Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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42
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PROPOSITIO XX.
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<
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>Omnis trapezij habentis duo latera parallela
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centrum grauitatis eſt in illa recta, quæ prædi
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ctorum bipartitorum laterum ſectiones iungit.
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>atque in eo puncto, in quo tertia pars eius media
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ſic diuiditur, vt ſegmentum propinquius mino
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ri parallelarum ad reliquum eam proportionem
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habeat, quam maior parallelarum ad minorem.
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<
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>Talis autem rectæ lineæ ſic diuiſæ, ſegmentum
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minorem parallelarum attingens eſt ad reliquum,
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vt dupla maioris parallelarum vna cum minori,
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ad duplam minoris vna cum maiori. </
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<
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>Sit trapezium ABCD, cuius duæ AD, BC, ſint pa
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rallelæ: ſitque AD, maior. </
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<
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>Sectiſque AD, BC, bifa
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riam in punctis F, E,
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iunctaque EF, & ſe
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cta in tres partes æ
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quales in punctis K,
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H, fiat vt AD, ad
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BC, ita HG, ad GK.
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<
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>Dico G, eſse centrum
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grauitatis trapezij A
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BCD: & vt eſt du
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pla ipſius AD, vna
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cum BC, ad duplam
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ipſius BC, vna cum
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AD, ita eſse EG, ad
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GF. </
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<
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>Ducta enim per punctum H, ipſis AD, BC, pa-</
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