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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 437, page id 851387705:0457
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CTOP. CI. LALEHEEOKUM.
cur per Y; prodibic ?   . F s AD L, vel eriam F + 3B ADF, et a
nique 3
x
ADL: Ouam aurem habet rationem :
eacum Ouactacorum omnium ocdinacim applicacarum; ad
P L)
2D
ADE, neere
dF  D
Conocides vel Ppramidoeides illud, ad Cstincrum vel Prisma circumseriprum
(propcer plana Quacraris illis proportionalia; ) nempe, uc 3 F L 2D
d
P + D
uc 3 F + 2D ad 6F + 6D. vel, uc = Y + sD ad F + D. ndeoque -
PROP. CLXIV.
Corollarium.
vel
T Semissis Dianatri Transversae auctus triente Diametri Intercepta ad
Transversae C Interceptae Aecreratum; seu ut Triplum Fransver sae si-
mul cum Duplo Interceptae, ad simul utriusque Sextuplum: le est Conoeides vel
Eyramidoeides Fyperbolicum, ad Cylindrum vel Prisma (super eadem basi)
circumscriptum.
Patet ex praecedente.
PROP. CLXV.
Corollarium.
Tem, Lyperbola ad Paradeloerammum circumscriptum, est it deries Ra
dicum universalium, respectise aucta, ad seriem iobidem Laceum maxi-
mae aequalium.
Nempe si aesic timuilacio Prop. 262, uc V: a t. + a: + V: BR + B2: + VcR. + c.
_c. (usque ad V: R3 F RZ:) ad A V: R = F R =: = A V ZR  = A RY 2. HOC
e, uc omnes ordinatim applieacae ad maximam tories poticam.
Si vero ua limicauio non adisic; Faltem exie ut V:
FY: =p = L: _. (utque ad V.
+ LL. 4.
F
Y = L:) ad AY: DF + L
est, (dividendo omnia per Y L de multiplieando in V F) vE V: a F
L: Hoc
PFD2. + Y: 0T +c _c. (usque ad Y: D T + D:) ad A Y: DF 1D.
ut Paree ex desmonCHatione P1OP. 263.
SC AZOFF V M.
pacum cocidem maxima aqualium, numeris explicari poreric, non ica, taeile
octendecur. c
quam supra aliquocies meminimus de Ouadratura Circuli vel Ellipseos, (aliarum.
que aliquortigurarum currilinearum:) nempe ucinquiratur jam ratio quar ha-
bec intinita series Radicum universalium Binomiorum, Pieut illic ABOLOIMAPIM.
FC quidem aliquando proctiris eram uc crederem rem plane impossibilem elle
ut Radices surdx numero intiniex se inricem incommenturabiles ica in unum ae
cregatum coire pollint uc illud, ad expolicam aliquam quancicatem rationalem, ra-
tionem haceat explicabite.
modi leried tinica ad seriem coridem manima aequalium vix aliam palta est racio-
nis
Ac quo pacto candem ratio Aggregal Lalctum illarum Univertalium, ad ABBCC
Arque hoc quidem eo magis adhC COLALCIALII CHC VIdEBATE, quoNau esHI