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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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De Calculo Centri Cravitatis. Cap. V.
Fi8. 1773 Si itaque intelligatur ex hujusmodi rectansulis compleri Solidum, ipsi AaC
quadranci incumbens, alcicudinem hatens, in linsulis rq rectis, sequalem respe.
ciris rectis 7 p; Solidum hoc inceorum Aa B, ejutre logmenrum A7 4; erit a8
srexarum omnium  V. 4
 quae vel totam Ao vel iptius partem A3,
spectant. Vel etiam (quod eodem recidet) si intellisatur A a P complementi Se.
miparabolocidis planum, Tuper circuli plano, in Aa ad angulos rectos crectum
moveri (invariaro ansulo) ab A a ad Qr, motu luo describens solidum Pris-
matieum seu columnare, circuli plano incumbens, duobus Trilineis ipli AaF B.
milibus de aequalibus interjectum; quod secet Cytindri recti superticies arcur
ga intistens, solidum inde ablcindens AOga: Solidum sic abscistum, comple.
bune istiusmodi rectangula. Ouippe y P recta, sic mota, super y9 rectam de-
seribet q2p rectangulum. EL Sic ubique.
Idemque Solidum, alia adhuc complebunt plana, rectis n g (ipA A a parallC-
lis, et aequaliter ab invicem dilliris,) insistentia; ipsis A x p respectiris similia e
aequalia. Ouippe, dum AaP, moru jam dicto latum, ad nq perrenit; ejusdem
ParS A XD, eidem nq, insiltens, plano solidi lic deseripri, eidem na intiltenti,
COnOTUIE. Et sic ubique. Adcoque, Omnia AX p plania, coridem ng rectis in.
Sltentia cotum AO ga Colidum complene.
Sumoris aurem in AO (= 2 R,) rectis A n (=-c) arichmetice proportiona-
libus; quae his respondennqe sunt tocidem V: 4 R=- ct: hoc ell, cocidem X
Ductisque qXP (ipsi O A ParallCLIS,) rectae in complemento Paraholocidis cildem
: (sune urique in Paraboloei.
dis cubicalis complemento, Ordinatim applicate, in triplicata ratione diametro-
TUM; PuTa, X P recta, ad rectam a P, ue cubus Ax ad clibum Aa; et sc ubique.)
Adeoque AX Dd rectangulum, ( urpote factum Cx AX = + q = X, in X P
4 23) CA ; hoc est (PrOPter X = V: 4 R - ∞:) 26R  = 8c R + a
4 R
Adeoque Ax P parabolocidis Cubicalis complementum (vrpore ad circum scriptum
ParalleloBrammum uE L ad 4, PEr PTOP. 6. hujuS;) cst - ~ -1B R. - 8c R f e
26R
16R
Ex sic ubique. Adeoque omnia A X D Trilinea, hoc est, Ommia u g plana, CoII.
dum complentia, sune Omnia 26 ~: - 8C = R + E co spectancia; sive corum
16R
AO40 Tolidum spectemus, sive iptius portionem aliquam ut A Y qa.
Sunc aucem (Ber PTOP. L. hujus) S torum A Q9a spectemus, (DTOPIeT
AC = 2 R,) Omn. 62, = 3R3; e Omn. c2, = 35 R5. Adeoque Omn. 16 R a
=15 R3. Hoc est, Omnia V: 4 R-
A. R =
16X = 88 X +C
16R
 seu Omnia d6, rectatu Aa H. 184
vel planum A av HC. 183. spectania. AdeoquE (PrOPHeT A = SB. 282. = 2 A a
Fip. 183.) hujus duplum, 2 R3, erit Aexrexacum Omnium L Spectancium pla.
num A ro, vel rectam A = tig. 282. vel curvam A ~ fig. 177.
Si vero Solidi portionem A V q0 spectemus; ve sit rectarum AL == C, maxima
AV = 7 4 = X; erum (per candem prOP. T. nujus) Omn. 1, = 5 X3; ee Omn.
e = = X3: AdeOque Omn. 16 R  - 8c R + et: = 16X R + - 3 X R 4 5 x3, e
Omn. 26 R 2 = 8c R2 + ca
16R2: = = R = 3  + 30 R
Hoc aucem AV ga Tolidum, ex solido A9q0. = 15 B5 lodo reperco) sub.
dluctum; relinguit Colidum V4G, = 15 R3 - X R 2 + 5X3 -
80 X
Huic vero V90 Colido; si adelatur solidum AV 47) hoc est (propter pla-
num
84.