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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 353, page id 851387705:0373
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 11C.
P R O P. XLVII.
De Area Paraboloeidis; e Conveidis Pyramidocidisve
illi accommodati.
T Archimedes (in lib. de Quadratura Parabolae) ostendit P2
rabolam (fsuram puta linea Parabolica et recta contentam)
esse ad Friansulum (Cuper eadem vel aequali base aeque al-
tum) ut 4 ad 3: Sic et demonttrari potest, Parabolocides cubicale
ad Friansulum (incellise, super eadem bale aeque altum) eAC ut 3
ad 2.
Trem, ut Conoeides Parabolicum ad Cxlindrum (ret Prramidoci-
des Parabolicum ad Prisma) est ut x ad 2: Sic demonstrari potelt,
Conocides à Parabolocide Cubicali ortum ad Cylindrum (vel ejul-
modi Prramidocides ad Prilma) ee ut 3ad 5.
Haec aurem alibi (Deo volente) inter ejusmodi alia mulea aliquando sumus de.
monstraturi. Arque insuper generalem methodum tradticuri, qua Parabolocidea
quaeliber ad Ouadrata, et eorum Conoeidea Peu Prramidoeidea ad Cylindros aut
Prismata reduei postine non minus quam ipsa Parabola aut Conocides Parabolicum
rectum, (quod et de Conocidibus d Pyramidocidihus P. lipricis dt Lyperbolicis,
sive rectis live scalenis, incelligendum else rolo:) Duae nemo, quod sciam, ance.
hac aggreltus elt.
P R O P XLIX.
De Parabolocidibus aliis.
CI Parabolocides Ordinatim. applicatas habeat in Diametrorum in-
d
cerceptarum ratione subquadruplicata, rel subquintuplicata, _c.
(in quibus nempe Diametri intercepex sunt Ordinatim applica-
tarum biguadeatis, vel surdesolidis, ec. proportionales:) diei poterie
Parabolocides Biquadraticale, rel Sur desolidale, ec. (nomine nempe ra-
tioni aptato.)
Latus rectum ejusmodi Parabolocidibus conveniens, appello rectam
imasinariam; cujus, in Biguadraticalibus, Cubus in diametrum inter-
cextam ductus aequatur Biguadrato Ordinatim applicatae; in Suver-
Solidalibus, Biguadratum in diametrum interceptam ductum aequatur
Suversolido Ordinatim applicatae: (et similiter in aliis Parabolocidi-
bus, respectu semper habito ad gradum Parabolocideos.) VE sit
(prouc gradus postularerit) p = dV, vel p = d V, & sic deinceps.
ReCtA VerO A F (diametri continuatio inter rerticem et tanoen-
teM InFeTCCPEA) est, in Parabolocide Biquadraticali cripla, in super-
Colidali quadrupla, diametri intCTCCDEX P A; (ex similiter in aliis: )
FIOc eAt, continuata diameter PF (applicationis puncto et Tangen-
tIS CONCUTSu InFEFCCPCA) CA DiaMEETIINECTCCPEX PA, in Biquadia-
ticali quadrupla, in Supersolidali quintupla; et sic deinceps.
Demonstracio pari modo procedet atque in Paraboloeide Cubicali; aue eriam
ipla Parabola.
Adeo ut jam Parabolocidis Cubicalis, Biquacraticalis, supersolidatis, auc alius
cujulris, doctrina, non minus cosnita habeatur, quam ipsius ParabolX.
Si ramen, post specimen hoc extibitum, operx precium centebitur rem hanc Fu-
sius prolegu, voceric illud a quoliber lacillime tieri cuicancum luppecic ori.
ROF