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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 823, page id 851387705:0843
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C
bB
PTOP. XXI. De Calculo Centri Cravitatis.
cum respectu BBV, est, 3C P + 3 5V R L ; a st R +  B R =  S v; per GV. Fip. 166.
PrOD. 16. EE Ongulae Frilinei bBA, aciem habentis b BY, telpectu bBV, est 170.
de R3 = 3 a V R2 + 3 a s R = 28 5 R - = a s V; per S f. PrOP. 10.
Erso, Unoula Sesmenti Semiercloidis B VA, aciem habentis bBV, momen
cum respectu BBV, cst - =  CR3 f- 3aD R + 35VR  = d a 5 R -
53se
== a 5V - ESV: Ejusque momencunt respectu Y A (idem, acque aciem b2
bentis PA, respectu bBV, ) C X + 3aV R 2 + 35V R 2 = 3 a s, R = 353 R
=6a52∞ = 253V; e respectu ra (idem aique aciem habenis ra, momen-
tum respectu bBV,) + C R 4 Z a D X 4 35VR L 2 aS R = Z53 R
+3a52V F 5 SeV. Erdo (piopier maenicudinem L C X= f  av R F Z 5uX
= = a52 =553; per SF. prOP. Praced.) Distancia Ceniri pravitacis a BBV,
=15CR3 +60 aV R + 455 R = 12 a5 R = 385 R, 24 a5 v- 653 v
28C R = + 36av R + 545V R - 36a53 = 125
= 3R - B (= 0 - 2) 1
2 a52V = 53V = e52R
3C F + 6au R + 95v, R = 6a5 = 2, 5
15CR. + 30aVR 2 + 4550R 2 = 24 45 R - 1653 R = 124 52 v -6530
= 3 R -
18CR =. + 36aV R + 54 5D R = 36 a 52 = (253 b 1IIF
245v + 53 v = e 52 R
3C R= + 6 a v R + 950 R = 6a 5 = 25
22CR 3 + 42 av R2 + 63 50 R= = 48 a s R  85, 3 R t 12 a152 y + 68V
== 3R 1
18CR2 = 36 a0R + 54. 5,~ R, = 364 52 = 12. 53 + 1Y
a52v. = 53 v = C 53, . p ta I. Semitolidique correspon.
30 R2 +6av R = 99VR = 6a52 = 253
dencis cirea h V; magnicudo, ad illam Dnxula ut Z. P ad R, nempe se R P ].
=a2P + 8507 - 2s 
5. 34
Momentumt, ael illud Onente, uc 2 ad +.
adeoque - 3e R 3 = 3 a V R 2 + 25 ~ R 2 = = a S2 R - - 13 53 R = 2 A 5 2 V - 1 532:
Diltancia Cencri Gravicatis  B V Curpore ad illam Vngula uE 2. R ad Z ~, )
=30c  4 + +20 a vR 3 + 00 5V R 3 = 24. 252 R= = 765 R22 4BaS VR- +25VR
oc R2D + 18 a D R + 275DX~ = 18a5P 853∞
Eademque habencur oDe Praperii bBa V, ee Oneularum huic insistencium.
Ouippe subductis Ungulis Praperii bBaV, ex respectiris Ongulis porrionis bBa A;
restane Ungula Segmenti BV A. Ec de momenes similiter. .
Est aurem Ongulae Prianguli B a V aciem habencis r a momencum respectu
2a 25B3; respectu F A, ZS h2 R = 25b3 per S W. prop. 16. Ongulaeque cor.
respondentis Paraltelosrammi bBaB, momentum respectu r en hab3; respectu
TA, aB= R = Z aB3; Der SF. PrOP. 19
Erso Vnoulae Praperii bBa V, aciem habencis ra, momentum respectu ro
5aB3 = + 5B: = 8 a R3 + 25 R3 = 3 a V R2 = 5V R - 3 a s2 R - 53 R + = a s V
= 253~; respectu T A, ab= R + Z sB2 R -= 3 aB3 - = 5B3 = 3 a R3 + Z5R.
5aV R 2 - 350 R2 = 5a S R + 553 R = 3 a 52 V = = 5d v. AdCOque (PrOPICS
magnicudinem, = a b F Esh2, per SC. prop. praeced.) Distancia Ceniri gravi.
catis d 7 a, 4a = 3s
6a + 4
B; atque d YA, 2 R, 4 9 + 35
6a + 45
Eademque momenta, ex respectiris correspondencis Ungulae porcionis B Ba V A
momencis, 3: a R3 + 32 5R3 = 85VR2 - 56SR, _ 37 a R3 + 3 5 R3 f 5V R
F 35 R, (d C. tracticis,) subducta; relinquune Ungulx Scemenei BV a aciem
hrabentis ran momencum respectu ra, = 32 a R3 + 325 R3 (=. - 3ZC R3) + Zav
+550 R 2 + 3a52 R + 3853 R = 5a 52 V - = 53V; e respectu T A, = 7 a R +
a S R (= - 2 C R3) + 3 av R2 + 35VR  3 a s R - 28 53 P + 3a 5 v + + 5ev;
uc supra SF. Onde reliqua deducentur uL PEIUS.
Similiter;
P
82