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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 Centro Cravitatis.
Cap. lV.
elt:) Matiifeltum et lon poste niti in unico puncto; vel Duos Axes A quilibrii
vel Tria Aquilibrii Plana, non in eadem recta concurrentia; le mucuo lecare
(Tercium ucique Planum, duorum communem sectionem, non nili in uno puncto
secat.) Cumque Centrum Craritatis, per 25 hujus, li in communi omnium live
Axium sre Planorum Aquilibrii concurtu; Daris illis, datur (quod in eorum
concursu est) Centrum Giraritatis. Ouod erat primo demonstrandum.
Sin illud Cirare sic vel Fisura Plana, vel. Linea urcunque curra in Plano de-
lexipea; erit, hoc ipsum planum, unum ex cribus illis Aequilibrii Planis requiliris:
(per det. Plani Aiquilibrii: quippe polito hoc ad horizontem recto in neurram
partem peaeponderabitur, per 3 hujus.) Adeoque (cum Centrum Graritaris in
illo plano esse constet) li vel duobus aliis Aquilibrii Planis (non in eadem ali-
qua hujus Plani recta le mucuo sccantibus;) vel, Axe uno; secetur Planum hoc:
unico lecabitur puncto, (quod itaque Craritaris Centrum erit;) per jam dicta.
Duod secundo demonltrandum erat. 1i1
Linea recta vero (cujus Centrum gravicaris in ipsa esse, similiter ostendetur; )
extribus Aiquilibrii planis duo suppler; sire communem duorum sectionem: Ad.
eoque, ( rel uno aliquo s: quilibrii vel axe, vel Plano, secetur; secatur puncto
unico, quod itaque Cencrum exit Crraritatis.
Denique: Ouod Puncti Cencrum Cravitaris extra iptum non sic, similiter osten-
detur acque de Planio, et Linea recta; (quippe s Planum aliquod extra ipsum
ponatur ad Florizoncem perpendiculare; cocum grare ad unas partes ponderabir:
Cum itaque Punctum sic indirisibile; eric ipsum sui Cenrrum. Quod crat ultimo
demonstrandum.
dCHOLTV M
Xempli gracia. Cencrum Craricatis Puncti C, elt ipsum C Punctum. Centrum
eraricacis rectae XS, est in ipla recta; ejusque Puncto C quo ab A quilibrii
Plano vel AXC XCT, sCcatUT.
Fixurae Planae, vel Linex Currae in Plano, YZ FS, cenrum gravicatis cst in
duorum Planorum Aiguilibriis putas ZS _ V T, communi sectione, (quae ipla
elt Axis Aquilibrii; ) hujusque puncto C, quod est in expolico plano
Fixuraxe rero solidie, vel linea cyrrx non in plano descripia, (quales lunc spi-
rales circa Conum, vel Gylindrum, ecc.) Cenerum graricacis erit in erium Pla-
norum Aeguilibrii; puta per YX P, duorumre hoc secantium ut in XCS, 8
TC T; communi concurtu C: sire duorum Axium A. quilibrii XES e Z T com-
muni sectione C.
Ejulmodi aurem duo axes habentur; ope +2 hujus. Puta suspenso primum
Crari ex sui puneto X, ut hrabeatur XSi deindem ex sui puneto Y, ut habea.
TuIE XCT
P LOL.. LXVII.
E18. 9C
trum Craritariss est in ea recta qua sua respectire Centra Crarica-
eis conjunsit, sie dirisa, uc Distanix sint Ponderibus reciproce pro-
-151 11LIC CEtSEIiS
Adteoque, daris allobus corumque Centris Cravicatisis datur commune
Ouodque de cuobus clertur; de pluribus similiters obtinebitur. cic
Irem: Datis Torius er Rolaci Ponderibus, et Ceneris Craritacis; dacur
Cencrum Craricaris religus. . sit IWBAC stirLSSI iAI
Vmco verbi pracia, duo Pondera, vel l quod
Deodem recidic, per 16 hujus) eorum Centra
Graricacis, in punctis A, B: Adeoque (per prae
ced. ) AB A xis A. quilibrii; et (per 25 hujus) in
illo, Cencrum GTaVITATIS: PUTa C. Fst, inguam
Ac Pondus A ad pondus B, Re (reciproce) distan-
eia C. B ad distantiam C A, (pex _B hujus) uc A qui-
Ponderenc.
Iavenco
porcionales.
Simut utriusque Conerum Craritatis. J.p. 111) duc00