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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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De Calculo Contri Cravitatis. Cap. V.
Fi0. 108, santia, ZbB = Z BV = = a + 35 = Zf: AdeOque mOmentum Z F a B. Frianonli
103, 170. magnitudo (propter BV = s, e V a = B,) ZSh; Centrique graricatis ab A a
distantia 3 x = BV = Z s: adeoque momentum respectu Aa, Zs B. Momentum
itaque Traperii bBa V respectu Aa, el, Z fa B = Es h = a R + a5 R - = a V
=2a5V =55 R - EsV. (Magnicudo aurem, ah = = sh: Adeoque Centri gra
vicatis ab A a Distancia, 3F a + 5.
6a + 35
3a = 25
1
a +6.
Ilud autem Fraperii Momentum, ex Porrionis BBa V A momento (modo
ReDertO) Z a 2R F 3 asR = ZV R2 + 35= R subductum; relinquie, = = a 2 R
FZaS R = AES R = ZVR F Z a V + 3 a5V fEsV, Momentum Scomenei Sc
miereloidis b V A relpectu aa; Onsulamre correspondentem. (Solidumque et
Semisolidum ejuldem circa Aa conrertione tactum, ad Ongulam illam, ut P,
_ 3F, ad R.
Ouod quidem momentum, per magnicudinem (S B. inventam) = = e R
(= = = a R = E5R) + a2 f5v, diritum; extibet Centri gravitatis ab A a
distantiam = 3a R = 6a 5 R + se R = 8 v R2 + 6 a 3 v + 6a 50 + 2 s2 v
= 6a R F 65R f +2 a v + 65V
hoc est = a + 3a5 R f 52 R = 8 v R2 + 3 a 5V + 2 52 v
6cR + 12a0 + 650
80R = = 3a5R = 5 R = 345V  252
sei
=6CR F 12 aV + 650 Unde habetur etiam ejusdem d rY
vel BK distancia; ejusque respectu hujus Momencum, Ongulare: Solidumque
et Semilolidum ejusdem circa ~ L vel bK convertione Factum.
Si aurem ex Parallelogrammi A. V B R momento rospectu Aa (S G. tradito)
f2V; hoc eltus Cx 5 a V = a5v, = L s v; auteratur momencum scsmenci AB V
respectu ejusdem Aa, jam invencum, - = a2 R F = a5 R F 
R
v
L= a V f = a50 fEs2 V: Relinquitur Prilinei AB K respectu ejuldem A a mo-
mentum Z V R= f = a R = Z as R = =S R = 3 a 5v = 3s V: AdeOqUE, PTOPTEK
magnitudinem (S B. tradicam) ZC R + Z su; Diltancia Centri praritatis ab A a
BuR2 + 3 a R- 6a5R = s R + 6a 5v + 45 ~
60R = 65V
Haec eadtem Momenta ee Solida, alia acdhuc methodo sic investisantur.
Fis. 160, Omnia momenta rectarum bV, aequalibus intervalsis sumprarum, (sive totam
Semiereloidem, Cire iplius seomentum ut BV A complencium,) respectu recta
Ra; momentum inteorum complentia: Vel omnia Frianoula rectangula TIOlCe
lia eildem insiltentia, Semiquadrantalem Ongulam, aciem hrabentem Aa com
plencia: Sune coridem Semiguadrata carundem b V rectarum: Hloc est, lemi-
summa quadracorum rectarum omnium bV = bB f BV = a F s: Hoc est
semilumma omnium a f 2 a5 = s; seu cumma Omnium, Z a + a5 = 252
sumptis u arichmetice proportionalibus.
Fi3. 170. Sunt aurem Omn. 3 a seu semisumma quadratorum omnium BB rectarum:
Fig. 268
169.
Idem acque momentum Frilinei relticuri A Ta, (quam figuram Arcuum, non mi-
nus quam sinuum vertorum tiguram esse, octendimus S. A. prOp. X7.) ejutre Les.
menti DB A, respectu Aa. (Fst enim magnitudo cujusque DB = a qua ila
que in sui semiltem, seu Ceneri oraritatis distantiam, 3 a ducta; extibet ejus
dem respectu aa momentum, E a.) Nempe Frilinei Ar a momencum, 5 R P=
=2 R3: Et Scgmenti bB A, momentum, - Z a R + a s R = v R= + = a V, per
SG, I. PrOD. 17
Irem Omnia Z S; seu semitumma Ouadratorum rectarum B V (aequalibus in-
cerralsis Tumprarum) Semicireulum A Da ejutre segmentum AB V complen-
cium; est ejuldem ADa Semicirculi, ejusre Segmenci ABV, momemum re
spectu diametri (ux Aa. Nempe Semicireuli mOmentM, 3 R3; d Segmenii
ABV imomencum Crespectu ejuldem A ∞) ZV R7 = 65 R F 65V; per 5Q. R.
PTOD. 15.
Eis aucem jam inventis Omn. = ae  2 s; si addantur Omn. a s, (ut modo
octensum eAt) habencur Omn. Z a f a 5. f 353: Momencum Semieseloidis, ejus
ve dexmenii b V A, respectu Aa.
Adeoque
BI2
68.