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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 566, page id 851387705:0586
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GURY A RUM CIDVIOIS.
quadratum; e tiat, ut rectae in parabola, ad rectas in quadrato; (hoc est, ut
YaD, ad D,) sC VB, vel A, ad quarram; eric ea 2B = -
Ya Z
t
.Vel etiam, si intelligatur eadem parabola inverse Dolita, (verricem habens
F, axem, basin, e lacus rectum, = D,) de sumatur uc ordinatim axplicata in se-
micireulo, ad ordinacim applicacum in parabola; hoc eA ut Y: d D = a: ad
V. D - d in d D: = v: D = aD: sic F B, vel B ad XB vel A
Vuroris modo eadem prodibir Y B recta.
licu
NV
Porro; Ductis tum iptis  tum =  in d = CY, (distanciam d verrice,)
habetur rario momentorum respectu rectae C. L tangentis in vertice; nempe ut
omnes d A, ad cocidem AV dD; leries primanorum, ad seriem Tublecundano-
rum; HOC esF (per PrOP. 64. Arith. Int. ) uc Z, ad 3; vel 3 ad q. Oux cadem
CA e rario Circuli ractio C F deseripei, ad Cupertieiem curra C Z. A circa C. L de
Seripcam.
Deinde; proprer linearum rectae e curra maxnitudines, uc 2 ad 2; _E MOMCnEA
uc 3 ad 4; FrIE PrOpter Z) 3 (2, distantia centrOrum GraVILALIS d C L, ut 3 ad 2:
adeoque currae cencrum graritaris distat 3 radii, hoc ell; diametri, d CF; ad co
que  racii, vel 3 diametri ab F A.
Ft consequenter; (proprer cenerorum diltantias ut 3 ad 4 e magnicuctines li-
nearum uc F ad 2;) cireutus radio lC deleriprus, ad superticiem cuera CZ. A
circa AF deseripcam, ur 3 ad 8.
Ouod iptum similier colligimur, ductiscum  tum AV =; in D - d dillan.
tiam ab F A. Frune urique momenCa, ut AD = d A, ad QVZ
vel 22
1D- 2d1∞
Hloc eltus ut 32d8.
re
ADVZ
eibine V. a
in D = d.
Similicer de centris graricatum semitaperticierum tum eirea C F, tum eirea F A,
constabit. Ductisnempe superkeiebus, cum rectis Z Y, cum curris Z Z, descripris,
in distantias Cas, Sive a CT, lire ab A F; habetur rario momenti lemiluperticiet
currae ad momenrum senticirculi. (Reliquaque Facilius quam uc iis opus sic insi-
Ctere.
Nempe, ductis tum d A Tu AV aD, in d; repericur momencum (respectu
rectae C P) Semicirculi, ad momeneum semiluperticiei curra circa candem C. F;
m series aA, ad seriem Ad V a BHoc est, ut : ad 5, sire ut 5 ad 6.
D V T
tiem, ductis cum AD= d A, cum   . WY A P, in D,  a. habetur
ratio momenti (resDeCi rectae A F.) SemicireulI, ad momencum Temituperticiei
curvae, cied eandem A F; _E series AD L. 2 a AD + 4 4, ad seriem
AD= YD
15d
Vd 2 aN a D +  Va D. 1100, ostu uE 5  3 = 53 242  8 + 3
Hoc est, ut5 ad 16.
Habicis aurem, cum magnicudinum, cum momentorum racionibus, ee unius cen-
ero pravitatis; distantia eerri praricatis alcerius non lacebir.
Sed, de parcibus similicer instimetur judicium. Diriforcique quadritineo incer-
minabili in ratione daca (quod per Srith. Infin. facile tiecud dividirus e CZ A
curra in eadem ratione. Nempes sumpta C. L ad C H, in ratione pE: 2d P2. erit
cum C ZBd ad C FBBd, tum CZ ad CZ A, in racione padt P. (Fr consequen-
Ter, Tumptis C.L, C L, eoc. quoclibet, in duplicata ratione Arichmetice propOr-
tionalium; eruntcorrespondentes C L. CZ, es arichimeciee provortionales, ipsa
que C. Z. A, in xequales parres in punctis Z divita. ). Distat aurem dF C18 recta ver.
ticis,