d DA, 5- d Da, = LA, eE C = DO) duadracum
ordinatim applicatae in EIlipE e3 1= d
1d- d2
at
 =dl-1d -- d2. (omnes enim hae nOtatiOneS FAn-
tundem valent.) Ec quidem (repetita Agura PrOD.
13.) cam sepacarim Ia FOr BD, _, d2 - = FS nDB,
qua conjunctim - 1a = d2 -- FD, DB- FS = DB =-SD.
DB. DO9.
Demonstratione non opus est alia quam quae proposicionis
curriculo pastim incerterieur.
Estq; hoc quidem essentiale Bllixleos Symproma; unde rcli-
qua dependent de calculo deduei pollune. Uc jam non opus sIE
reliquarum affectionum in ipto Cono inrestigacio; led melius
_ clarius deinceps in absolura Ellipsis contideracione (line ul.
Io ad Conum respectu habito, incticuecur: quam proB. 26.
asgrediemur.
PROP. XVII.
De Hyperbola Sectione Conifacta.
N Experbola; Ouadrata Ordinatim- applicaca-
rum, aequalia Cunc aggregaris binorum rectangu-
lorum; quorum quidem altera sunt intercepeis-
Dismerris proportionalia, altera vero in carundem
ratione duplicata.
Sune enim Omadrata DO, aequalia Rectangulis BD, DS
(Per PFOD. 7.) Ducta verO recta SF F ipA AH paralle-
la, (qux Traperium SSHa in Parallelogrammum
SFH A _ Triangulum SFS, dirimat) erunc ubiq; recta
DS- DFtFS, _ Rectanonta BI) aDS =BD = DPt BD+FS.
Sunc aurem (propcer aequales DF) RectanGula BDKDF, re-
etis BD proportionalia, ideoq. B rectis DA Diamerris. intercep.
ed