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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 748, page id 851387705:0768
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160.
De Calculo Centri Cravitatis.
Cap. V
Fis 159, nem a a TOn BV = S,) Tunt ut bales C a Ba; hoc CAt C a, V a; Seu, R, B: Puta
25 R, ZSB. Distatque illius Cenerum graricaris ab A a (recta planove) Z V B = 35
Rujus vero, ZBV = 25. Frunque, propterea, eorum momenta relpectu A a, ut
55 R, 3SE B. AdEOGUE MOmEnCIM tOTII SS2R F SS? B, per cotam magnicudi
nem Zs R F=sh dirilum, exhribet corus Fraperii dictanciam CenCI BPAVITaLIS,
quod puncto B delignacum incelligatur (ioro scilicet Praperio, in rectam cni in-
Sleie, B Ci projecto, ) ab Aa  R + 252 B
R + 2B
35R + 35B 3R = 3h
= 87. Adeogue (PrOP.
tex similia Friansula BVC, B, C,) ut BV = s, ad V C = x; GCBY, ad rC. -
R = 2l
L 2B
3R F = G V. Sumpeaqne a3 =Z a B, (ductaque, ut
3R F 3G~. FL 7a = se
B7, _C BC, ipti r a pacallela, d erie a C. = + 0 7 = 3 R + R + 2B, p = 3 RL
5R - 2.2
4 R + 4B
Ex, diltancia Centri praricaris pyramidis a (plavo Tangente ) r a. H0c
2R = 42
est (Propiex v = R = 0, supra Cenrum, addendum; vel x = = X + v, intra
Centrum, auterendum; adeoque L v = R - v,) 3 R 1 5 R 7v R + 2 v
7 R2 = 5VR L v2 7 R2 = 3VR = 52
SR = 2V
12 R = 40
6X = 20. Acque haec distaneia, in Pramidis
magnicudinem ducta, hoc ct, (per SM. prop. praecect.) in Z5 R. - 55V R, exhibet
eyramidis illius respectu ra momencum 7 _ = 3V R 5
e
5 A
3 3
A3 -
25VR2 = 353 R. Atque hocdemum momentum, lubductum ex momento Dnou-
la Sectori Ba A insistentis, (aciem item habentis 7 a) respectu iptus Fa; hoc
el (uES W. ) Cx ZaR3 F s R - 35V R2 - 35 R, relinquit momencum On.
sulxe Sectori BC A insilteneis, aciem habenus Za respectu iphusr a, 3a R3 
EsR3 = FsV R. (Semilolidique correlpondentis momentum, hujus duplum.)
Duod quidem Ungulae (ipsi BC. A insiltencis) momencum, per magnicudinem
Ea R + 55R (ut SI. prOP. praeced.) diritum, exhibet ejuldem Centri grarica-
vis dillanciam d ra, 25 a  = 195 R = 3 52
12a+ 85
(Adeoque Semisolidi correspon.
34F + 258
R; prpore adt
illam Cngulae ut 4 R adt P.) DC proxterea dillancia Ceneri pravicatis Ongula,
a TA, 3 a R - 35 R + 352
12a f85
; Ongulaque iltius (Sectori BC A insistentis, aciem
habenris r a) momencum respectu T A, 3a R3 - 55 R3 + 55V R2. (Ouod Se.
misolido Facile accommodabitur.
Auc etiam, propier P pramidis illius, Friangulo B Ca, incunbeniis, magnitudi.
30R -
nem = S X = 85VR; Cenriguo gravicacis a r. a distanciam 6R = 2V Cut
dictum ett,) adeoque d Y A
5X - v R + 5
6R = 2V
 eric ejuldem, respectu F A, mo.
mentum BS R3 = i. 5V R2. + 3 53 R. Ouod quidem momento Ongulae sectori
Ba A incumbentis (aciem habeneis ra) respectu T A, 3a R3 + 2SR3 +  5~R
L 3S3R, (ut SW.) Tublacum; relinquit Ongula Sectori BC A intiltenis.
aciem habentis ra, momeneum respectu T A, 3a R, = 85 R3 F s5VR7. (IC
DriuS.
Oux rero Friangulo illi B Ca insistit Semiquadranicalis Ingula aciem habens
TA, idem plane haber respectu ra momentum, quod habet respectu T A ea qua
aciem habet sa; (Propter Alcicudines de Distancias ubique reciprocatas, ue pridem
aliquories:) HIoC eltus (ur modo ostentum est) 3s R3 = 1SV R2 = L53 R; quod
per Ongulae magnimdinem Zs R F S5V R (ut SM. PCOP. praced.) diritum; ex
hiber sui Cencri praricatis diltantiam a ran
R2 - v R +5
6R + 22 Adeoque, d F A,
7X.