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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 771, page id 851387705:0791
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PFOD. XVIII. DeCalculo Centri Cravitatis.
Porro; Si intellivatur Solidum inegrum ita poticum, uE Za n planum sic in sieu
horizontali, adeoque A ra (super illo crectum) in plano ad Florizontem recto:
Momencum Tolidi corius, respectu za rectae; erir Duplum momenci Ongule (c
micirculi aciens habentis A ay respectu iplius A a. (Bc linsiliter in parcibus respe
etire Tumpris.) Sunc neique singula b eo Parallelepipeda Solidum hoc complencia
(ne ostentum eltSA,) ad respectiras Pyramides a D Ongulam illam complentes
ut 3 ad T. Porumque Parallelepipedorum à perpendiculari plano r0 A distantix
Cenri GravitatS, hoc est Z Bo respectire, (per PrOP. 2. trujus; ) ad Pyramidum
illarum diltaneias Ceneri graricatis a perpendiculari plano Ra ZBV, (distane Uci-
que ab a, 3a B, per proP. B hujus; adeoque, ZBV, ab A∞;) seu 2B0; U Z ad Z
Ieu 2 ad 3. ErBO, (PrOPteF ZX 3 ==E,) momenium cujusque Parallelepipedi, (adeo.
que et limul omnium,) ad respectirae Pyramidis (adeoque et simul omnium) mo-
mencum; ett Ar 2 ad L. Ouoll quidem momeneum, ell aggrexatum Omnium ? SB
sire cocum Solidum, live iplius portionem, spectantium. (Sunc urique masnicudi
nes, asgresatum Omnium sB: diltanciae que Cencrorum grarieatis respectire, 25.
FIL aurem Ongulae Semicirculi A Da ZC em habentis Aa momentm respecti
A_, 16 R3 P; Onsulaeque Sectoris Ba A, BC R3 F 55V K2 F 153 R; (Der SP, R,
PrOp. 16.) Ergo Tocius Solidi aFa (Pieu illo polici) momentum relpectu a 7)
est S R Z; d porrionis AbBa, momentm, LC R3 F, sV R2  853 R. AIGVC
hraec momenta, per respectiras magnicudities divila, (hoc elt, pet 2 R3, e V R 2 +
252 R, Ut ad S A.) extribene Cencrorum gravitatis ab A + a platio distancias:
nempe corcius solidis etP; et porrionis Solidi Pibca, 3e  + 350 X f 2 5
120R + 65
1a
Si vero ex eo Solidi Ab ea momenco; auteracur momencum iplius bB d R: se.
stac momencum Solidi ABB.
c1
Est aurem Solidi BBa B magnicudo (per SB.) s R = vB se; ejulque Cenrei
Braricatis ab Ara plano diltancia, (quanta plani ABv d F a Der GCi. DEOP. 5.) ell
eR +52
 Per SO. DrOB. 17. adcoque momemum (in co situ) relpectu r a,
ZCbR2 = 4 5VBR = d eB R2 + 253R = = C R3 = = ev R2 + 4 53 R =  C R -
2a0R = = +5V R 2 F +53 R: FIOC itagHe  ex FOTIIS A B Ba MOMeNIO, ZCR3. 
25V R 2 + 353R, (SC.) subductum; relinquit = =P _3 + Z a V R 2 = 1 53R
momencum Solici Ab B ( super Planio abo erecti) relpectu ra. CQua est sum.
ma omnium 2 R Colidum complentium in suas respectire distancias  ducta
+ 2
rom: seu, omnium : c RE. + + 5V R; sumpris v acictmetice propoccionalibus. H
Judque momentum, pes magnicudinem dirilum (S B. cradITam) V R2
Ev R; exhiber ejuldem AbB, Centri gravicaris a plano A r a diltanciam
=3e R + 3a0R - 5
220R - 652=60
Idem eriam per le (absque ope porcionis ABB a) sic colligitur. Cum sinoula
plana rectis bB insistencia, Solidum complentia, aequalia lint iplis respectire a B0
=2 _, (ut dictum est;) lincque eorum Cenira gravicalis in eadem ab A r a plano
distancia, qua ipsorum a Bv d ra; hOc CR  F respectire: Prunc singulorm
momenta, respectu ipsus Ar a perpendicularis plani, Le R=  = 5V R, seu ; a R
R2 = =5VR. Adeoque Solidi AbB momentum, eri Omnium Summa; hoc
C, Omn. = a R2 = = s R2 f =5V R: Tumpris v arichmetice proporrionalibus.
Sunt autem, Omnes a, (lumptis arichmetico proporrionalibus,) ipsut ABB
planum; hoc est, = e R F a V, (per SB. PrOP. 17.) Adeoque Omn. L a R = = i∞ R
+aVR2
Frsimiliter, Omnes s, (sumpris e arichmerico proporrionalibus) sune iptum
in semicirculo ABVY planum; hoc esti Ze _ f 3 52, (per BP. prop. 15. ) Adeo.
que Omn. = 5 R3: = de R3 4 5VR2
trem, Omnia sv, (hoc sentu,) Cunc iptius, in semicireulo, plani ABV, mo-
mencum respectu P A, C est enim ingulorum s, d Y A diltaneia v, respective;)
E eecc2
hoc
C
Fi8
69
170.