Iordanus <Nemorarius>
,
Iordani opusculum de ponderositate
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dere aequales duabus aequis partibus b, 6. sequitur ut to
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tum toti.
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">Si inaequalia fuerint brachia librae, et in cen
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tro motus angulum fecerint: si termini eorum
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ad directionem hinc inde aequaliter accesserint:
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aequalia appensa in hac dispositione aequaliter
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ponderabunt.
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b, c, breuius, et descendat perpen
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diculariter c, e, 6. </
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pendiculariter cadant hinc, inde a, 6.
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"> et b, e, aequales. </
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qualia appensa a, c, b, ab hac positio
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ne non mutabuntur, pertranseant enim
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aequaliter a, 6, et b, e, ad k, et z, et
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super eas fiant portiones circulorum
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m ,b, h, z, k, x, a, l, et circa centrum
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c, fiat commune proportio k, y, a, f,
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similis, et aequalis portionis m , b, h, z,
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et sint arcus a, x, a, l, aequales sibi at
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que similes arcubus b, m, b, h. Itemque
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a, y, a, f. </
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"> si ergo ponderosius est a, quam
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b, in hoc situ descendat a, in x, et a
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scendat b, in m, ducantur igitur lineae
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z, m, k, x, y, k, f, l, et m, p, super z, b,
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stet perpendiculariter etiam x, e, et
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f, d, super k, a, d, et quia m, p, aequa
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tur f, d, et ipsa est maior x, t, per si
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miles triangulos erunt m, p, maior
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x, t, quia plus ascendit b, ad rectitu
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dinem, quam a, descendit. </
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"> quod est
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impossibile, quum sint aequalia: desce
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ndat ratione b, in h, et trahat a, in l,
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et cadant perpendiculariter h, 2, super b, z, et l, n, et y, o, super n, m, fiet
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l, n, maior y, o, et ideo maior, h, r, vnde similiter colligitur impossibile. </
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<
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maiorem autem euidentiam describamus aliam figuram, hoc modo. </
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