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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 827, page id 851387705:0847
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PFOD. ZXI. De Calculo Centri Cravitatis.
cractiris: Auterancur respectiva Oncula AbBa, Magnicudo 3a = R + 34 S R = F1B. 166,
30 P2 +, 352 R; mOmenTuM respectu 24, 3a2 R 2 + 23a5R  = 2 a 5V R - 170.
50R3 + 92 52 R2 = 585 2 V R; e respectu T A, 3a2 R + 1 a5 R = = 8V R4
2252R2 + 3a5VR = 85 2 V R: Habetur Ongula BB7, aciem habentis A a M2∞-
nicudo, 3 R~ 2 - 3 R3 = = a = R - 3 a 5 R + 3~ R 2 -  35 = R; MOMENCuM re
spectu Ta, 3R = D2 - 15 R 4 - 3a 2R3 = 23a5 R2 + 30R3 = 935 R3 +, 3 a 5VR
= 3652 ~R; respecta Y A, 2 R 2 D 2 - , R a - 3a2 R2 - 1 a5 RE + 3V R3 -
2s 2 R2 = 325VR = 56s 2V R: Adeoque Diltania Centri gravitatis d Ta, 8R-
202R3 = 96V R 2 F 240a5 R + 645 2 R - 120a 5V -56570
d
5+22 - 384 R 2 = 216a 2 - 432 a5 f 192VR = 120522
TA, 3R f 292 R3 = 96v R + 240 a5 R + 64 sR = 120a5V = 5652V
54D = 384 R - 216a = 432 a5 F F92DR = 22O52.
Acque hinc facile derirabitur, Ungulae bB, aciem habentis Fr, Nomentum
respectu ra, vel TA, Centrique graritaris inde distantia.  1
Sed e haec omnia quae Onsulas bBr in Semiereloide (Ag. 166.) Spectant, por-
Tunt etiam per se exquiri, sine ope Ongularum A B Ba. Nam e hic etiam perinde
ralet quod SC. demonstratur: Nempe Momentum Ungulae bBr, aciem habentis
2a relpectu Aa; ad momentum respectirae Onoula sermenei a Ba, aciem haben.
eis ra respectu Aa; elle ut 17 ad 3, acque intuper ue Omn. 10aB2, ad Omn.
3sh2; seu, uc Z ad 3, acque insuper uE Visecuplum Momenii Ongulae bBr in F.
sura Sinuum verlorum tig. r70. aciem habentis ra, respeetu Aa; ad Sexcuplum
Momenu Onsulae Scemenci circularis a B a tig, 169. aciem habeniis ra, respectu
Ac. Ldemque erit, Ongulae BBr tig. 166, 268. aciem habenEiS Aa, IOMENEIM
respectu ra. Unde et caetera eo spectantia derivari porerunt; cadem quae priis.
Deinde; Si ex Momentis Ongularum ABBa, auferantur respectira Momenta K.
Ongularum Fraperii bB a V; reltabune respectira Ongularum A b V Momenta.
Constar aurem Onsula Frapezii bBaV, fs. 266: aciem habentis ra; ex dua-
bus Ungulis; Nempe Frianguli B a V, de Parallelosrammi bB0B.
Est aurem Onsulae Friansuli B a V, aciem habentisra; Momencum respectu
Aa, 352B2, per S MI. prOP. X6.
Onsulaque Parallelosrammi bBa B, magnitudo (quippe eadem quae respectirae
Onsula bBa B t18. 270.) EaB2, Der S F. PrOD. 17. Cencrique sravitaLIS d ra
dittancia, 3B, (Der S C. DFOD. 5. ) adeoque ab A a, 3a. f, 3s, Cuc ex schematis
aspectu tacile coMlisiuT:) Et propierca, ejuldem respectu A e momencum, Z a s
+: a5B:
Ereo; Ongulae Tocius Fraperii bBa V, aciem habeniis re, momentum respe.
du A0, cst = a = B= = 5asB2 = 352 B, seu ( PrOpter B = 2 R - v, adeoque
B2 = 4R2 - 42 R + v2 = 4 R 2 = 2v R = 5,) a2 R2= = a = V R-
2 a5 R2 = 3a 5VR - 3453 + = s= R2 = + 5 = V R - 852. Idemque est Ongulae
bBa V, aciem habeniis Aa momentum respectu ra; propier Distancias ee AIIi-
Eudines reciprocatas.
Ouod iaque momentum, per Ungula aciem habeniis ra magnicudinem : a H
=SSh= (uc B F. oltentum elt) divilum, extriber ejuldem Ceniri gravicaris ab A e.
distanciam, ia f. 4a5. + 35 -.   4a + 35
120+65
121+85
= : a + 1st 36 a + 245
Idemque momentum, per Onsulae aciem habentis A an magnicudinem : f a b +
5S h = h a B + =ash + 5s2 b (per Sk. prop. praced.) divitum; exhibet
hujus Ongulae Diltanciam Cencri Gravicacis d Xa
3B + 2a5. + s
6a t 8 a 5. F 35
22 a7 + 12a5 + 45
12Fa fq5 B: Adeoque d FA, 2 R - : B (= R + 5 2) - 2a + 5 - 5B. FL
125 a + 4.
propcerea ejuldem respectu TA, momencum, fa B R = 3 52 BR = + a B = = a sB2
5S2B2. Ouod etiam (propier alcicudines ee distancias reciprocatas) est mo.
mencum Ongulae bBa V, aciem habentis Y A, respectu Aa: Adeoque per Vnou
lae bBa. V aeiem habentis Y A, magnicudinem 2 a b R + 5b R = 3a B7 - 3 5 h
M m m M M 2
(PeF