Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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ALITER.
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<
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>Dico hemiſphærij, vel hemiſphæroidis ABC cen
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trum grauitatis eſſe G. </
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<
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>In plano enim ſemicirculi, vel ſe
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miellipſis per axem BD deſcriptæ intelligantur duæ pa
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rabolæ, quarum diametri AD, DC, & communiter
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ad vtranque ordinatim applicata ſit BD: & connectun
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tur rectæ AB, BC: ſumptis autem in BD tribus qui
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buslibet punctis, æqualia axis ſegmenta XF, FY interci
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pientibus, ſecent per ea puncta tres figuras hemiſphærium,
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vel hemiſphæroides ABC, & ſemicirculum, vel ſemielli
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pſim per axem, & figuram planam ARBSC, quæ lineis pa
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rabolicis ARB, BSC, & recta AC continetur, pla
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na quædam baſi hemiſphærij, vel hemiſphæroidis paralle
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la. </
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<
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>Erunt igitur ſectiones hemiſphærij, vel hemiſphæroidis
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circuli, vel ellipſes ſimiles baſi,
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expan
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quarũ
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diametri ſint KXH,
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LFM, N
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foreign
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grc
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O: figuræ autem ARBSC ſectiones rectæ
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lineæ PXQ, RFS, TYV. </
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<
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>Quoniamigitur per IV hu
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ius eſt vt KH ad LM potentia, ita KQ ad FS hoc
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eſt in earum duplis PQ ad RS longitudine; erit vt PQ
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ad RS, ita circulus, vel ellipſis KH ad circulum vel ſi
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milem ellipſim LM. </
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<
s
>Eadem ratione erit vt RS ad
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TV, ita circulus, vel ellipſis LM ad circulum, vel </
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