Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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atque ideo & portionis baſibus parallelo; ſuper ſectionem,
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quæ erit circulus maximus, cuius diameter LM, duo cylin
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dri deſcripti intelligantur, ad oppoſita portionis baſium pla
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na terminati ex illis autem totus cylindrus compoſitus EF,
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cuius baſis æqua
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lis circulo maxi
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mo LM. </
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>Deinde
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in ſegmento GH
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ſumpta OH, ter
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tia parte minoris
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extremæ maiori
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GH in proportio
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ne, quæ eſt LG ad
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GH; & in ſegmen
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to GK, ſumatur
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NK, tertia pars minoris extremæ maiori GK, in propor
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tione, quæ eſt LG ad GK. </
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<
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>Dico portionem ABCD
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ad cylindrum EF, eſse vt NO ad KH. </
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>Sumptis enim
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ijſdem, quæ in præcedentis ſumpſimus, demonſtrationem
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ſimiliter oſtenderemus tam portionem LBCM ad cy
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lindrum EF, eſse vt OG ad
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K
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H, quam portionem LA
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DM ad eundem EF cylindrum, vt NG ad eundem axim
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KH, vt igitur prima cum quinta ad ſecundam, ita tertia
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cum ſexta ad quartam: videlicet, vt NO ad KH, ita por
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tio ABCD ad EF cylindrum. </
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<
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crat. </
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PROPOSITIO XVIII.
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<
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>Omne conoides parabolicum dimidium eſt
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cylindri, coni autem ſeſquialterum eandem ipſi
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baſim, & eandem altitudinem habentium. </
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