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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 746, page id 851387705:0766
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De Calculo Centri Cravitatis. Cap. V.
Fis. aciem habentis r∞.) Acque ex hoc demum momento respectu ra, auterendum
159, quod tc ex ipsa Ongulae BV A F magnicudine, in V a = B; hoc cst, (per SL.
260. PrOD. praeced.) = = eB R 2 F Z a V B R = Zs B = - C R3  Z CV R = + Z a S R
 353 R = 5 5D: FF habebitur dCR3 = E5V RZ = = a s R Y 13 S R =  s V mO-
mencum Onoulae BV A F (semisegmento BV A insistentis, aciem habentis BV,
respectu aciei sux BV: Adeoque (per magnicudinem diridendo) diltantia Cen-
iri gravicatis a BV, L5 C R + 255V R = = 12 a s R F 25 R = 2 5. 2
N.
12CR2 + 12 aV R = 45
=de R3 + 12a0 R + 350R2 = 65 R + 2. 5 
=T2C R2 F LZaVR = 45
(Semilolidigue corre.
spondentis momentum, sire respectu ra, sire BV, est duplum momentum Vn.
gula: Ejusque Centri gravicatis, distantia sive d r a, lre d BV, est ad di-
stanciam Cencri Ungulx, uc 4 R ad P.) Cemrique Ongulae diltancia d F A,
= 25CR3 = 12 aVR 2 = 35VR 2 = 25 R - 253q
12CR2 + 12a0R - 45
; ejusque momentum respectus
TA, = Ee R3 F ; aV R 2 = 85VR = = 1 S R - 1 53 v. (Idem acque, respectu B V
momentum aciem habentis FA.) Similiter, li Semisolidi distantia Cencri pravicaris
d ra, auteratur ex A a = 2 R; habebiur ejuldem d P A distancia. AEque haC
in semisolidi maenicudinem ducta, exhibet ejuldem respectu P A momenium.
PorrO; Triangulo B V a intistens Ongula Semiquadrancalis aciem habens r a
CAPgramis; Cujus magnicudo BV X V a. X 3 V ∞ = Z SB. = 3s R 2 = 35V R + = 52
=85R2 = 352R = 3 5: Fjusque Centi Braricacis, d + a, distantia 3 V a = 3 B:
Adeoque Ongula momencum respectu ra, ZsB. == 25 R3 -- 35V R 2 + 3522 R
=25V = 25 R3 - 353R = = 52 = 25 R3 = sV R 2 = 5 R +  53V.
Alque hoc additum momeneo Ongulae ipsi B V A intiltencis, aciem habenris ra
respectu ejusdem ra, 8e R3 F 35V RE F i S R = 2 5 V (ut S F. ) Teu 3a R.
f5R3 = 35V R2 = 2E B R - = sV; extibet Za R + 8s R = 85V R = 12S R,
Seu 3fR3 f 3SBR2 = ~ S R, momentum Ongulae sectori Ba A insistentis, aciem
hrabentis ra, respectu iplius ra. (Flujusque duplum est momentum correspon-
dentis Semisolidi, respectu ejusdem r a.) Idemque per magnicudinem diritum,
hoc CIb, per Z f R2 f SSBR = = a R 2 + 35 R= = ESVR; (UES MI. prOP. praeced.)
extibet distanciam Cenri pravicatis d r a 25 a R = = 335R, - 9 50 s - 25
25 F R2 + 9sBR = 253
22FR F 4 5B
12 a R = 205R -- 45V
Adeoque ejuldem Cenri distancia d FA,
Da R2 f 75A2 F 5VR + 25 9FR2 = 5BR + 2s
c2a R F 205R = q 5~
12FR = 4 sB; _ PrOPterea eju Idem
Ongulae momentum respectu TA, 3 a R F 13 s R3 + ,  5~ R 2 = i S R = 8f R3
sh R F =B R. (EF correspondentis Semitolidi, ditancia Ceneri craritatis
d2
distantia a P A; aeque haec in Semisolidi magnicudinem ducta, exhibet semisolidi
momentum re
Ejuldemque Priangulo B V a insistentis Ongulae, Pgramiditre, Centrum pravi-
ratis d T A, diltat 2 R - 3B = 2 R f. 3~: Adeoque ipsius respectu TA momen-
tum (distantia in maxnicudinem ducta) 35 R3 + 352 R 2 = = sV R = 35 se
= 2 5. 2 = 35 R3 - 3 5V R 2  253 R - = 5 v = 35h R =  5B3 = 1 3 s B3 f  53 B.
DTOPIEE S= BV.
Acque hoc addicum, momenco Ongulae ipsi B V A insistencis, aciem irem haben.
2i8 20, 3aR3 = 85 R (= 3eR3) F 35VR2 = 2 s R F a 5~, (UtGV.) extri.
Bet 3a R3 - = 5 R 3.F 2 5V R = + 35 R, SCU B f R3 = 2 5 b R 2 + ,  5 R, MOMEM.
tum Ongulae sectori Ba A insistentis, aciem habentis ran respectu iptius T A. VE
prius.
Fidem vero Friangulo B Va intiltens Ongulau aciem habens PA, conltat ex
Prilmate eictem insiltenre cujus alticudo A V = 2; cique suxerjacence pyramictem
cujuo