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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 853, page id 851387705:0873
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PFOD. XXII. De Calculo Contri Cravitatis.
3X 10X. Quod itaque elt Momencum Ongulae A B fig. 177. aciemFis. 17)
habeniis A∞ respectu A a: Fujusque Duptum (ue saepius dictum) Superticici
lemiconvertione lacta momencum respectu axis conrersionis Aa. Adeoque, li
rocum A 5 EpCCtCMUS, (PEOPEOr a = E~, e 6 = 2. R, C X == O, ) CTANE OmM.
2+ 52 + 2a5: = 2 2 R 4 18 R3 - 234 R3 - 16 13 = D 3 Pe = 1839 523. 9u0d
itaque est Ongulx Ar, aciem habencis Aa momentum respectu Na: Fujulque
Duplum, Mst correspondemis superticiei lemiconrertione cirea Aa deleripta mo.
mencum respectu ejuldem A0.
Momenco iaque per magnimdinem (SC. inrentam,) diviso; habetnr On-
sulae A b, aciem hrabentis Aa, distancia centri gravicaeis ab ipsa A a,
180a c 2 + 6003 R2 - 11206R 4. + 406X R2 + 720 aX R3 = 60a X R 9
180aC R 2 = 480 R + + 240 X R3 F (60DX R2 =) 30C2 X K
ec superticiei Cemiconvertione circa Ra Factae, distancia centri grarIatIS d CON-
vertionis axe Aa erit ad illam Ingula, Vt 2 R ad 3 P, seu 4 se ad P; ut alibi:
Nempe quocies idem est Axis Conrertionis et Aris LibrX.
Fociulque ar Ungulae, acieni eandem Aa habencis, distancia ab A a, simi.
liter habebicur, 45~2 = 2024. R.
90 P = 290 : (e superticiei semiconvertione lactae, ad
hanc Ongula, uc 4 R ad P;) Ongulaeque propterea distancia cencri gravitatis
2F~, 5∞, 4522 = (024 R2 1024 R 2 - 120RP 5I2R = 60Y
90 = - 240 R 11 90Z =240 R
452 = 120 8
O24. R3 = +20 P29
. It
1827 s
P2P. Onod icidem est (propter alcicudinum et distanciarum reciprocationem)
eomentum Onsula A7, aciem habeneis Fr, respectu Aa. Adcoque, per hujus
mannicudinem 5 R2 (per S C.) dirisum; extribet hujus, ab A a, diltanciam cen-
tri graricatis, 53  - = 2: C ab acie (Va YY, Z - E+ RP: e PTOPIETCA MOeN.
cum respectu aciei (uX LZ, 15 R2∞ - 1924 R3.
Elis ita peractis; ea quae jam extribuimus (SC, F, T.) divita A = Curra in par. K.
LC5 aquales; adeoque sumpiis TuBCENSIS AB =c, arittimetice proportionalibus; F18. 177.
non exic inucile, aliguatenus protequi secundum alteram methodum (qua SB, C
D, E, ut Cumus,) dirita Aa in partes aequales; adeoque sumpris linibus vertis
A V = 2 arichiuccice proporcionalibus.
Si itaque incellisacur recta A a fig. 177. in exiguas partes aequales numero inti-
nitas diridi; quarum una incelligatur VO = B: Oux his respondent b8 can
sences, seu (quod in parribus infinite exiguis pro eodem repurabitur) bX CuEVH,
sunc ut cocidlem Va = BY ZE, seu =Y , (pes SB, C.) Farumque ab
Aa diltanciae, sunt B V = a f s, (sinibus vertis arictimerice proportionalibus re
Spondentes,) iptam Ara semieycloidem complentes, (vel criam, cum tionram
ArCnuM A Fa H8. 270, 185. tum lemiciiculum ABa HS. 169, 185. complentes.
guixpe illam complent omnes a; semicirculum, omnes S.) Adeoque parricularum
curra A + fis. 277. momenta respectu Aa; sunt uc rocidem rectangula bV ∞ 18.
277. Boc est rocidem, BY 2R; seu cocidem bY c F BV a Fig. 285. HOc
est, tocidem = BV 2 R
SBV24
paerem iptius Rasieniticat, seu rectarum cralliciem planum complencium,) cocidem
1o28+1
Et quidem, Reeregaum omnium -,  Y 2 P Faeile habetur: Cum enim (iC s. -
odus alled ee S= YvB, eeit
Vh; doOmnes Y2 A3 dele alglle
PPPPF
Omnes