Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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lum per quoduis punctum S dimidij axis ED, faciens
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que ſectiones circulos, vel ellipſes ſimiles ſcilicet ba
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ſibus oppoſitis ſolidi FH, & ſectionum diametros LM,
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TV, abſcindat ſolidi ABCD maiorem portionem
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LBM, & ſolidi FH cylindrum, vel portionem cy
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lindricam TH, cuius axis BES: duorum autem ſegmen
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corum BE, ES ſumptis duabus quartis partibus extre
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mis BQ PS, fiat vt cubus ex BE ad cubum ex ES, ita
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PR ad RQ. Dico reliquæ figuræ ex cylindro, vel por
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tione cylindrica TH, portioni LBM circumſcripta, dem
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pta portione LBM, centrum grauitatis eſſe R. </
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<
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ctis enim parallelogrammo TH, & ſolidis LBM, TH,
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plano per centrum E, baſibus ſolidi TH parallelo, ſit ſe
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ctio, (vna enim communis erit vtrique ſolido) circulus,
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vel ellipſis, cuius diameter AEC in parallelogrammo T
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H diametris TV, GH
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oppoſitarum baſium pa
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rallela. </
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<
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ſes oppoſitas circulos, vel
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ellipſes circa GH, FK
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ſtent coni, vel portiones
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conicæ GEH, FEK:
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& planum per TV baſi
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circa FK parallelum ab
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ſcindat à ſolido FEK
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conum, vel coni portio
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nem NEO ſimilem vti
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que ipſi FEK, hoc eſt
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ipſi GEH, propter ſimiles baſes, & ſimilia triangula per
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axim in eodem parallelogrammo FH. </
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<
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NEO, ex ijs, quæ in primo libro demonſtrauimus, cen
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trum grauitatis erit P; quemadmodum & Q ſolidi
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NEO. </
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<
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>Quoniam igitur tàm ſolidi GEH ad ſoli
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dum NEO propter ſimilitudinem, quàm cubi ex BE </
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