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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.
PR OP. 21.
henlo:) Acqi eadem ratione reliqua orclinarim. applicat DO
reliquis sa conGrMUnE, a debq; & Parabola Parabolae ConBrHIE.
earabola isieur a nobis definita, Parabolae sectione cont tacta
congruit, adcog; calis eA qualis lectione coniettici poBet. Ouod
erat primo demanerandum.
Concra veros Parabolam lectione Coni factam talem elle
qualem nos delcripsmus (nempe ouadraes ordinaci applI
catarum habere diamereis incercepeis proporcionalia) lupra
demonstratum cM prOP. 8212-
Eadtem ipicur est Parabola qux ab Apollonio (alii(93) & qua
a nobis detinicur. Quod ostendisse Darerat.
Sed e cadem opera docnimus; Conum construere, eique datam Pa-
rabolam ita aptare, ut data ipsius diemerer frat Diameter- ex penerarione.
Acq; eciam Theoremacice verum esse, Parabolae diametrum quam-
libet fieri posse (in aliquo satrem ConO) diametrum ex generatione; e
guomodo ilbiu frat. (ouamris et illud aliis mille modis heri pol.
IC. )
An veronnivertalicer verum SC, Datam Parabolam dato Cono ila
aptari posse, ut data ipsius diameter fiat diamerer ex generatione, eAt alia
dilguitirior EA aucem e illud rerum, modo datae diametri ad
Luas ordinacim applicacas obliguitas major non lic quam obli
quicas axis allignaci Cori ad batin Euam. Si lecus aurem; illud
non hec dummodo solum circulum pro C’oni bale agnolcimuso
Si vero admictatur, ue non modo Circulus, sed et EILip(S qua
libec probale Coni repucetur; cciam eniversalicer illud rerum
erie, neqi decerminacione indischie Theorema. Hoc aucem
obicer eancum sine Demonstratione moneo; quoniam nec illud
eshujus loci, nec mihi animus est ad singulas minucias delcen-
dere. Ad reliquadisicur Parabolae acCiones CaLCUIO COMPIO
Bandas festino.
E O P. XXII.
Corollaria.
datet ex dictis; duodeum st(ut oltentum elt) p2 -- d3
a erune, in Parabola, Diamecer intercepta, Ordinatims
applicata, ex latus. Rectum, continue proporcionalia.
Ad eo43