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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 795, page id 851387705:0815
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PFOD. XIZ. DeCalculo Contri Cravitatis.
respectu F an - 3 a R 2 + Za5 R 2 - v R3 = 3 52 R 2 = + a 5V R + = a V R +  a 5
Ouod per Ongulae ABB, aciem habentis Aa magnicudinem, - = a 2 R F a 5 R 16C
=vR 2 F Z aV, (per SI. prOP. 17.) dirisum; extribet hujus distanciam Cenrri p70.
Graritatis  7 a ZR = 2 a sV R F a v R = 2 v R + 5 N = 2 a s
+ a R + 8asR = 8vR + 4 a V
R + 2a5V R + a v R = 2V R3 = S R2 = 2 a25
4a R L BaSR = 8 v R 2 + 4 a V
(= v - 2 R)
Adeoque d bB, 3 X - 1
2250R + a vR = 2V R3 +S P2= 2 9 e
4 a R F 8 a5 R = 8VR2 + 4q
Et PrOPterCA,
ejuidem respectu BB momentum, 8 a R 2 - V R3 = 3 s R = = 3a5R 2 = 3a 5VR
=a252; ut prius. Acque hinc etiam, regrediendo, reliqua qua Ongulam
ABB aciem habencem BB spectancia modo tradebantur, similiter derivari po-
TeTINE.
Sed et haec omnia Momenca Ongularum ABB, (quaeque hinc dependent,) E
milicer haberi possent, ex Ongulis ARBB, Subductis respectiris Ongulis ABK.
TTabentur aurem Ongularum AK b B momenta, reliquaque inde dependentia, co-
dem plane modo quo Ungularum BbBa: Cublticuris ubique v pro B, et Y A
Pro ra, e vice verta. Oux monuisse sufticiat.
Restat, ue Ongularum aeies habentium Aa, (aut huie parallelas,) mOmenTa R.
respectu acierum suarum (rectarumque his parallelarum) oltendam; et Centro-
rum graviraris inde diltantias.
Si incelligatur portioni AbBa Semiquadrantalis Ongula insistere aciem habens
bB; quae hane complene plana ip( Ar a parallela, TunE ipla A XEa, A L C et, eC.
ulque ad ABBa; seu Omnia ABBa, eo spectancia, ut ad S F. octentum cAt:
Adeoque, e eorum omnium, respectu Aa momenea; hoc olt, (per S FI. prOV. 17.)
Omnia, = a R F as R = V R2, eo spectantia, (sumpris a arithmetice proportiona
libus,) est iplum Ongulae AbBa acieri habeneis bB, momiencum respectu A a;
auE etIam (proprer alticudines de diltantias reciprocataS) aciem habentis Aa ma-
mentum respectu bB.
Sune aucem Omnia a (sumpris a arictmetice proporrionalibus,) 5a3; Per
DEOD. T. hujus. Adeoque Omn. = a R: = 5 a R.
EE Omnia as, (hoc est momencum respectu A a omnium Bo crilincum a Ba
complencium;) Lune, = c R = F aD A, DEr S Q. PFOP. 17. AdCOqHE, OMM. a5R:
R3  a v R 
tiem, Omnes v, (sumpiis a arichmerice proporcionalibus,) hoc est, iptum
ABK crilineum, elt C R; per SB. PrOP. 17. Adeoque Omn. = V R2
R
Ergo, Omn. Z a R + a siR  2 R2; hoc est, momencum Onsula Ab Ba aciem
habentis bB respectu Aa; aciemre habentis Aa momentum relpectu bB; elt,
=2CR3++ aV R + 5a R.
Hoc itaque momencum, per Ingulae ABBa, aciem habeneis bB, magniudinem
Za R = v RZ (per S HL. prOP. 17.) divitum; exhiber ejuldem Dictantiam C’eneri
26 R3  2 a.
i
Bravicaris ab ACy a - -
3a + 6VR
Adeoque, d bB.
22CR 2 + 2 a3
terea; ejusdem, respectu BB, momencum, 2 e R3 + 3, a R.
3a +60X. Et prOp.
Idemque = 2e R F aV R + Z a R momencum, divilum per Ongula ABB a
aciem habencis Aam magnicudinem Z a R F as R = v R, (per B FL. prOp. 17.)
extribet hujus Diltanciam Cencri gravicacis d BB,
eoque ab A∞ =2 C R = = 12 aV R f 2 a f6 a’ 5
5a +6a5 =6v R
22CR= + 6 a VR L a
32 + 6a5 -6vR
1d-
et propterea, ejusdem, respe
Au Ran momencum (teu Omnia a. h eo spectancia, ) 2 C R. - 2 av R +; a. A
a 5R.
Et quidem A TOEUS A r a Ingulam speclemus; exit (propter a = 38, V = 2. R,
et 5 =O;) aciem habentis Fr, momencum respectu Aa; aciemve habentis A
momentum respectu Pr, + R~ 3. Adeoque (proprer illius magnicudinem s R~
f2. R3; hujulque S R D2 - 2 R, per GC. prOP. 17.) eris Aeiem habentis F.
EhhHH 2
Distancia