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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)
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DeCalculo Centri Cravitatis. Cap. V.
Fig. Aa: FLa BR = = a 2B2 momencum criam aciem habentis Y A, respectu BB vel
169, A∞. FAque uriusque horum, Distancia Centri graritaris 2bB vel A a, Za, Per
270. DroP. 2. Magnicudo aurem, aciem habentis ra, E a h7; aciemque habentis Y A.
2ab R = Z Bh2 (per SF. PrOP. 17.) Adeoque Diltancia CeMErI graVILatIS d + di
EB; d T A, R = 3
Si ilaque ex Dneulae ABBaq deiem habencis F A, momento respectu bB; aci
emre habentis bB, momento respectu T A; 3a 2 R2 = VR3 = 5s E RZ, (BerSF.
Auteratur respectirum Ongula BBBa momentum; modo extribitum, a 2 B R -
a2 B2 = a 2 R 2 = = a 2 V R + + a 252: RelinguetIE, IngnIX ABB, aciem haten-
tis T A, momencum respectu bB; aciemre habentis bB, momentum respectu P A;
3a2 R2 F ~ R3 = 8s R2 + La= V R = = a752. Quod per Vngulae AbB, aciem
habentis TA, magnicudinem,
3a R= = 35 R2 = aV R f =5VR - ZaS, (Der BF
ProP. 17.) diritum; exhibet ejuldem distancam Ceneri craricaiis d bB, Z a
8V- s R - 3a5R- aSVR
=6eR FBavR + 250R - 4a5. ; ab Aa, a dvR  5 R - 3as R - asv R
Ses = 8aVR + 2SVR - 445
Trem; si ex Ingulae ABBa, aciem habentis T A, momento respectu Aa=
aciemre habencis Aa momento respectu LA; 3a 2 R2 = 2 asR 2 = V R3 L + S2 R
F=aSVR, (per S F.) Anteracur correlpondens momentum Onoula BBBa, modo
extribicum, a 2 BX = Z a = B2 = a R3 = Za  V R + 2a2 52: Relinquetur, Onoula
ABB, aciem habentis T A, momentum respectu Ra; aciemre hrabentis Aa mo-
mencum respectu LA; = 8a2 R F 3a5 R2 = v R + 5s R + 2450 R F + a vR
Tiem; Si ex Ongula ABBa aciem habentis ra, momento respectu bB; aciemre
hrabeniis bB, momenco respectu ra; 8a R2 F V R3 F 3sZR2 (per SF. ) AufC
ratur correlpondens momentum Onsulae BbBa modo extibitum,  a = B2 = a R
=a2 V R F + a2 v2 = a 2 R2 =  a V R = + a 2 52: Rclinquitur, Ongula ABB.
aciem habentis ra, momencum respectu DB; aciemre hrabentis bB, momencum re-
spectu 2a -8a R2 = V R3 + 5s R + Z a 2V R F + a 252. Ouod, per Ongula
ABB, aciem habentis a magnicudinem 2 FR 2 F = 5B R = = a BE
2a R = +
35 R + av R = 4 sv R + 2 a5, (Der SV. prOp. 17.) divitum; extribet ejusdem
Dillanciam Cencri gravicatis a bB, La +
Ea
80R = 5 asR F S R + aSvk
10c F + 8av R- 250 R + 4as2 i ab A a 7
8vR3 =5 a 5 R= = 52 R2 + a s~R
=10C R = 8aVR= 25u R + 495
Idemque, per ungulae AbB, aciem
habentis bB, magnicudinem, = =a 2R f. V R2 - f 3 a 2v, (per S. T. prop. 27.) divi-
sum; extibet hujus Ongula diltanciam Ceniri Graricatis a 7 a, Z R -
20R + a vR = s R- L 2a 5
4ue R + 8vR + 4a2
quen a b. B, : R - B (= v-
2
FA, a  f 20 _ + a vR = b. R = 2a. 5. Adco
4ae R F 80 R + 402
20A+ a vR = sN + 2a s
 = 4a R F 8VF f 4ae FL DTOPICTCA C.
jusdem, respectu BB momentiim 3a 2 R2 f v R3 L 352R2 - 29252. Idemque
ell Ongulae ABB, aciem habentis BB momencum respectu bB. Ouod iaque
per hujus magnicudinem 2 a X 2 = 85 R 2  35D R - - Z as2 (Der SF. DrOD. 17
ceritum; exhibet hujus Ongulae AbB, aciem habenis BB, distanciam C’eumr
eravicatis a b B, = a. f 82 R - 7 52 R + 3a 5 R3-
1-
1.9. DC RE∞+ 6SVR= 4a s
8o R = 75 P H 3asP. = 3asuB. ejusque respectu A a momencum, 3 à 3 p
SCP L 65VR = 445
oA3 + Bs P =3as R + asuR -  a s quod eriam (propier alcicudi-
nes et dictancias reciprocatas) est Ongula A b B, aciem habentis A en momencum
respectu bB.
em; s ex Oneula AB B aciem habencis re, momenco respectu A ey aciem-
ve habencis Aa, momenco respectu 24; 3 a R + Zas R2= = aSVR = V R
=3sR= (per S L.) Auteratur correlpondens Onsula BbBa momentum, mo-
do exhibicum,  a B = a R = 3 a v R - + e s: Relinquerur, Ungulae ABB,
aciem habeniis xan momencum respectu AB; aCICMVC haBEHEIS A a momentum
respectu