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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 828, page id 851387705:0848
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De Calculo Centri Cravitatis. Cap. V.
(per S G. prop. praeced.) dirisum; extibet hujus Diltanciam Centri gravicatis ab
252R f5B
A∞, =4 + 5 
f5V- 2a5R
4Ba . +24sR - t 2aB -- B5B :  t a t 24a R. + Bs R + L2aV + 850
Fig. 166. Si itaque ex Ongulae portionis Semicycloidis ABBa aeiem habentis T a, MO-
mento respectu Aa; Peu, aciem habeneis A a, momento respectu 7∞; 3 a 2  2 f
23a 5 R 2 F 325 2 R 2 = 8 V R3 =  a 5 V R = 365 = V R (Der 6 G.) auteraLE
respectirum noula bBa V momenium modo tradicum, a 2 R2 = Z 2 5 R 2  Z52 R
=Ea 2 VR = Z a 5V R = + S V R = = a 25 2 = = a 53 - Z 5+: Ilabetur Ongula
AbV, aciem habentis ra, momentum respectu A a; aciemve habentis A a, MO-
mencum respectu 50; = 3a 2 R 2 = 2 a 5 R 2 + 35= R 2 = 3 V R3 + = a 2 v R
F= a5V R F i s2 V R + + a2 5 2 + 5 a 53 = 854
Duod per Oneula AbV, aciem habencis ra magnicudinem, - 2 a R = +
35 RZ = aV R = +5V R F =a 5 = f 353, (Der SF, G. prOP. Praced.) divitum;
extribet ejusdem distantiam centri graricatis ab A e Z a F
27 a5R2 f55 2 R 2 - 64V R3 f 9a5VR + 4 5= V R + +2 a53 + 954
=54e R2 +72 a V R = 185VR + 36a5 F 2453
Idemque momentum per Ongula AB V, aciem habenus A a, magnicudinem,
a R + asR + 3 S R = 3v X + 3a V + = a 5v = 55= V, (Der SR, L. PrOP. PrX-
ced.) diritum; exhibet ejusdem distantiam centri gravitatis d ra, 3R -
q X = 80R + 18a VR + 36asVR + 245 VR - 18425 = 24a5 - 952
= 18a R + 36as R f 65 R= 480  + 36a v. f 36 a50. F 12 5V
Adeoque d F A, 3R +
452 R 2 = 8v R3 f +8 a VR = 36a5V R = L4SVR = 18a 2 5 = 24a5 - 95t
= +8a R = 36a5R f 6s2 P = 48uR = 36a V + 36a 5V F 1252V
dbV, 3R = B (= v - = R) -
4  = 8v R + 18 av + 36asuR + 245 V R = 18 a 5 - 2445 = 95
= 1Ba R - f 36aSR + 65R = 48VR + 36a V-  36452. + 1252V
Ejusque propterea respectu T A, momencum, = 3a 2 R2 = = a 5R2 + 252R =
qu R3 =  a2 V R = 3a 5VR + 18S2 VR = + 4252 - 5 a53 = 5 5+: Et respectu
BV, (Factum ex 2 in maonicudinem, dempro momento respectu Y A,) 1a 2 P
+a S R2 = 252 R2 + 3 V R 3 - 3 a V R = = a 5V R - -8 5 = V R + + a 2 52 + 3  S
F 554 = 3V2 R2 + = a 2 v2 = =a 5v 2 = 352 V23 TCU (PFODLET V2 = 2V R -5,)
5a RE = 3 a5 R2 f 92 52 R2 - 3V R3 + + a 2 V R + 3a 5V R + 8 s  VR = = 4  5
=6253 = 5+. Oux duo, tune etiam (propter alcicudines et distancias reci.
Procaras) momenta, respectu A a Ongularum ABV, acies habentium F A, e
b V: Adeoque per harum respectire magnicudines, - Le R = (= - = a R  + 2 5 R.)
= avR F35VR = 3 a 52 - Z53   C R2 (= = a R 2 - 4 5 R2) + Za V R +  52R
=Za S2= 353, (Der S F, G. ProP praeced.) divita; exhibenc earum distanciam
cencei gravicaris ab A a: Nempe, Oneulae A B V, aciem habencis T A, distanciam ab
A a 3 a f 3 a S R f 7 52 R= = 32 V R = 27 a 5V R = 205 V R = 12a5- 954
28CR 2 + 72 a V R + 545V R = 36 a 52 = 24 53
aciemque habenris B Y, ab cactem A e distanciam = a Y
4L SR = 9 a 5 R = = 64 vR3 + 27 a 52 R = +OS2VR = 6453 - 3 5a
180 R2 F 36 av R + 54 5V R = 36a 5 = 22. 53
Fadem Momenta, Vngulas ABV spectantia (et quae hinc dependene,) sic ad-
huc alias inrestisantur, absque ope Ongularum AhBa.
Tnoutam AB. V, aciem habentem B V, (Ei planis ipsi A B V plano parallelis.
aequalibus ab inricem distanciis remoris, sectam incellisamus,) constituent, omnia
ABV plana, eo spectancia; Cumpris AV, hoc est u arichmerice proportionalibus,
ulque ad AV, seu V, maximum. Adeoque eorum momenta respectu A a; HOC
t (per SH, L. ProP. Praced. ) Omn. = L a R + : a 5R + 1n 52 R - 3V L +
242