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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 841, page id 851387705:0861
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PFOD. XXII. De Calculo Centri Oravitatis.
HIudque momencum, 8R, vel ZVV 2V R = 3C~, Der IDEUS CUTVX AF vel F18. 177.
Ab maonicudinem, 4  vel 2 V 2VR = 20 (modo invencam,) diritum; extri-
hecu cenri Braricacis d FA, dictanciam; nempe, iptiuo A2, 3R; iphulque AB,
Adeoque; ipsius Ar diltantia cencri sravicatis d ra, erie 5 R; ejusque prop.
terea relpectu ra momentum, seu semiquadrantalis Ingula, 5 3: Ipliusque
AB, Diltancia Centri Graritatis d bV, 3V; e d 78, B. +
R2
V; ad
eoque ejusdem momentum (rel Semiquadrancalis Onsula) respectu b V, ZV V 2 V R
=3 2c; e respectu 7a, 2B V2~ R F ZVV 2VR = 2h0 + 40C, vel 4 RV2V R
ZVV2VR = 4C R = 3CV. FL superticies convertione vel lemiconvertione la
etae, ad haec MOMenCA; ut P vel = P ad R.
Deinde: Forundem omnium V22 R (Ongulam A r vel AB, aciem habentem F.
TA, complencium,) distantix à PA, LunE AV = V respective: Adeoque co.
rundem respectu PA momenta, sune omnia v Y 2VR (Cu Y 2~ R (vel VC;)
hoc est, ipta rectarum VD semiparabolam A a P vel A V p constiuencium mo-
menta respectu T A. HIOC CH, (per PrOD. T. vel 6. hujuS,) Semiguadrantalis On-
sula superticialis, ipli A7, vel AB, insiltentis, aciem habentis Y A, respectu
ejusdem PA, momencum, est 1S R3, rel Z V V 2V R = Z CV. Adeoque, luper-
ticiei Pemiconrertione circa Y A Factae momentum respectu iplius Y A, (quippe
duplum momenti correspondentis Onsula Semiquadrantalis, pronter magnicudi
num rationem, uc Z P ad R, seu P ad 2. R, e distanciarum ut 2 R ad Z P, (eu
4 R ad P; ut Caepe ostentum est;) 33 L3, vel 3c2 = 3 V Y2VR; Prout de 1O14
A7, Partere AB, incelligitur.
Iudque Ungulae Momencum 15 R. vel 3 EV ver maxnicudinem 3 P2 vel
Ec dirisum; exhibet distanciam cencri oraxicacis illius A5 vet AB superficia
lis Ongula (aciem habenris I A) ab ipta PA, E R vel 32; (adeoque COrrC
spondentis Superticiei Semiconvertione lacta, ceneri inde distanciam, 2
T2VR
3 vel
distanciati cencri oravicatis ejuldem Oneulae A = Caciem habemis F A) d XC, E X
(ejusque isitur respectu ra momencum 33 3;) Ongulaeque Ab (aeiem item ha-
BenCIS Y A) dictanciam, CenErI GraVICaLIS d B V, 3V; 2 7a B + 3V = 2R-
adeoque iplius, relpectu b V, momentum, 13 V Y20R = B0V e relpectu ra
306Y20R + 1~ Y20R  3570 + 13026, vel 3VR Y 2VR = ZvEV 2V R
36VR + 3CV.
Sed ee idem 8 R. (propier magnicudinum et diltantiarum reciprocattohetti)
elt etiam Ongula Superticialis Ar, aeiem habentis ra, momentum relpeet T R
quod itaque per magnicudinem. 15 X3 (modo invencam) divisum, extiber distan.
riam ceneri graricatis dPA, 3R; adeoque, d ra, 3 R, ejulque propierea re
spectu aciei lua ra momentum, 173 R3: Superticiei vero lemiconvertione cirea
ra deseripiae respectu ipsius ra, Momentum, (urpore Momenci Onsulae duplum,)
5R; Capirique graricalis a r0 dillanciam, ( vipore ael illam Ongulae u A 
ad P,) 32 t
Tiem (propter eandem magnicudinum ee distanciarum reciprocationem)
3 Ve Y 2VR == 3 CV, momentum eriam erie Onsulx Ah aciem habenis BV
respectu iptius FA: Ouod iraque per magnicudinem modo inventam 3V Y 2V X
=300 dirisum, extribet distanciam centri pravicaris d Y A, 3V; adeoque a bV.
V; d re B + 3V = 2 R = =v; ejulque proprerea respectu iplius D V (aciei Lua)
momencum I5 VE Y 2VX -5 18002; e respatu ra, 36B0  13002 = dcVR-
3522: Superticiei vero semiconrertione circa D V Cacta, momeneum respectu ipsiuS
6V, BC V; ejusque inse distancim ceneri sravicacis 26 V 
Tremque (ob eandem cantam) 3C2 R = 3CV, est etiam Nomentum Ongula
Superticialis AB, aciem habentis ra respectu P A: Ouod iinquo per maxnicudi-
nem modo inremtam 4c  -35V dirilum, extribet illius d T A distanciam ceneri
00000
Bravicatis