Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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planum per BE ſecans ſphæram, vel ſphæroides faciat ſe
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ctionem circulum, vel ellipſim, & in ea parallelas LFM,
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NGO, communes ſectiones iam factæ ſectionis ſphæræ
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vel ſphæroidis cum circulis, vel ellipſibus inter ſe paral
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lelis quarum diametri ſunt AC, KH. </
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<
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>Quoniam igitur
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E eſt centrum ſphæræ, vel ſphæroidis; omnes in eo per
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punctum E, tranſeuntes rectæ lineæ bifariam ſecabuntur:
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ſed idem E eſt in ſectione ſphæræ, vel ſphæroidis, circu
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lo, vel ellipſe ABCD; omnes igitur in ipſa rectas lineas
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bifariam ſecabit punctum E, & centrum erit circuli,
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vel ellipſis ABCD: quædam igitur ex centro recta EB
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ſecans parallelarum neutrius per centrum ductæ alteram
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AC bifariam in circuli, vel ellipſis ALCM centro F,
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& reliquam in puncto G bifariam ſecabit. </
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<
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oſtenderemus rectam NO ſectam eſse bifariam in pun
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cto G: atque adeo circuli, vel ellipſis KNHO centrum
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eſſe G. </
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<
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>Recta igitur E, tranſiens per centrum ſectionis
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ALCM, tranſibit per centrum reliquæ KNHO ipſi
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ALCM parallelæ. </
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COROLLARIVM.
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<
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>Hinc manifeſtum eſt, ſi ſphæra, vel ſphæroides
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ſecetur plano non per centrum: & recta linea ſphæ
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ræ, vel ſphæroidis, & factæ ſectionis centra iun
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gens ad ſuperficiem vtrinque producatur; talis
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axis ſegmenta eſſe
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portionum, earumque
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vertices extrema dicti axis, vt in figura theorema
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tis ſunt puncta B, D. </
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