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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 501, page id 851387705:0521
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eL
E
9. Similicer, li luper Semereloide A lC erisatu
Prilina, sive Cylindri recti quadrans, alticudinem ha-
bens A V, quae lic ad A L, ut q. A F ad F C; (nempe
ut circuli Perimerer ad Radium;) secetur antem pla-
AO FCV: Solido FV CiZ A aequatur Tolidum ex
convertione plani FCZ A cirea rectam FC; e leg.
menca scemencis respectire Cumpris; pura segmentum
ZZ Y C lesmento convertione plani ZC X tacto.
Nam et hic errangulum LA V aequatur circulo ractii
E A; e Friangutum LL x circulo radii YZ: FLdie
ubigue.
10. Atque hactenus quidem utur cum planorum
cum Colidorum omnium expolicorum dimentionem
aliquatenus hac merhrodo cradidilse rideamur: Cum
camen de Graritaris Cenrris nihil hinc constet, libee
in sequencibus, relumpio icerum ioro negorio, rem ali-
res expedire, hoc modo.
LL. Or lupra oltendimus rectam ZZ Fs. T. aequalem areni Z C: ita ostendetur, angulu
angulum ZG A, hoc eltZF A, arcui Z ClIre ZF, hoc est recta AC, prOpOrtIO. ZE 
Baum else: (nempe, ut arcus PZ, hoc elt AG recta, ad arcum F Z C, Hoc est re Fig. Y
Ctam AF, sic elle angulum ZG A vel ZF A, ad C F A rectum:) propier angulum
2G F anguli2 F a ubique duplum, e proprerca urrumque aceut PZ. libique pro.
Borrionalem.
F2. Adeoque, dirita recta A F in partes quoclibet aequales, in punctis h, U, B, G.
_c. ductisque rectis a L, V. MI, BB, 6Z, dc. 2 puncto contactus ad plinctum li-
neanS, (quibus parallelae exiltune in cireulo F I, F M, F B, FZ, _c.) anguli L. N A,
ML p. A, BB A, Z. SA, ec. sunc Acutimerice proporcionales; quorum concinuus
exccllus primo aequalis eles nempe angilo L a A.
23. Ductis itaque cum in Cyelorde recis n L AM, BB, GZ, ac. tum ipES rC
spondencibus in circulo FI, F m, FB, F Z, ecc. distrituencur Semicyclois et Semi-
ercculus in seementa numero aqualia; lierita linsulto. (tespectire) correspon-
dentia.
74. Ductis icem in Ciycloide,  piinctis vyZ, B, _. rectIS VF, G P, B8, etc. quae
DaralICIa LInC reCtIS 5Z, bB, LMI, dc. Frum anonomnes NV =, L. C et BB8, Sc
aqualescum incer se, cum ansulo ln A, cum etiam clssibet anoulorum AFI, IF m
MEB, ecc. qui icem (propier aequaleo arcilo FI, L p,  b, dc.) lunc. Ihlet se x
quales.
25. Ductis porro cum in Cycloide rectis NO, Z P, BR, Scc. Mui IH Eireblo
RO, 2 P, bC; dec. inleribacur cum Cyeloidi figura ex Praperiio, rum cireulo lixura
ex Priangulis correspondentibus conltans.
26. Erunt aurem illa Frapezia, Friangulorumm horlim respectire sumptorum
ubique plusquam tripla. Conttac enim quodlibet Frapeziorum, et Frianoulo (
ut e Patalleloscaminio. Quorum illud, criangulo correlpondenti in circylo (
ex dictis lacile collixilie) ubique agale ell; hoc plico lucjant ollencetut) plus
quam duplum.
27. Nam, verbi Bralia, in Praperio ONd F, Friangulum On F est utrigue F.
surx commune; _ ParalleloBramuI NHF, (aeguialcum) plulquam duplum
Frianguli, proprer rectam Nn, hoc esteurram nC, majorenino recta.
18. Sin aliud sumacur Praperium, Duca PZC.; Err inibi Priansultim P i
Friangulo pF Z aequale; de Paralleloeramnum Z. C, r plusquam duplum, proptet
rectam Z n, hoc elb, 51 Hoc est Curram Z h majorem quam ZB, vel + P. Nam
S apretur chorda ZB; exit angulus p F X (Propier rum semiperipheriam CLF
tu
e angulum rectum CF A, in sex partes aguales dirilum) sanouli recti; 2dc0
que ansutus Y DF, HOC Ct ZBn, E recti; cui A adelacur augutus n ZB, qui est
recti, (subrendic urique duplo arcus ZC, minus Zn;) asoresatum ZrCCLI Ex 2FC.
Etis subductum, relinquer angulum Zn B, 8 recti. Major irague est anolilus Epn
ansulo Z. n D, (nempE uE5 ad 4,) adeoquelatus oppositum Zn recta, major quat
2p; ideoque d Forciori, Zn curra, hoc es recta L F, multo major ctiequam rectu
2P, hoc et x P. Ec similirer octendetur (inleripta chorca BZ) ariculuim BFZ
masorem elte ansuilo b2 5, l hempe Vc 4 al 3.) et licalibi. Nemre, univettalicer
d
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