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# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica (shelfmarks Leibn. Marg. 100:1/2, Stück 1; Leibn. Marg. 100:1/2)
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DE SFCTTONTBOS
PcoP. XV.
enim omnia rectangula BD x DS, HBC est, omnia quadrata DO, aequantur ont
nibus rectansuslo BDX VF, demptis omnibus BD X LB, Patei propolium. Om
MIa CHH SCCaS la BD X D F consticuun cuncum Parabolicum, (per PTOP. TF.)
Omnia vero BOX FS, Pyramidem; (PeF PTOP. 6.) Forum isitur ditterentia à
quatur vel Cuneo EIipeico, rel etiam EIliprico Pyramidocidi.
PROP. XV.
De Conveideos e Dyramidocideos Flliptici Sectione.
27 Poramidoeides vel Conocides DNipticum plano per Arem (vel,
Ei maris, Diametrum) sccetur; sectio exit (vel circulus, rel Cal-
C) LFtdo
Probato ejusmodi uenda est, qualis prop. 6, _ r0. ubi Sectio Pyramidis
per axem ostenditur esse Priangulum; e Pyramidocidis Parabolici Parabolom
Alias rero lectiones non per-Axem, non liber hic speciacim actinsere. Moneo
tamen Conoeideos Fllipriei (hoc elt, Sphaerocideos) Ares (nisi Diametros malis
appellare) numero infinitos esse in communi centro (ue FIliplrum Diametri) cocun-
tes: qui omnes sua plana habent ordinatim applicata. Noca etiam Conoeideos FL
liprici (vel Sptiaerocideos) Sectiones omnes plano factas (Cire per-axem, adeoque
et centrum, transeunte, sive non,) esse (vel circulos, vel Paltem) Fllipses.
etis aurem diurius insistere non est hujus loci. Sulticit monuilté.
PROP. ZVT.
De Fllipsis Latere. Recto.
AFTNE manifestum  ex dictis, Ouadrata DO, (Rectanoulis
BDKDS aequalia,) ex cognitis rectis BD, DS, cognolci posse;
non autem, e contra, ex cognitis DO, cognolci rectas BD, DS5
(possunt enim rectangula BD x DS infinitis
modis rariari, dummodo eadem maneat ordi-
natim applicatarum quantitas, adeoque eadem
Eliplis in conis distimillimis reperiri: ut pa-
tere poterit ex eis quae supra de Parabola dicta
Tunt ad ProP. 12.) Placuit isitur Conicorum
Scriptoribus (ue in Parabola, HC) in FIliph aliis
mensuris ordinatim applicatarum quantitatem
determinare, quae eandem Fllipsin ubique co.
MIEONEUE.
Nempe pro singulis rectis BD, substitmunt
singutas AD, diaMEErOS INCETCEPTAS; quae qui
dem illis sune proportionales.
Pro recta vero AS, substituunt aliam, puta L A, imaginariam,
(quod Latus Rectum appellanE) quae tribus AS, BD, D A, sit quarta
reciproce proportionalis; ut sic ubigue BDK AS =D AXL. A. Ad.
eoque Latus rectum L. A =
X AS, _ AS =
DB+ L. A.
Tum (continuata Diametro AD donec oppotito Frianguli per-
axem cruri occurrat in a, ut habeatur Diameter tranlrersa Aa;) erit
propter similia crianeula) AA. AS:: Da. DS = - = x A5. 1d00.
Ad
eaC
nd