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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 763, page id 851387705:0783
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Ccop. V.moiravitatis.
hoc cl X A, = a,) ex Z a R2; Si auteratur momentum Frilinci AXG, hoc est, FiB. 169,
(per S F. ) 3a R2- 2s R3 L =SV R; habecur quadrilinei X LC A momentum re 170
spectu PA, = Z a R3 +Z sR2. F =SV R.Adeoque (proprer masnicucinem sR.
per SB.) distancia centri gravicatis, d F A
 f35. +52
; adeoques adC
a R. + 5R = 50; ejusque respectu dC momencum,  a R +  s R 2 L ; 5y p
=+a A F = SN R. Idemque est momentum porionis vBs uy respectu r a potico
SB (= XZ) ==a: Sed, Dolito aB = a, adeoquo (ejusdem complemencum ac
quadrantem, auc etiam excellus supra quadrantem,) SB =-DB = L D i a, (areus
a ditterentiam 2 quadrance = P,) quem arcum q dicemus; eritque hujus fnus
rectus, non s, Sed n == O C (sinus complemenci arcus a == X A.) AdCOquC MU
caco a in g; permutaris eriam si opys s’et x (sed hic nihil opus, perinde enim
cA sN e N S;) PrO Za R F as x R, habebitur quadrilinei vB sa momentum re
spectu ra, (DOsito aB = a,) ag R F EN SR; (HOC es omnia L S seu Semi-
summa quadratorum sinuum rectorum complenrum porcionem ves u, leu arcus
DB parriculis respondentium.) Pjusque a Z a Dictancia Cenri Gravitaris 2 F v 5
Adeoque; (propter Frilinei as u, respectu ejusdem ra, momentum 3 N 2
ut lupra;) Portionis a BV = e dn F Sn vB (prout aB minor majorre quadrante
Everic) momentum respectu ra, CriL =S R F = = G R2 F F5 N R; HlOC elL (prOPter
D = an et N = R = 2, si a B lic quadranie minor; vel q=
P +
e
X = - R + V,  a B quadrante MajOF;) Ea R2 = = sR2  =5VR: (OUX Ita
que est, Semisumma quadratorum Sinuum rectorum, complentium portionem a Bo
leu omnia 352 arcus AB particulis comperentia, Cumpris a arichmerice provortio
nalibus.) Factaque, per magnitudinem aβ0 = V R, dirisione; habecur distan
cia Ceneri pravicaris a ra, 2 R - s R  5y es + s0
Similiter, Frilinei a. d momentum respectu Aa (productae,) Hoc est, Frili. P
nei dCA momentum respectu sd (producta;) est, (per SI.) = Z a = R +
vR 2 f = a 2V. HOc est, in praesenci catu, (PrOPter V = R,) R3. (HOC cst
omnia a s, cocius quadrancis. ) Acque hoc, per magnitudinem R2 dirilum; extri-
bet R, dictan
que CentrI=
eeder
ucri sraricacis eritinci dC A, a sd; vel ad n ab Aa. Adeo
momentum correspondens (seu Semiquadrancalis Ingula, ) nemDe Frilinei dC a
respectu Aa, vel a s n respectu s n, 2 R2Y. R
Fx similicer in Portionibus, (licet perplexiori paulum caleulo, ob mucandum
ut prius, symbolorum valorem pro mucaco licutisurae,) idem obtinebicur
Est urique (per S F.) quacrilinei X Ea A momencum respectu A a, (potito
XZ = ag) 3a R F aS R = v R2: Adeoque (dempto Paraltelogrammi ElC 8
momento respectu ejusdem Aa, = a= R;) momencum quadrilinei X LC A, respecti
ejuldem Aa, as R =V R2. Aique cancundem eris momentum Ouadrilinei v Bd
respectu s in PolO SB = X X = a: Cenrrique gravicacis d du (propter magnitu
dinem sR,) distantia,  - - . Sec, polico ab = a; adeoque BS = + P si a = g
Et proprerea mutatis sin x (sinum complementi areus q;) et V in R ==s: Frit
Guldem vB Sn momentum respectu su, q V R = R3 = s R2; ex centri graricaris
a du distaniia, 2 r = R2 + 5
E: Adeoque, ab A a, 1 ∞. = G ~ = R= + s A
momencum respectu A a, = N R P FG ~ R L R3 F 5 R = d X R L R2 = 5 R=
EE, Proprerea, Momentum porcionis a B = a sn F S uv B, respectu Aa, (PrOptet
iptius asa, respectu Aa, momentum, R3) erit F a X R F 5 R=
R F av R. Centrique gravicatis ab Aa diltanria C propier magnicudinem,
VR,) eric =   + sR + aV
spectu B0 momentum eR.
=eR + a2
: Adeoque, d 8v, ; ejusque se
Ddd dd2
Verum