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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)
# Folio 327, page id 851387705:0347
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PEOB. XXV
 O X
Rectam nota l’insienicam, (lin
neam puta imasinariam, quae cum
intercepeis diametris, concinere
supponitur rectangula Majora,
diameeris interceptis proportiona-
lia,) axpello Latus. Rectum.
Rectam rero alteram, quae no-
ta t designatur, (quam quidem
supponimus Diametri sesmentum
esse, a verrice versus concaram
Currae partem ductam; quaequ
ita se habet ad latus rectum ut diametrorum interceptarum quadrata
ad rectansula Minora, illis quadraris proportionalia.) Diametrum trans-
versam appello; (ut quae oppositos vertices conjunsit, puTa A2, ut
mox dicetur:) ejusque punctum, medium, (quod in ip la Diametro
intra Ellipsin jacere luxponimus, nempe intra oppostOS rertices,)
appello Centrum.
Fellipsin a nobis definicam eandem esse cum ea quam desinit spollonius, (niti
quod nos etiam circulum, scu circuli Peripheriam, eadem voce includamus, quam
excludir Apollonius;) eodem fere prosreltu demonstrari porelt, quo lupra octen-
dimus Parabolam noltram eandem esse acque illius.
Nempe, FIiph Apolloniana, Sectione Coni factae (quae ab Apollonio deseri.
bicur P. 23. Lib. E. COZ.) univertalicee conrenire detinicionem noltram; jam pro.
batum clL PTOP. L3, _ 26.
Ellipsin d nobis detinitam quamlibet (modo circulum seu Peripheriam excipias,
quam eso sub ea roce comprehendo, concra quam ApolloniuS,) ita COnO aptari
posse ut condiriones eas habeac quas postulat EHip LiS APOlloniana; SIC BTOBaTUT.
Exponatur F. Iliplis quaelibet a nobis detinita, aco cujus ordinatim applicatarum
guadraca sine c = 1 d - = 23. Dico hane Cono ica aprari poste ut postulacur.
Ducantur enim rectae A2 = +, AS =I continentes angulum S A a quemeun-
que acucum, (modo major sic complemento anguli inclinationis in F.lliple expo-
lita, quem Faciune ordinacim applicata cum expolica diameiro;) ipsique AS Pa-
raltela ponatur aB = Aa = F, angulum faciens AaB == S Aa: (Taltem TANEX
sine lonsicudinis AS, aB, UE SE ASxaB = IF; modo incerim non LnE AS, aB,
inricem aequales; eo enim casu non Conus, sed Cplindrus Prodiret:) FL junean-
tur rectae aS, BA, quae continuatae coeane in V, complenres triansulum V a B
(A nempe a B major sIc quam AS, prouc jam supponimus; rel, l secus, crian.
pulum VAS:) quod esto triangulum per axem Coni mox construendi.
VB SN C ACBA L1I
Deinde super rectas Aa, 2 B, duo plana ita CrIGAnEE VE COMMUHIS CatuI Le
Etio aco faciar cum recta a B angulum rectum, cum recta vero A a angulum desca
lem angulo inclinationis Ellipleos PrOPOLI. HloC enim omnino ficri polle con
ICac: St CHI exIgATuE in punelo a recla dcon qua Ht iccla Pa Ualili
(adeoque