Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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PROPOSITIO XIV.
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<
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>Omnis parallelogtammi centrum grauitatis
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diametrum bifariam diuidit. </
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>Sit parallelogrammum ABCD, cuius duo latera AB,
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BC, ſint primum in æqualia: &
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omne parallelogram
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mum habet ſaltem duos angulos oppoſitos non minores
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recto, eſto vterque angulorum B, D, non minor recto, ſit
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que ducta diameter AC, ſectaque in puncto G, bifariam.
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>Dico G, eſse centrum grauitatis parallelogrammi ABCD.
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>Trianguli enim ABC, ſit centrum grauitatis H; iuncta
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que HG, & producta, ponatur GK, æqualis GH, & re
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ctæ à punctis K, H, ad angulos ducantur. </
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tur AG, eſt æqualis GC, &
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GH, ipſi GK, & angulus
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AGK, æqualis angulo CGH,
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erit baſis AK, æqualis baſi
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CH, & angulus GAK, æqua
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lis angulo GCK: ſed totus
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angulus DAK, æqualis eſt to
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ti angulo BCA; reliquus igi
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tur DAK, reliquo BCH,
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æqualis erit, circa quos angu
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los latus BC eſt æquale lateri
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AD, & CH, ipſi AK; angu
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lus igitur CBH, æqualis erit
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angulo ADK. </
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<
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>Similiter oſtenderemus angulum CAH,
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angulo ACK, & angulum BAH, angulo DCK, & an
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gulum ABH, angulo CDK, æquales eſse: ſed latera
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triangulorum, cum quibus rectæ ductæ à punctis K, H, ad
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angulos triangulorum ſimilium ABC, CDA, ſunt ho-</
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