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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 739, page id 851387705:0759
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PrOD. XVI.
De Calculo Centri Cravitatis.
bentis sive T an Eive FA, Momencum respectu A an CAt Z RL; Solidique correspon. F1X. 150.
dentis ; R3 P; ee Semisolidi, ; R3 P: Centrique praricaris ab A a distancia, 8 N2 160.
Trem, Semiquadranralis Ongulae super B V A Semilesmento, aciem tabentis ra
momentum relrectu Aa est (UESF.) 3V R3 = 35 R + 35 2 V R = 354; (50-
lidique correspondentis, et Semilolidi, momenta, ad hoc; ucP, vel = P, ad R.
Adeoque, proprer Onsula magnicudinem (vel momentum Semilectoris BV A re
Spectu 7a,) Za R2 - =s R= + =sv  + 353, (Der S L. proP. praeced.) Diltancia
Cencri craricaris istius Ongulae (adeoque Solidi Semisolidire correspondenris) ab
8VR = 45 R + 4s V R = 35 4V R + 4s R f 352B
3 2a = +25 R = 12 5VR = 85 12CR F 125V R + 85
Onoulaeque Semiquadrantalis Cuper eodem B V A Semisermento, aciem haben-
eis TA, momentum respectu ejuldem A a, esE (utS F.) ZV R3 -  s R = Es V R
352; (Solidique aut Semisolidi correspondentis momentum, ad hoc; ut ~ vel
~ ad R:) Adeoque, propter Ongulx magnicudinem (seu plani BV A momen.
cum respeetu F A, ) Ea AZ = ES RZ = LSVR = Z53, (Per SL. prOP. praeced.
Distancia Centri graritacis Onsula (Solidire aur Semisolidi convertione facti) at
A
82 R = 4 s= R2 - f 4 s V R - 2 54 -- 4 2 R  4 s R - Zs B
12a R = 125 R + F2SVR = 8s Z2CR + 1250R - 85
Similiter, Semiquadrantalis Ingula Caper eodem BV A, aciem Habentis B V,
momentum respectu, Nas e (UES C,) 30 R3 L352 R  A = 89 P - 122B
Solidiquene Semilolidi convertione tacti momenta, ad hoc, ut P _ ; P ad R:
Adeoque proxter Onsula magnicudinem (rel plani respectu BV mOentum)
a + s A + havR Es = F ex R = t522; (per S L. PrOP. PrXC.) Distancia Cenrri
Braricaris ab A a -
62 f2 52 ct 3 1B
8VR3 = 452R
12 a R = 125R F 12 avR = 453: Vet Cquod codem recidic)
toV2+ 1er X D3Ceu + v- 2R + B
quRS2B
4502 + 12   ~ seu =2 p + 12 avR = 4
Trem Semiquadrantalis Onoula super Ba A, aciem hahentis ra, momentum
respectu Aa, (ucSF. ) 3V A3 F35= R  = 25 2 V R = = 52 R2 + 1V R; (Soli.
e convertione factius 15V R7 X + 352 R P = sevD; ee Semilolidi 6V R2F
ccleste
=35 RZ = s= vF:) Adcoque, propier Oneula magnicudinem (Teu plani
momencum respectu ran) aX F 8sN = 5s2 A (per SM. prOP. PracCd.) diltancia
Centri graritatis ab Ag
42R 4 4sR = sV 4R + 4BA = s
Sak F TOSR = 250
6fR. = 25h
Opoulaeque Semiquactranralis super eodem B a A, aciem habenris P A, omen.
ium respectu ejusdem A a (ULS F) ZV R3. f Z se V R; (Solidique e Semisolidi
conrettione Pacti, ZV A2 P. = 15 = V F, 5VA =F + , 2 5 2 D P: ) Adeoque, prOPtCI
Ongulae magnicudinem, (seu plani momencum respectu J A,) Za R3 + 65 R 2 +
55~R, (Per S M. PrOB. Braced.) Distancia Cenri pravicaris ab A a
4u + sev er 4 R F s2
6ak + 25R + 250 6s R = 25B
K.
L
Eodem modo, semiquadranalis Oneulae Teianeulo B Ca intiltentis aciem ha. M.
bemis ra, momentum respectu A a, elt (UES F.) 352 R2 - - S V R; (ec 50.
lidorum, conversione vel semiconressione descripiorum, his proportionalia; nem
De in ratione P seu : P ad P: quod et in sequenribus incollise.) Adeoque (prop.
ter maxnicudinem =s R Z L5VR, per SMI. proP. Praced.) diltancia Centri ora-
vicacis ab A a, est 35 _ + 25V d5X  20
12R = 4V +ZX 4V
Oneuleque Semiquadrancalis su-
per eodem B Ca intiltencis, aciem habencis TA, momentum respectu A a est (ut SF)
2s R + =S v X; adeoque (proprer masnicudinem 35 R + 35u A per S M
PrOB. PEacect.) distancia Centri pravicatis ab A a,  3 f F 2V
12 R + 4V
Ongulaeque Semiguadrancalis super Frianeulo B V C, aeiem habencie F , MO.
memum resprectu A a; est (ut BD. )
24  N: FL magniendo (per SH.
A a a 22 :
1 PFOP