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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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.
l 13.
Cid p. V
in Parallelogrammo, aut quod hujus instar est, saltem Recta; in Prismate, QuE
Porro; Cum sinc in Parallelogrammo
(sire sic Ouadratum, Oblongum, Rhom
bus, aue Phomboeides,) bis bina latera
oppolica: Hhabentur hine duxe rectx, ut
XCS (media intex AB, e DF,) e
TCT, (media inter AD, et BF,) in
quarum utraque (per jam demonttrata)
el Centrum Gravicaris: Adeoque; in nO-
rum communi sectione, C. puncto. Per 26
CaD. 4.
Denique; Cum fint in Cubo, ec quoris
Parallelexipedo, cer bina Plana oppolita:
Elabentur hujusmodi (per jam demon-
strata) eria Plana, in quorum lingulIs,
(adeoque in communi omnium concurtur
Cy) elt Cemrum Graritatis. Per 15, _ 26
Adeoque, eum Puncti (sive per 26
Cap. 4. sirc hinc, quia nihil est quod
n Prxeponderet,) cum Linex rectae, cum Ouadrati aut
cujulris Paralselosrammi, irem Ciubi aur P’arallelopipedi cujulvis, datur ipsum Cira-
viracis Cenrum; per jam demonstrata. Quodque de Cubis et Parallelepipedis,
dictum elt; perinde valet de horum superticiebus
Ec propterea, Punctorum quoritiet, vel quortibet rectarum; item Guadratorum
aut Parallelozrammorum quoclibet; quortibet item Cuborum rel Parallelepipedo-
rum; quodibet denique Superficierum Cuborum aut Parallelepipedorum; datur
commune Centrum Ciraricaris, modo ipla linc magnicudine et potitione data. PCx
Prop. ult. C ap. Praeced.
Od.
Aia Demonstratio.
Id. 2d. 3d. ec. usque ad D.
6a P F raP F 24 P f 3a P F _C. usque ad DP. = L NDP.
Idem demonstratur ex F hujus. Incelligatur urique, per C. mediam longicudi-
nem incedens, Perpendiculare per Axem Planum; (cui incellisancur parallelae,
Paralleloerammi vel Prismatis Bases oppolicx:) Ouxeque sunt vtrinque C A, C. B.
recta, ex intinicis numero Punctis (eo sentu quo def. T. Cap. 4. detinitum cst
constare: (de similiter ex intiniris numero Rectis, Parallelogrammum; _ Planis,
exisina, ec.) Dux incellisantur omnia, aque cralta; (de Timilicer alibi incelli-
sendum, ubi hujusmodi constructio adhibetur, nil aliud IMNUatE:) Adeoque
cum ipla (ut Rectarum, Parallelosrammorum, e Parallelexipedorum, natura po-
Pulat, ulpote in omnibus sui parribus aeque altorum;) cum _ ProPIerca Corum
praeced. Pondera, incer se aequalia: pura, ut P, P, P, P, Ec. quorum omnium numerus in-
celligatur, N: Sed e, in Diltanciis a Perpendiculari Plano per Axem, UF Od, F d.
2d, 3 d, ec. ulque ad D, maximam. Adeoque momenta seu Ponderationes (Per TZ
Cap. 3. Vel 4 Cap. 4.) ucOaP, EaP, 2a P, 3dP, dec. u(que ad DP. Ouae qui-
dem intinitae series Primanorum, simul valene ut ZNDP; (nemPE, ad NDP
summam coridem Maximo Agualium, uc T ad 2:) per L hujus. Cumque hoc.
utrinque perinde concingat: Aiguiponderabitur utrinque. Adeoque (Der 25
Cap. 4.) Cencrum Cravicacis est in illo Plano. Quod erat demonstrandum.
Reliquaque hinc deducuncur ut prius.
De Calculo Centri Cravitatis.
Cylindro, Planum; in quo est ipsum Graritatis Centrum.
AExI
Dem
a
3d. ulque 2
peet
∞dP. F FaB, + 2 aP. F 3 aP H es. alque ad DP. = L NDP = NP ~ ; 1
Idem