Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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DE CENTRO GRAVIT. SOLID.
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quod diuidat fruſtum in duo fruſta triangulares baſes ha-
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bentia, uidelicet in fruſtum a b d e f h, & </
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<
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</
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<
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">erit triangulum k l n proportionale inter triangula a b d,
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e f h: </
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xml:space
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<
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xml:space
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">triangulum l m n proportionale inter b c d, f g h. </
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ſed pyramis æque alta, cuius baſis conſtat ex tribus trian-
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gulis a b d, k l n, e f h, demonſtrata
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eſt ſruſto a b d e f h æqualis. </
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xml:space
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<
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militer pyramis, cuius baſis con-
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ſtat ex triangulis b c d, l m n, f g h
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æqualis fruſto b c d f g h: </
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nuntur autem tria quadrilatera a
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b c d, _k_ l m n, e f g h è ſex triangu-
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lis iam dictis. </
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<
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ſim habens æqualem tribus qua-
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drilateris, & </
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ipſi fruſto a g eſt æqualis. </
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modo illud demõſtrabitur in aliis
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eiuſmodi fruſtis.</
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">Sit fruſtum coni, uel coni, uel coni portionis a d; </
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ſis circulus, uel ellipſis circa diametrum a b; </
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c d: </
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<
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ctionem circulum, uel ellipſim circa diametrum e f, ita ut
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inter circulos, uel ellipſes a b, c d ſit proportionalis. </
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conum, uel coni portionem, cuius baſis eſt æqualis tribus
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circulis, uel tribus ellipſibus a b, e f, c d; </
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<
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quæ fruſti a d, ipſi fruſto æqualem eſſe. </
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<
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fruſti ſuperficies quouſque coeat in unum punctum, quod
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ſit g: </
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<
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">coni, uel coni portionis a g b axis ſit g h, occurrens
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planis a b, e f, c d in punctis h _k_ l: </
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<
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ſcribatur quadratum m n o p, & </
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m n o p, quod ex ipſius diametris conſtat: </
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g n, g o, g p, ex eodem uertice intelligatur pyramis baſim
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habens dictum quadratum, uel rectangulum: </
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<
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quibus ſunt circuli, uel ellipſes e f, c d uſque ad eius </
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