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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 565, page id 851387705:0585
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1110
de-
AK
LT TIanouos.
plicatione opus non crit; (cum ipla quaneitas expolica, ejusque poceltas primatan.
cundem Tunc:) Tunc icaque omnes p (crilineum complentes,) MMIbuS a F 2 a R
ligillarim proporcionales, hoc est, uc quacicum  apicatarum IH AV PCt.
bola; Sire, ue ipsae rectae (diametro parallela) ucommplemento trunci parabo.
lici, (quod nempe cum ipso crunco complet circum ler  ParalICtOSFAIMMUI
quae quidem recta, quacratis ordinatim, applicacarum in hyberbola luNC prOPOr
rionales.
Ouories reroN CILMILMCLHS PaL, allCOqueS nuMeTO MIISO NO aLSaBI
1i3: Pro 3:
:=p, Eistendum erie in : a 2 +
=p2. Ouo catu-
LiCet K~ S quactraturx capax non sic, adeoque nec AO uduionos: FH ramen C0.
nocides, istius conrerlione cirea R s, magnicudinis norx; adeoque de complanari
poterit superticies curra conocidis quae recta A O circa A D describitur. Sed non
_ exinde, propterca exhibetur etiam semituperticiei Conoeidiex momentum resie.
ctu AXis. Ouories reron eltnumnerus par; porerunt ea omnia exhiberi. Aique
dehishactenus.
Denique, ut cocum hoc de parabolocidibus negorium Cimul et lemel absolvam Sit
n numerus quilibet, m = n = X, 2 = n = ∞, TIrgue 2 = 2 ∞, _ W = 2i: delignet
aucem ipsius n ad in respectus, quota poceltas diametri quoca ordinacim applicata
Pocelloci proporcionalis Sic. Tabebieur V: a.  + 2 a H
= D2. Adeoque aBr ee
cum omnium p2 extriberi poteric; ut de omnium poteltatum iptiusp, quae deno.
minantur d numeri z mulciplici. Si vero insuper n et 2 numeri, communem ali-
quem dirisorem admittane, puta f: sirque f) N(S, _ f) Z (c. Fxhibebitur
etiam omnium pe aggregatum, ut ee poceltacum iplius pqua d numeri e musciplo
denominantur. Acquehinc dijudicandum erie, quatenus vel ipsa A O curra, vel
conocidis Cuperticies ab hac deleripta, aur hujus lemisuperticier momentum respe
ctu axis, aliare hujulmodi, exhiberi polsint rel non postint. Acque de Paraboloci-
dibus hactenus.
Pandent, Coroniais loco, splauis Csclordis curram ad examen revocabimus. Curr
Nocum eAt. Crcloidis ransentes L. I, subrentis Crculi Cichlcoris Z C, parallelas Cycloidis
Tuvra insinuatas) concidere encia Tu. Da aet C L MH Partes aequales
quoclibet in punctis Y, quae dicantur 2 = L l; unde tlane C larichmettceplo.
porrionales, qua dicantur du colaque C L =D CruHL lbique ZC = V d D. Trem
uE C X = du 2d 2. C. = Y aD; HiC Y Y vel M 2d 2. 5 = Z 1 =  2Y a L
1d  1 Sy VD IDeMMUI 
N
Adeoque, omnes  ad omnes AV vel  hoc est, Cl recta, ad cul-
vam CZ. A; uc series A qualium, ad seriem Rceiproedm subsecundanorum. Hoc
est (per prop. 87. ec segg. Arich. Intin.) ac C F Brectansutum, d conorUai fi
puram incerminabilem C F B B DC: (et partes partibus respectire proporcionales.)
Hoc et (per prOP. 202. Lrict. Intin. ) ut 2 ad P. PL prOptered C Z. A semiereloi-
dis curra, diametri genitoris circuli C F, dupla. 1011,
(Tlabentur autem ip(x YB, si incellisantur cum semiparabola (cujus vettex C,
axis C F et balis axi aequalis, adeoque e lateri recto,) tum huic elreum leripeum
BbbB 3
quadratum;
elle, et aequales; Adeoque et earum parrieulas Z. I, iplio Zd. Oulae quidem laneen.
rium parciculae (in partibus exiguis) ipsis Z. Z Pyeloidis parriculis (ob rationes