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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 909, page id 851387705:0929
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PFOD. XXIZ. De Calculo Centri Cravitatis.
A = = B, hic A a = 2 R,) eric Friangulum ABY, Seu AB, -
20i dt A rV
seu AB, = 4 =; et (horum disterencia) Fraperium pyun, (eu bB, - 4 - B.
HOc elE (propter B = 2 R = v, ad eoque B2 = 4 R 2 = 4 V R = v2, _ 4 R2
=4. V R = 22,) += ~ B. FE SC ubique,
Ve igitur, Omnia A B Friangula, hoc est Omn. ZV B. (sumptis arcubus a arichmetice
proportionalibus usque ad a maximum seu arcum A B, quorum communis differentia
B,) complencia ret corum Semicirculum ADa, vel illius Sesmentum AB A, vel
Sectorem BAa; ad Omnia PYVr, hoc est Omn. 4 P -
cum spatium Cistoidale interminatum O BB A ar, vel ipsius partem (icem inter-
minatam) bBr areum AB spectanem, vel partem reliquam A b bBa areum
Ba spectantem, (nam de toro et de partibus perinde valet demonstratio;) vel
(Propter omnes ? Pinricem aequales) uc Omn. V, ad Omn. 4 R = 2, eo spectan.
tia; lic spacia illa Circularia, ad resrectira Cissoidalia.
Sunt autem (sumpris, ur dictum est, a arichmerice proportionalibus) Omnes v
arcum AB Spectantes, (hoc cA, ADR Ag. 170.) =e R (Per S B. prOP. 17.) 8
Omnes 4R, = 4 a R. Adeoque Segmentum AB A, ad correlpondens spatium Cil
Soidale bBr , uc e R ad 4 a R = e R, hoc est, ute ad 4 a = e, vel (Propter
e == a - - 5) UE a = 5 2d (4 a - a - ] 5 =) 3 a = 5. F.S aUTCM SCGMENTIM ABA.
=ECR = = a R = ZS R (perSG. PFOD. 25.) FrgO, Spacium Cilloidale DBT.
=3a R = =5 R. Hc additis Friangulis illic a B A, hic aHB, (invicem aequali.
BuS, propter aequales bases AB, BB, ee alcicudinem eandem,) quorum utrumris
5R; tiet Sector Ba A = Za R = =s R, et Spacium CiMoidale a bQ7 = 3 a R +
25 R, Sectoris Triplum
Similicer; Omnes v arcum Ba Spectantes, (hoc est R B Z F F3, 170.) =Z ~ R
eR = = P R = a R + 5R = a R ] sR (per GB. PTOP. 17.) _ Omnes 4 R.
=4 u R. Adeoque Scctor B Aa, ad correspondens Spacium CilToidale ABBB a
UE a R L 5 R ad (4 a R - a R - 5R =) Z a R  5 R, HOc ClC, UC a + 52d 30-
Fst autem Sector B A a = = a R-  :s R (per SFL prOp. 15. ) ErsO, Spacium Cis.
Lo
todale AbBBa = 3a R = =5 R. Fc, sublacis aequalibus Priangulis, (illic a B A
hic a bB,) = 5 R; tiec Scemencum a Ba = Z a R = E5 R, e spacium Citoidale
a b b A = Za R = 35 R, Seementi PriplUM.
Porum aurem, quod AD a semicirculum spectac, Spatium Ciltoidale AbbOra
urroris modo consequemur, propier eranelcentia criangula aB A, a bB; lcy
5R = 0
Eadem non mulio aliter contequemur, ope Triangulorum P∞ Y. Nam, Ut
(Omnia Friangula P a. V arcum A B spectancia, hoc est) Omnia = B B, ad (omnia
respectiva Fraperia B Yva, hoc M) Omnia   = B; seu ut Omn. b. ad Dmn.
4R = v =) 2R + b; SC Sector (quem illa complent Triangula) B a A, ad Spa
tium (quod ea complene Trapezia) BbQr. Sunt aurem Omn. B, eo spectancia
(HoC Cst ABBatB. 170.) a R F sR (per SB. prOP. 17.) adeoque Omn. 2R f 1
respectiva, 2a R F a R F sR = 3a R = sR. ErSO, u a R F sR ad 3 a R +
SR; SCuUE a F sad 3 a F s; sIC Sector B a A = ; a R F 3 5 R (Per B FI. prop. 15.)
ad Spatium BbOr = 3a R FZS R. Si huic itaque addatur Prianoulim Bpa-
a BA = 5R; Het tocm spatium a bO7 = 3a R f 35 R, criplum SectoriS Ba A.
Tiem, uc Omn. (Frians. Pa. L, Teu) EB B areum B a Spectancia, ad Omn.
(TraPCZ PVVr, sen) 4 = Brespectiva; seu Omn. B uet Omn. (4 R - v -)
2R = B eo spectancia; sic Segmentum (quod illa complent) aBa, ad Spacium
(quod haec complent) Bbb Aa. Sunt aurem Omn. B areum B a spectantes (hoc
eltus bBr Ai8. F70.) a R = sR (Der SB. PrOP. 17.) adeoque Omn. 2 R = b xe.
spectira, 3a R - 5R. ErGO, uE a R = sR ad 3 a R - 5R; sen Vt a = 5 2e
a = 5, lic Segmencum a Ba = = a R = = s R (per SG. prOP. 25.) ad Spatium
BbbR. a = 3 aR = = 5 R. Unde si auteratur Friangulum Bb a = a B A = sR; rC.
Linguitur