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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 744, page id 851387705:0764
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DeCalculo Centri Cravitatis.
Cap. V.
Fis. 159. Lullasue Ongula momencum, per iptius magnitudinem diritum, hoc cst per
6V R = 5V R = 5sR (per S Q. prOp. Praced.) extibet iltius Ungula Ses.
mento AB A intistentis, aeiem habentis Aa, diltanciam Ceneri graritaris ab A a
plano, 3 C R + 3 50 R = 253
80F = 452 == 4 V2
ltanciam 3 C R 2 F 3 5V R = 2 5.
2V RP - 5 24
Semisolidique correspondencis, Ceniri inde di-
Rectat, ut timilicer expendamus Solida, impertecta convertione circa ran L A
BV, deleripra: Ongulalque correlpondentes: Porum Momenta respectu r an l A,
BV, respectire, decerminando; Cenerique graricaris inde distantiam.
IncelliBacur vaque super A D a Semicicculo, Ongula Semiguadrancalis, aciem
habens Fa. Cujus iraque lingulis ordinatim applicatis, ut B V, coridem inlictune
Parallelosramma Rectangula, Ongulam complencia; quorum alcirudines sint iplis
Varrespectiris aquales; corumque d J A distanria V A. Frirque propierea RC
ctangulorum horum cujusque momencum relpectu TA, (OPPOTIX lansenIS,)
aequale tacto ex Bale BV, in alcicudinem V a, ee diltanciam a vertice V A, Con
iinue ducta: HOc cAt, BV X V aXV A. FK aucem a V X V A = BV 9, (PrODteF
BY mediam proporcionalem incer Diumetri sexmenca AV, a V:) Adeoque BV x
aV XV A = BV C. EF Lic ubique.
Idemque cric ( eadem de calisa) momentum, respectur a Onpulae, aciem p2
bencis T A. Ouxe enim MMt, in alcera, alcicudo; est, in reliqua, diltantia: 
rice verta.
Sune iaque Parallelogrammorum torum omnium (sive quae Vngulam coram
ipti Aa D insiltenrem; live quae ipsius portionem ipsi BV A, vel BVCD, insi-
stencem complent; quippe utrobique eadem est ratio;) momenta respectu I A, A
acies lic ra; vel respectu r an A acies _Y A; Summa cuborum ordinatim appli-
catarum balin complentium. Puta, omnium o, respectire.
Eequidem in ea quae Semisesmento BV A intiltit, (ad Verricem A cerminato)
Omn. 03, = 8C R3 f 35VR = =5 R + 553, ut 59. oltentum est. (Idem-
quen i opus suerir ad aliam porcionem, ut BV CD, facite accommocabicur; u
ibidem eriam ostentum elt.)
Ellud itaqe momentum; A dividatur per Ongulae magnitudinem ipsi BV A Sémiles.
menco insillencis, aciem habentis re, 3e R F S0 R f ; s (per G L. prOP. Praeced.) ex.
hibet diltanciam Centri graricatis ab (opposica) PA
3
R. 1
653R - 353V
6eR +65u R. f 453
53B
35.B
16 A) + 9522 = 65t R f 6534
12eRE + 125V R + 8st
Sc R +65uR + 45
5
Adeoque ab ipta ra-
SeR + 65uR + 453
Ongulaque
DEOPECTCA respectu iptius BV, momentum = 3C RR 3 = 3 a V R f 35VR  - = 53 R
F ESV: Fjusdemque respectu ipsius r a, aciei lux, momencum, J0 R3 = 3SV R=
F253 R-
53V. Hlujusque duplum Z0 _3 f 35V R2 f 15 5 R - =5 3 V MOmen-
tum semisolidi, semiconvertione semisesmenti BV a circa r a, respectu ipsius r a
axis convertionis: aique hoc, per semisolidi magnicudinem diritum, exhibet
ZSCR F L5SVR7 f 225-65V
R
+25 R 6532
3C R 8 = 350 D + 253∞
P: Semisolici istius, distanciam Ceneri
pravicaris a tan (nempe ad illam Ingulae, ut 4 R, ad P.) Adeoque, d TA.
F = 5B
3C k. P + 3 5V R P. L3 5   Semisolidique illius, respectu iptius
T A (axi opbila) momencum  e R2 P + : 5v R P + 3 s P = 3C R. - = sV R
853 R + 35v.
Idemque (quod Prius) momentlm se R 7 8  a5 R F 253V; si d
vidatur per Ungula magnicudinem ipli B V a inciltencis, aciem habentis T A,
SCR + 35~ R = 35, (per B L. prop. praced.) exhibe, hajus, Cenri gravicacis
distanciam
3C R F = 3suA P + 2537
350RD + 2534