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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 907, page id 851387705:0927
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l1op. L2.  ciatt cdiais.
cc DicO, SpasiuM A V P E FB aequari Pripio seemento C B F una cum Frianeulo
aNOB: HOC est, Sectori AR B una cum Spario C VBK. FI enim Secm.
ccCB Y =Spat. C FBK. Nam (juncta C Z,) CxIt ANS. CZ. B =- Z AnS. C AB
ec Adeoque Sect. Z. CB = 5Sect. AKB. ErgOSect. Z CB = Priang. AC7 1
cSDaT. C TBK. Auterancur aequalia, hine Frians. AC.Z, inde Prians. Z. C. B.
Fic, Spat. C F BK = 803m. CB Y
 Ostendendum ergo, quod Spat. AVPKF B = Sect. AKB f Spat. C LBK.
 (Praesumitur autem, tanquam facile demonstraru, per noras exhraultionum me
cc codos, Sectori A L. B Inseribi posse e Circumseribi ficuram Dentatam, ita ut
ce sera alteram excedat spatio minore quolibet dato: Et similiter, Spatio Cissoidali
cc A V P F. XB.
ac Si dicamr Ciltoidis Spatium AN L L. H B, TNUS CNC GtaH Scll. AL BF
amilta perpendiculari C R) ut AB f BR ad R A. FrBO, componendo, VTa-
DeZ. E. C F Frians. ACil ad Triang. A C. L, nt 2 AB ad AR; TIOC est, ut
2 Ouadrat. AB ad Ouacrat. AC; Hlocett, ut 2 Oi. A R ad Ou AC; HOC est,
cc. L FrapeZ. C. N = LTap.  C CatetIS. LISO, LBMTa III SeclOrC
ec In(eripia F OMM. FTaDCZ. C H = PIBUEX Spatio CModis Inlcript. Sed H-
a Ciltoidis spacium A V P H. P B  a aGuatur CRAPOCC SCOARB F Spac
aCFBK. LreOHBura i Cilloide ipso Cilsoidis spacio major exic. Ouod clt ab.
ec furdum.
a Cp2t. C T BK: Sit horum excettuS 2. FC inseribatur sectori A R B tioura ordi-
a pate, ut duplum omnium Fllincorum d ND _C MIIIS quam su. Et CiIoidis
cc Spatio AV P F. FB, Aigura inscribatt ex toridem arapestis. Otendetur Fra-
a perium L. F O ( = FFIanS. AR N F Prapez. C. N. EHt enim Fraper. F C ad
a FrianS. ACP, ut F G-F F O ad C. L, (quia eandem habene alcicudinem;)
aHOC elt, uE F A f AF ad AC; HOC ell, vE A F F FC ad AC; Hoc eAt, (de-
eC 2 FTIanB. AK N ad FrianO. AC L. CIBO, LFapCZ. H. G -F FFianS. ACL
C2 Frians. AZ N. Ft, ablaco utringte LFIanS. AC L, IaHCB LLTaIIZ. A AH
agura in Sectore altumens omnia L NB, item Frapezia C N altumeneia omMid
KND, ilta inguam omnia simul Cumpra superant Sectorem ARB. L SpaL
CFBK. AIBO Hgura in Sectore L craperlto CH lHoc est tieura in Cirtoide,
Dicacur jam Spaciu
ac astumens spatium s, lonse superabit Sectore AK B. F (pac. C P BR. Sed ipsum
in AVP F. PB, majus
a i
a sine miltota excelli s. Fr Cistoidis spatio, figura ex toridem Frapeziio; (nili
e quod, Pro ulcimo Traperio, habeatur in Cilloile Frianoylum A HLB = Lrians.
A HB Moectore.) Ostendetur, ut supra, PrapeZ. P O F G = FrianS. A D. N +
K
aSitque excestis s. Fx circumleribatur Sectori Fgura, ut omnia K N D bis TuM PCA
Tcaper. L. D. ErSO, corm figura circumseripra Ciltoidi, aequalis circum lexipia
12
dectori