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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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PFOP. IX.
a O e L C 1, 5
inter ipsas ordinatim. applicatas et verticem in-
TCrCePEIS, P A, D A, _C.) aequalia quippe re-
Ctansulis BPS, BDS, _C. Qua PrOPteI aqua-
les PS, DS, ec. (in parallelogrammo APSS)
Tune aeque alta, et propterea basibus (PB, DB,
ec.) proportionalia.
Adcoque ipsae ordinarim applicatae sune in
subduplicata ratione Diametrorum intercepta-
rum; nempe in subduplicata ratione Tuorum
Quadratorum.
Si isitur ordinatim applicatae quotlibet aequa-
libus ab inricem distantiis CIANEUT; CrunE cacum quadrata in COn-
tinua progrectione Arithmetica, (ut patet ex dictis ad PrOP. 2.)
Constabit isituT (PeF PEOP. L.) Semiparabola planum (adeoque et
torius Parabola) ex infinicis numero lateribus quadratorum Ariitime.
tice proxortionalium.
PROP. IX.
De Converde, Cs Pyramidoerde Lalabolo.
A
A quadratis, ad communem axem ordinatim posicis, Formetur Py-
ramidoeides Parabolicum (eo modo quo ProP. 5, 6. Formarimus Pyra-
midem e Conum,) erit illud infinitorum numero planorum Rrittime
tice pro portionalium aegregacum, (sicut Friansulum rectarum,) ab
o incipiendo ex continue progrediendo ad butin usque
TInc sequitur; Si ex omnium in Parabola ordinatim applicatarum
Adeoque si Basis tigura lic conttructa in lemistem Alticudinis du-
catur, prodibit corius figurae soliditas: (eodem argumento quo us
Tumus de triansulo PFOP. 3.)
Cumque idem (eodem argumento) raleat de circulis, aliitre Rou-
ris planis similibus quibuscunque, (sunc enim ad inricem, ut diame
Erorum, vel rectarum quarumlibet limiliter ductarum, quadrata;) erit
univerlaliter Conoeides vel Pyramidoeides Parabolicum, quacunque bale,
(sire etiam crectum sic, sive scalenum, sive etiam quocunque modo
luxacum, per ea quae dicta TunC Pr. 4.) aequale basi in semissem altitu-
dinis ductae; hoc ett, Semissis Prismatis (ul parallelogrammi Priansu
lum) super eadem basi aeque. alti.
Fsenim (ex dictis) Pyramidoeides Parabolicum (Fub quo et Conoei-
des comprehiendo) Asoregacum planorum similium numero intinito-
rum Ariclumerice proporcionalium (ab 0 continue proerediendo,)
Circa