Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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per præcedentem ſectæ erunt hæ diametri bifariam in pun
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ctis H, G, K. </
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>Quoniam igitur eſt vt EH, ad HA, ita
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EK ad KD, parallela erit KH, ipſi AD; igitur & EC;
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ſed recta KH, ſecat latus AE, trianguli AEC, bifariam
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in puncto H, ergo & latus AC, bifariam ſecabit; igitur
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in puncto G. punctum igitur G, eſt in linea KH. Rurſus,
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quoniam eſt vt GA, ad AC, ita GH, ad EC, propter ſi
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militudinem triangulorum; ſed dimidia eſt GA, ipſius
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AC, igitur & GH, erit dimidia ipſius EC, hoc eſt ipſius
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FD. </
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>Similiter oſtenderemus dimidiam eſse KH ipſius
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AD. vt igitur KH, ad AD, ita erit GH, ad FD: & per
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mutando, vt AD, ad DF, ita KH, ad HG, & diui
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dendo, vt AF, ad FD, hoc eſt vt parallelogrammum AE,
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ad parallelogrammum ED, ita KG, ad GH. </
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monſtrandum erat. </
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PROPOSITIO XVI.
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<
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>Plana grauia æquiponderant à longitudini
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bus ex contraria parte reſpondentibus. </
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>Sint plana grauia N, R, quorum centra grauitatis ſint
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N, R, & longitudo aliqua AB: & vt eſt N, ad R, ita ſit
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BC, ad CA. </
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>Dico ſuſpenſis magnitudinibus ſecundum
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centra grauitatis N, in puncto A, & R, in puncto B, vtri
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uſque magnitudinis N, R, ſimul centrum grauitatis eſse
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C. </
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>Nam ſi N, R, magnitudines ſint æquales, manifeſtum
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eſt propoſitum. </
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>Si autem inæquales, abſcindatur BD,
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æqualis AC, vt ſit AD, ad DB, vt BC, ad CA. </
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>Et quo
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niam ſpacio R, rectangulum æquale poteſt eſse; applice
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tur ad lineam BD, rectangulum BDKE, æquale quar
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tæ parti rectanguli æqualis ipſi R, hoc eſt quartæ parti
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ipſius R; & poſita DG, æquali, & in directum ipſi DK, </
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