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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 388, page id 851387705:0408
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PFTOP. ZLIX.
circumra H detcribatur Conoeides rectum: vel, universaliter, S (juxra
methodum a nobis indicaram prop. 5, 6, 9. Con. Scet.)
diametro vel axi AT, ordinatim applicentur cireu
Ii, vel similia quaeris plana, quorum vel radii vel
rectae Cimiliter polux rarionem eandem habeane in-
ter se quam rectae TO, TO, ec. ut complealur C0.
nocides rel Prramidocides live rectum sire inclina-
cum: dieo illud Conocides rel Prramidocides elle
ad Cylindrum vel Prisma Cuper eadem bali aque al-
tum uc X ad 5. Nam, cum rectae omnes YO, IO.
Ec. Tine Teries Secundanorum, (quibus convenitra-
tio L ad 3:) similia quaelibet plana super has rectas
similiter constituta, erune incer se uc harum rectarum
quadrata; lire in duplicata rarione rectarum O,
FO. Aeque ratio seriei rectarum illarum conveniens (seriei quippe secundano.
rum,) estr ad 3; ergo seriei planorum conveniet ratio F ad 5: quia nempe I, 3,
5, Tune Arichmerice proporrionales: (prout Onitas, Radix, e Ouadratum sune
Cieometrice proporrionalia.) Ft quidem, si rectae YO, FO, ecc. Tinc Series Se-
cundanorum; earum quactraca (vel plana quadratis proxorrionalia) crunt series
Ouarranorum; cui in FabeIa COnVEHII EAHO + ac 5.
PROP. XLIX.
Corollarium.
T similiter; Si complemento semiparaboloeidis cubicalis aptetur (circa
ipsus Diametrum) Conoeides vel P yramidoeides; erit boc ad Cylinarum
vel Prisma (super eadem vel aequali base aeque altum) ut 2 ad 7.
Nam, cum rectae YO, YO, _c. (in complemenio semiparabolocidis Cubicalis,)
Tinc series Tertianorum, quibus in Pabella conrenieracio c ad q; horum qua-
dratorum (vel planorum quadratis proportionalium) feriei conveniet ratio L ad
7; quia 2, 4, 7 Tune Arichmecice proportionales. Vel eriam, quia plana lunt se.
ries dexcavorum, quibus in Pabella alsionatus ratio r 2d7.
ape P Rs C. Po ecI s
Corollarium. ) Sectileeu aue
cs fsitayc
F Pariter; si semiparaboloeidium aliorum (puta Biquadraticalium, Su-
persolidalium, C3C.) complementis aptetur (circa eorum diametros) Cono-
eides vel Pyramidoeides aliquod: habebit illusd ad Cylindrum vel Prisma (su-
per aequali base aeque altum) rationem notam (puta 2 ad 9, 2 ad TF, (3c.)
Cum enim complementorum illorum rectae sinc series Ouarcanorum, Ouintano.
rum, ecc. adeoqne rationes in Pabella altignatas habeant L ad 5, F ad 6, e. Teries
Ouadracorum (vel planorum quadratis proportionalium) rarionem habebunt =
2d9, +ad TE, _C. quia 2, 5, 9, vel L, 6; TF, _c. Tune prichmetice proportionales.
Vel etiam, quia E rectae Sine feries Onartanorum, Guincanorum, etc. plana simi-
lia ad has rectas similiter posira, erunc series Octaranorum, Decimanorum, ec.
quibus conrem ratiOL ad D, Z ad FF, eC.
SC T2OF TV M.
Atque hoc pacto figurarum Colicarum superticiebus curvis comprehentarum
insens mulcicudo reduci vollunt ad alias superticiebus planis comprchen(as; et
corpora non modo coniea (quod docverunt veteres,) led et alia quamplurima
conoeidica, ad estindrum reduci. Quod neleio an quilpiam alius ancehac osten.
deric.
PROL.
LRLIAMETTCA