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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 811, page id 851387705:0831
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PFOP. XX. De Calculo Centri Gravitatis.
32~ 3 = 3R3. Solidunque convertione tactum (pirpoce ad Ongulam ut Z ad PB 168.
s) circa Aa, 8P3 = 3 RZP; ed cirea r T 16D  3 A P: Semi sOlidaque H0. 269, 170.
rum dimidia.
Lademque Momenca, ex retpectiris Paralletosrammi A ax F moinencis, hoc. cst,
(DTODIEF, a = LP, et A a.=7 2R, diltanciamque Conori gravicaris d Cre d = Psive
ab Aa, 274 == +7,) ex = RDE, lubdueta; relinguunt Complemenei Semiercloidis
AZ P, momentum respeetu Aa (seu correspondensem Onsulam Semiguadranta:
lem) a6 R~ 2 f L R3. e relpectu r d, 16 R 
Ct es (lic Solica Semilolida-
que correlpondenua, ad hac Momenca Ongulatre, ut D seu ZP, ad R:) Fadem-
que momentaCompleniene senriquselgidtis, ecr magnicydinem,  R P (per 5B.)
dirita; extlibene ejuldem abst a ctamiaui centri graricaio +P +
La des LBKIL HI
12
26K2
Clii 331.
5i
6X
19X.
 1s1 AHIi et _) GCIBI HBCL 1C SBI (1IS
et arF.
Sutiluer, in Semieyeloidis portione Be a V A. Momentum hujus) ad momen.
rum Sectoris in Semicirculo chrrespondencis, D a R, respectu iptius Ro, Cut modo
oltentum ell,) clt uc 5 ad 2; aeque insupers ut Triplum momenei correspondenus
Porconis Frilmei rellicuti b RaB A, ad Duplume momenci. dectoris Semicireuli
Ba A; respectu A a.
tlt autem Momencum Porrionis Prilinei Rellituti B BaB A, respectu A a, = a2 R
F asR = v R2, (per D EI. prOP. 17.) adeoque ejusdem Priplum 3 dR F 3a5R
=ZVR_ omencum SectotiS B a A, respeCtILA a, ZV R 2 = 352 R, (per 55.
DTOB. 255) hujusque Duplum 3.V R E f F. 5E PP. B. Racio itaque quam haber l’riplum
illud ad hoc Duplum, hocelb B a 2R  3a sN - 3.2 R 2 2d 3~ R 2 +- + 52R, lCI
9a 2. F. 28a5= 18VR, ad 40X Y252: dalisni 8 2d 2, lcu 100 R f 5522d
42 R +12 152 P acdetos Consdeiaca; extriber Monienui Porrionis semieyclodis
bP a V A ad momencum cortespondcurio Sestorts: (B a A, relpcetu a a rationem
Dat 845∞ 8V R + 15 5 d A ~ R F. 252 Cum itaque Sectoris momencum
illud lic 5V R  + is s Cinnatioco dictum; Jerir Porrionis Sanieycloidis bea V A,
momencum respectu Aa, (seueorrespondons Cngula SemiguadrancalIS) 222 k f.
2a5R = 3V R 2 + 35 2 X
Acque hoc momencum, per Porcionis Semiexcloidis b Ba V A magnitudinem
3fR = 3a R + ESR, (Per SB.) dirisum; extribet diltanciam Centri Graricacis ab Aa,
94 + 18, 1= 82 R + 55 st 5
1 sc 1Ba AEBS ui
03CH.~ (  2521. d 4u_ + 25
0a +95
. Unde cciam en
jusdem d h. L et b K diltancia tacsle colligicur; de momencum respectu illarum,
Icem Solidu ejuldem circa Aa convertione factum, 3a 7 P A. Ba5P = ZV R ∞
F1552∞: e lemitolleum, hujus dunicium.
Si aucem ex iorius Semlercloidis sespectu A a, momento, 3 X X 3
3R, sulodii.
catur hoc potiionis b B a. V A momencum 3 a2 R + 3 a s R = ZV R2 +. 3S2 R: RC
lingnitur, Scemenei b 6. 5 momencum respectu ejuldem Aa, 1 R P. E- 1 3 R3 -- 312 R
2a5 R + 30 R 2 = 25E R; TeU (DFOPICF a = 3 P = a, e B = 2R - v,) 3 a p 
=35R~ (3 a 2 R + 3 4. s R = 3 B R2 = 352 R: OuOd per MaenicudIneM 3 a R -
35 R; (8 B.) divitum: Fxhibet Cencri sravicacis ab Aa distantiam, 5 P - : a. +
55-
3
-05
 Adecque d Y+, 1a - 35
9a - 951
du -os: Ejulgue, cespectu F +, momencum 3 et R - 3 a s R. + 3 5. R + ; V R.
EX illo aurem Porrionis Semiexcloidis BBa V A Momenio (Ongulave) IC. B
spectu Aa; Si subducatur Praperii bBaV, respectu ejusdem Aa Momencum
Onculare: Relinquicur, respectu ejusdem AC, Momencum Ongulare Sexmenci
Semcercloidis ABV
Componiur aucem hoc Fraperium, ex Parallelogrammo bBa B, et Friangulo
aB V. Parallelosramnni magnicudo (propter baln BB = a ee alcicudinem
V a ==B, elt aB; Centrique Pravicaris (mepore in sui medio polici) ab A a di.
K H H H K 2
llantiam
8TF