Jordanus de Nemore
,
[Liber de ratione ponderis]
,
1565
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ex parte c, pondus b, datum, sitque b, e,
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aequalis b, c, et in medio a ,e, notetur
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z, á quo dependeat pondus h, aequa
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le a, e, et in eo etiam situ aeque pon
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derabit. </
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">Quia ergo in hoc situ aeque
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ponderant h, et d, eritque proportio d,
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ad h, ea z, b. </
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">ad b, c, et permutatim
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quae proportio d, ad z, b, ea est a, e,
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hoc est h, ad b, c, et coniunctim quae
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proportio d, et dupli z, b, hoc est a, c,
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ad z, b, ea est a, e, et dupli b, c, hoc est
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e, c, ad b, c. </
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">Si ergo tota a, b, c, ducatur
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in suum dimidium, et perductum diui
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datur per d, et a, c, quod totum est da
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tum, exibit b, c,. datum.
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<
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id
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">Quod si portiones datae fue
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rint, et pondus datum erit.
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<
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">Cum enim ut praemissum est d,
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pondus cum tota a, c, sit ad eius
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dimidium, sicut tota a, c, ad b,
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c. cum sint a, b, et b, c, datae, si ducatur
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a, c, in suum dimidium, ut prius, et pro
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ductum diuidatur per b, c, exibit pon
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dus d, et tota a, c, detracta ergo a, c,
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relinquitur pondus d, datum.
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<
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">Si uero pondus datum fue
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rit, et pars cui appenditur da
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ta, totum quoque datum erit.
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<
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sit, et b, c, portio data. </
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<
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id.2.14.03.01
">Quia
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igitur d, ad h, siue ad e, a, sicut
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z, b, ad b, e, erit, quód ex ductu d, in c,</
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