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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 845, page id 851387705:0865
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PrOP. XXII. DeCalculo Contri Cravitatis.
= 2, ad BY = 5 = cY: 4 2 - c2
CX
2X. Adeoque Omnes bu complences 1 81. 103
vel cotam A ro, vel iptius parrem A Bo, sunc Omnia CY: 4 R2 = C = vet E X.
eo
Spectancia; tumpeis carictmetice proporcionalibus. Ouarum asgrexatum sc col.
lisitur.
Si intellisatur AaC (L5. +83.) Circuli quadrans; qui Ractium habeat A a -
2 R aequalem circuli genitoris Diametro; iI quo FIMANEUF A 3 == c arichimetice
proportionales; rectaque 79, ips AO ParallelX. Frit ubique y9  V: 4 R2-
2: = x. (Nam quadracum qA, hoc est Aa, dempto quadraro A 7, XquatIE qua-
dracor 4.) Adcoque Omnes 7 4 sive quae toran A a  quadrancem, sive qux
iplius partem A7q complent, Tum Omnes V: 4 R 2 - 52: (Teu OmneS X) eo
spectantes. Cumque harum ab A O distancia LIHE Ry = c respectire: FrunE Ommia
CV: 4. R == ce: (scu Omnia CX,) idem acque iltius A a ( quacranris, eju(Ye A79
segmenci, momentum respectu AC recta.
Ouadrancis autem A aG, li ponerecur radius = R, momentum respectu AO
estet Z R3 (per SO. prOP. L5.) ergo, politoradio A a = 2 R, crit 3R3: Ouod
uaque est aggresarum omnium cV; 4. R 5E: eo spectancium. Adeoque BR
=Omn. CV: 4 R 7
CE ipsum A av Bilineum L8. 283. (sumpris ubique, ue A a
ad A, Eic Y9 ad 7v.) Ejusque duplum (proxier duplam alticudinem) 3 R2,
est Bilincum A=v. Fis. 182. duod ab A a.v FIg. 1283. non aliier disfert, quam quod
(recenicis cildem lavicudtinibus respectiris bv = 7 v) alcicudinems duplam habeat,
2Y= 2 Ac
Tiem, Scctoris q AO mbencum re spectu A C, posico Radio = R, ENeL (Per
5O. prop. 45.) =0RZ; hoc elt, Priens tacti ex areus linu verso in quadratum
Racii; hoc elt, in praesenri calu, ex OV = A9 - 7 4 = 2 R- V: 4 R - c
=ZR == X in guactarum A a, = 4 R2: HOC Clt, 8R = 3. R 2 Y: 4 A2 = c2.
=3R3 = 3X R2 Cui si addatur Momentum (rospectu ejuldem A Q) Frianouli
A97: hoc est (prOPteE y q = V: 4 R7- 621: 9 == X, _ R v == 0j; centrique sra
vitatis ab A O distanciam 3c;) 302 V: 4  2 = 62: == 5024. FTabeLUE tOTIIS
AygO momencum respectu A C, 3 R   B R2 V: 4 X   02: + 362V: 4X
vel SR. = 3X R F 3xCE: Hoc est ( propier 4 X2
2c3
Ouod naque icaque elt. Omnium cV: 4 R 2 =c; cospcetancium aserexatum: A.
deoque : P:  = Omn. EY: 4 R c
2. X 1711
6R
 ipsum A ro ti8. 183. Fjulque
duplum ? N. - = x. (propiet duplam alicudinem) est iptum A B. liL. 182.
Est itaque (PrOpTeT AAY = 2 RP = 8 R 2, _ A rV = 3 R2,) cotum AaXy
A8. 182. = 2 R D L 15 R2. Ouod itaque est currae Semiercloidis A= fis. 17
momencum respectu rectae Aa; vel Semiquadrancalis Ongula eidem insistens aciem
hrabens Aa. (Adeoque Superticies curra ejusdem circa Aa convertione deserixra
2D2 16 x ∞. e, semiconverlione, D2 = 8 p ∞.) IIIudqueCUEVE A F momen-
 per maonicudinem (4 R) dirisum; extribet ejusdem a r currae distanciam
cencri gravitaris ab Aa, ZP =3 R: Adeoque d Pr, 8 R, caneundem scilicet quan-
cum d
SD.) acque cancundem est ejusdem respectu ncriutvis Momentum,
nempe S R2: e aequales urobique superticies conversione extibira, 1S RP; e Se
mieonver lione 8RP.
liem (propiet ABB = 22c - 8  + +XR; et AB. = 5 p - X porum
ABb0Fic. 283. = 2ac = 13  + 4X. R =  ; vel (proprer X3 = 2b. s; la
SIEa. A, a B, a. V; hoc e 2. R, X b, concinue proportionales; d 2ac = 15 R2 +
AX R = 3BX = 2.aC - 16 P2 +, 3X R + 3VX. Ouodicaque, est iptius A B CUEVX
momentum respectu Aa; vel Semiquadrantalis Ongula cidem intistens, aciem ha-
000003
bens