Commandino, Federico
,
Liber de centro gravitatis solidorum
,
1565
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33
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quod diuidat fruſtum in duo fruſta triangulares baſes ha
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bentia, uidelicet in fruſtum abdefh, & in
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fruſtũ
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bcdfgh. </
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<
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<
s
id
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s.000689
">erit triangulum kln proportionale inter triangula abd,
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efh: & triangulum lmn proportionale inter bcd, fgh. </
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<
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id
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">ſed pyramis æque alta, cuius baſis conſtat ex tribus trian
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id.023.01.073.1.jpg
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xlink:href
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gulis abd, klz, efh, demonſtrata
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eſt fruſto abdcfh æqualis. </
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<
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id
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s.000691
">& ſi
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militer pyramis, cuius baſis con
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ſtat ex triangulis bcd, lmn, fgh
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æqualis fruſto bcdfgh: compo
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nuntur autem tria quadrilatera a
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bcd, klmn, efgh è ſex triangu
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lis iam dictis. </
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<
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id
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s.000692
">pyramis igitur ba
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ſim habens æqualem tribus qua
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drilateris, & altitudinem eandem
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ipſi fruſto ag eſt æqualis. </
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<
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id
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s.000693
">Eodem
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modo illud
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abbr
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demõſtrabitur
">demonſtrabitur</
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in aliis
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eiuſmodi fruſtis.</
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>
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<
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id
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">Sit fruſtum coni, uel coni portionis ad; cuius maior ba
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ſis circulus, uel ellipſis circa diametrum ab; minor circa
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c d: & ſecetur plano, quod baſibus æquidiſtet,
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abbr
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faciatq;
">faciatque</
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ſe
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ctionem circulum, uel ellipſim circa diametrum ef, ita ut
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inter circulos, uel ellipſes ab, cd ſit proportionalis. </
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>
<
s
id
="
s.000695
">Dico
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conum, uel coni portionem, cuius baſis eſt æqualis tribus
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circulis, uel tribus ellipſibus ab, ef, cd; & altitudo eadem,
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quæ fruſti ad, ipſi fruſto æqualem eſſe. </
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>
<
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id
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">producatur enim
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fruſti ſuperficies quouſque coeat in unum punctum, quod
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ſit g: & coni, uel coni portionis agb axis ſit gh, occurrens
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planis ab, ef, cd in punctis hkl: circa circulum uero de
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ſcribatur quadratum mnop, & circa ellipſim
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rectangulũ
">rectangulum</
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mnop, quod ex ipſius diametris conſtat:
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iunctisq;
">iunctisque</
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gm,
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g n, go, gp, ex eodem uertice intelligatur pyramis baſim
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habens dictum quadratum, uel rectangulum: & plana in
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quibus ſunt circuli, uel ellipſes ef, cd uſque ad eius latera </
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