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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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PROP. 27
De Sectionibus Coneis.
eo, ue hic duorum planorum communis scctio qualis impero
Tueo
In plano aucem aaBsic potico, Ceribi inecllie tur circulus di-
amecrum habens aB, qui sic balis C oni; alsiq; huic paraIIcli eo
num complences, juxca prop. 5; qui plano Aoa sectus EIliPCN
extribebie, per Prop. 7. cujus ordinacim. applicarae cand. m ad
Diameerum inclinacionem habebune, quam quae in FIIips ex-
polica, adcoq; limilicer policae lunc; eruntq. etiam lonsieudine
aequales, uc probari poterit per prop. 13e 16. Conoruune igi.
cur Elliplis expolica, et quae in C’ono extribetur. Adcoqi, cadem
eAt Elliplis a nobis definica (nisi quod nos eriam circulum ca
detinieione comprehendamus) acq; Flliptis Apollonii. 990d
crac demonstrandum.
Sed e eadem opera docuimus, Conum construere, eique daram PL.
lipsin ita aptare, ut data F.Iipseos Diameter fiat Diameter- ex. Gener atio-
ne. Acq: etiam Theoremarice verum esle, Ellipseos di ametrum
quamliber, fieri posse, in aliquo salsem C. DnO. Diametrum. ex gevera-
None.
PROP. ZXVII.
De Ellipseos Diametro- transversa e Verricibus.Oppositis.
I Ellipleos Diameter- intercepta AD intelliga
tu (a vertice A verlus concavam Curva par-
cem) tanca allumi, ut rectae quam t diximus TIE
aequalis, (hoc est, ita se habeac ad latus rectum, ut in-
cerceptarum diametrorum quadrata ad Recrangula
quae diximus Minora) erit e reliquus iptius terminus
D in Ellipleos curra. (Nam IId - 1, crit - d2 = - d
Idi ideog; e2 = 1d - - d 2 - 1d - 1d =- O. hoc cA,
Ordinacim applicata eranescit, puncto nimirum pe.
rimerri cum puncto diametri coincidente.)
Ondepater; Omamlibet Fllipseos Diametrum binos
habere verrices, (ut quae in binis punctis perimetra
Occurric;) quos Vertices Oppositos appellamus. Diame
C