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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 521, page id 851387705:0541
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eadem bale consticuca, alricudinem habere 4 AF = L f, estet ea semiparabola
aequalis superticiei convertione currx C A fig. 8. circa AP lectam descriprae;
(nempC Z D P, Sire 3Z circuli genitoris:) ejusque partes respectira respectiris par
tibus hujus aquales.
6. Ouod aurem FX A Fg. 9. sit Parabola, sic oltendirur. Rectae ZX sunt
ubique uc=  Der  2. HOc est, ut D = a; adeoque retidux X5, hoc
CAF EF diamerri, ubique ut a; hoc est in duplicata rarione ZC, Hoc eAt ZE Or.
dinarim applicatarum. Ouod Parabolae proprium est.
Z POrrO, eju(dem curra C. A H8. 8. dirilae ur prins in punctis Z, omnium centri
punctorum Z. (seu parcium aequalium his punctis designatarum) distancix d C. F, curva di
LInE Z Z, Hoc eAt Z. Z = 2. Y.
8. Adeoque S curra C A Hg. 8.
aequalis excendatur recta C A tig
20. Timiliter dirila; atque per di-
vitionum puncta Z ducantur re-
etae VZV, ita quidem ut ZV
tig. 20. Linc respectiris 2Z fg. 8.
aequales, et Z0 relpectiris ZY.
extribebunt ha rectae VZ.0 lingu-
lae lingulorum currae punctorum
Z momenta respectu rectae CF
fis. 8. adeoque omnes omnium.
Hioc c, Figuta F V Cv A momen-
cum cOciuS AC currae (respectu
rectae CF,) e illius ParteS, par
tes respectiras hujus.
9. Cum vero rectae CZ FIg, 10.
hoc CA CZ curra fig. 8. SInEUE
CF.
C2 chordae in Pemicireulo aequaliter crescentes, hoc est, ut sinus recti in quactran-
ce crelcentes aequalirer, puta uc B V in crilineo BCC fis. 7. (si nempe incellisa- F18. 7.
cur cB in punctis V aequaliter dirita:) iplaeque rectae ZV tg. 10. hoc eAt ZZ
tis. 8. SIre arCUS ZC, hoc est arcus chordarum in semicireulo (vel linuum in
quadrance) arichmetice proporrionalium, ue rectae VZ crilinei B Cc H8. 7. (Nam
licut recta Z Z Fx. 7. hoc clt rec
tig. 7. Quae una cum Z Z complet cotam VZ = Bb, hoc est b Ci arcum quadranta
lem, aequatur arcui ad quadeantem reliduo Zb, cujus sinus rectus est ZB = = BY)
F3. 7. adeoque omnes VZ. crilineum BC C fis. 7. complenres, aequalibus diltantiis
sumDEX, TunE ut arcus Linuum arichimerice proporcionalium in quadrante, tire
chordarum aequaliter crescentium in Lemicireulo; hoc est, uE Z. Z FIB. 8. CorrCIDOn
dences punctis Z aequalibus incerrallis in curra C A Sumpris:) Frunc omnes V Z
erilinei CZ AF f8. 20. ad F A tories politam, hoc est crilineum illud ad circum.
seriptum parallelogrammum; uc trilineum BCc (8. 7. ad parallelogrammum cir-
cumseripium sibi. (Fc illius partes parribus hujus respectire Lumpris propOr.
eionales.)
20. Frilinei aurem B Cctis. 7. (aut eriam parris hujus cujustibet) mensirz
habetur ex calculo523. Fst enim BB = +~, et BC = R; ergo parallelocram.
mum BBCC = = R∞: irilineum aurem BCb = A = (ut 576 dictum est,) ergo
irilineum reliquum BCc = = RP = R2 = 8 D P - =D2; (HOC C(t = AF = , CY
In CF.) Onde et crilinei C F A mensura colligitur; quippe ipsius octupla, (prop.
Tex AF = Z P e AC. = 2 D = 4 R, ad eoque paraICIOOTAMMUII F C = 2 RP,)
mucandis, codem modo colligitur.) Momentum itaque CUEVX CZ A F0. 8. resvectu
rectae C H. quantum ad diltantias Z 2, esset ad ejuldem currae momenium in di-
stancia F A TuIpenIX; ut CZ AF f8. 10. ad circum seriptum parallelogrammum
hoc CAE, ut DP = 2 D ad DP, SiveUt P = 2D ad P; HOC est, Wt AF = C F
ad AF.
FY. Fum vero, quancum ad distancias Z Y FS. B. (quae simut cum Z Z complent
inregras LY,) hoc ell, L0 (bulinei A Cio) he 28. Cum rectae Ct, 18. 10. 10e
E
Ci Y C L O FD