Jordanus de Nemore
,
[Liber de ratione ponderis]
,
1565
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ideo, et pondus in, h, ad pondus in d, contin
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gens b, f, in e, u, m, transeatque linea e, u,
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p, et ducantur perpendiculares f, r, f, x,
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ad b, a, b, c. </
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Quia igitur ponderis e, b,
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ad pondus f, b, ut l, b, ad r, b, siue x, b, ad
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p, b, a puncta f, et e, aequedistent (ex
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hypothesi) a punctis c, et a, siue a puncto
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d, pondusque f, b, in u, ad pondus eius in f,
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sicut f, b, ad u, b, siue r, b, ad m, b. </
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<
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">Et quia
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x, p, ad p, b, sicut r, b, ad m, b, erit pon
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dus e, b, ad pondus f, b, sicut pondus f, b,
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in u, pondus eius in f, tantum ergo est
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pondus e, b, in e, quám f, b, in u, quia figu
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rae, a, b, p, est similis figurae, f, r, b, c, (quod
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facile probabis) et figura a, u, m, b, p, circa diametrum f, b, (per sextum Eu
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clidis) erit similis eisdem. </
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">Ideo sicut b, l, ad b, r, sic b, r, ad b, m, et ideo si
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cut b, e, in e, ad pondus b, f, m, f, sic erit idem pondus f, b, in u, ad idem pon
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dus f, b, in f, et ideo (per quintam Euclidis) pondera e, b, in e, et b, f, in u,
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erunt aequalia. </
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">Quod autem in e, sit leuius, quám in h, probatur quia d,
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h, est longior, et est etiam d, r, maior, quám e, z, et angulus b, e, 3, minor
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angulo u, k, z.
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dens breuiorem partem secundum
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proportionem longioris ad ip
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sam grauitatem redditur.
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In, quo suspenditur sit a, b, c, et pon
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dus e. </
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<
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">Diuidatur autem e, in d, ac f, ut
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sit d, ad f, sicut a, b, ad b, c. </
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<
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">Si igitur su
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spenditur d, in c, et f, in a,
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tanti ponderis quodlibet eo
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rum, quanti e, intellecto quód
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in opposita, sit quasi cen
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trum librae. substinentibus igi
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tur in a, et c, pondus c, de
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pendens a, b, erit grauitas
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in a, ad grauitatem c, sicut
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c, b, ad b, a.</
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