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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)
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PrOv. XLI. De Calculo Centri Ccravitatis.
ee Pyramis ejusdem Friens,) alcicudini ceneri Prismatis addicis duabus quintis Fiy. 166.
ditterentia alticudinum, hoc est Z X E b = oB, habetur Ongula Frapezii y 5Ep 168, 170.
(ex utrisque constantis) alcicudo Cenrri sraricatis, leu diltantia d 7a, ZB + 35h
= 2oh. Adeoque ejusdem ab A a distanca, bB + SBV = a + 135.
Cum itaque Cnorila Prapezii cujusque Y sSp, ad respectivam Prianguli Y a D
Ongulam sic, magnicudine, ic 5 ad 2, (ur ad d A. ostentum est:) Sicque illius
Diltancia Ceneri gravitaris ab Aa, ad hujus distantiam, ut a F 135 ad 3 s; exit
Vnsulae Fraperii cujusque y sEp momencum ad momencum correspondenis Vn
sulae Prignouli Pa P, respectu ejuldem Aa, ut 5 a = Z5, ad, 25.
Cumque hoc ubique obrineat; (licque eadem ubique magnicmdinis, Ungule
Prapesii ad magnicudinem Ongula Friansuli ratio, uc 15 ad 2:) Fric momen-
cum Onigulae Porius Semiereloidis, ejulre porcionis, AbBa aut BBd d, aut bB7
ecc. (nam in parcibus perinde procedie demonstratio acque in toris,) ad corre
spondens Momencum Onsula Semicireuli, ejutre. Sectoris Ba A, aut Ba D, aut
a Da Termenti, scc: (quacum deies Cino roy) respectu recta A a: UL omnes illa
Frianguli Ongula, Pyramidetre, eo speclances, in distancias respectire 5a. + 35
ad caldem in 3s, ductas; seu ui omnia quadrata V a (quibus, proprer X P ubi
que aequales, proportionales lunc illa prramides) in 59 = 35, ad eadem qua
drata Va in 3s: HIOc C, ut Omnia 5 a B f 2 sh eo spectancia, ad Omnia 3.5 h
respectira; Teu, ut Omnia 10 a B + 75 B2, ad Omnia 3 5B, eo spectancia: HIoc
eltus We 7 ad 3, acque insuper ut Omnia 20 a B, ad Omnia 3 sB, eo spectancia;
Cumpeis a arcubus arichmetice proportionalibus.
Sune aurem (PrO ABBa Portione) Ommia a s (Tumptis a ariitimerice pro.
Dorcionalibus;) hoc elt, Omnes a arcus arichmetice proportionales, in quadrata
Sinuum. vertorum, areuum ad Semicireutum residuorum; idem acque Duptum
Momenti correlpondencis Ongula ABBa EB. 77 aciem habencis ra, respectu
recta A∞; (propier Triangula sinrulis BB rectis ibidem insiltentia, = B; e0
runque ab Aa distantiam, a; adeoque momenta = a B:) HHoc cA, Duptum ip
TiuS 3a R 2 = Za5 RZ= = aSVR = V R3- =s R=; PeF S F. DEOB. 1O. Adeoque
corundem Decuplum, Icu Omn. 20 aB: CA hujus Momenci Visecuplum; hoc
Clt 3 a R2 f 25 a5 R= = 5 a5VR -= 20V R3 + Z5 R
Suntque Omnia sB2, eo spectantia; hoc ct, corundem arcuum arictimetiće
proporcionalium Sinus recti, in Sinuum vertorum, arcuum ad lemicireulum reli-
duorums quadrata: Idem acque Duxtum Momenei Solidi, quadrilineo ABB ∞
fg. 270. incumbencis, ex duetu rectarum BB, in B0 facti, respectu rectae ra:
Hoc cA, Duplum ipHuS, 32 R3 f Zs RZ = 5S2V R per S F. prOP. 18. Adeoque
corundem Criplum, lcu Omn. 35b7; ct, hujus momenri ledcuptum, hoc ett
4V R3 + 45 R = 5V R.
Preo Omn. 20 a B2: ad Omn. 3 sB2: (portionem ABBa spectancia;) Tunc.
vc 3 a = kZ + 25 as R2 = 5a5VR = 20. VR - 3 52 R, act 4V R3 f 4 52 R
=s V R. Cui li adjunsaeur, prius memorara, ratio 7 ad 3; (en 232 R3 +. 28, 52. R3
ZSVR, adt 4V R3. = 45 RZ = SV R; Hlaberur ratio momenti ungula porrio
nis Semiercloidis AbBa ad momentum Ongulae decloris BaA, lquarum acle
Ta,) respectu ipuS Aa;
a R. + 25 a5 R = 5aSVR = E V R3 + ac s2 
35 d, dd 4. dk + 45 R2 - s V R
Cum icaque momentum illud Ongulae Sectoris B a A fit (consequentis Tubiduo.
decuxlum )Ev 3. - Zs R2 = 2s= V, (Der SL. prOP. 16.) erie, Ungula porrio
nis Semiercloidis ABBa, aciem habencis sa, Momencum selpectu Aa, (lubduo
decuplum ancecedentis,) 3a R = 23 a5 R= Ba 5VR 3V R + 3+ 52 R 2
36V X
adenique est, Ongulae porcionis Semieyeloidis AbBa aciem habentis A a, mo-
mencum relpectu ra
Ouod quideti Momientum; divisum per Ingulae illius ABBd aciem habentis
Ta, magnicudinem, Z f R2 + 3 sB R = 2a R2 + 235 R2 = B S V R, (per SD
DrOP. Praced.) exhibet Distanciam Cencri graritaris ab A a
64VR 75 asR 4F s R f 15a5V + 14 5V
90 ak  15OSR-- 305V
45 a.  +640   4 25 R + 14 5
90aR. = 1505R 3050
Idemque Momencum. diritum per Ongula ejusdem ABBa portionis Se
micycte aet TIabenTS Aa, magnicudinem Z a  R + 3a5 R = Z V R
F2S, , per 8 I. prop. praced. exhibet hujus Diltanciam Ceniri stavila
Mt in n m