Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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rallela NO, abſcindantur EL, FM, ipſi GK æquales, &
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iungantur ANE, EOD. </
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<
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>Quoniam igitur NO ipſi AD,
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parallela ſecat omnes ipſis AD, EC, interceptas in eaſ
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dem rationes, & eſt EH, pars tertia ipſius EF, erit & EN
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ipſius EA, & EO, ipſius ED, pars tertia. </
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<
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>Eſt autem NO,
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parallela baſibus BE, EC, duorum triangulorum ABE,
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ECD; in ipſa igitur NO, erunt centra grauitatis duo
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rum triangulorum ABE, ECD: ergo & compoſiti ex
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vtroque in linea NO, erit centrum grauitatis. </
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igitur K, centrum grauitatis trianguli AED, eſt in EF, &
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totius trapezij ABCD, centrum grauitatis in eadem linea
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EF; erit & reliquæ partis, duorum ſcilicet triangulorum
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ABE, ECD, ſimul in linea EF, centrum grauitatis: ſed &
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in linea NO; in puncto igitur H. </
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AED, ABE, ECD, ſunt inter eaſdem parallelas, erit
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vt AD, ad BC, ita triangulum AED, ad duo triangu
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la ABE, ECD, ſimul: ſed vt AD, ad BC, ita eſt HG,
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ad GK; vt igitur triangulum AED, ad duo triangula
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ABE, ECD, ſimul, ita erit HG, ad GK. ſed K, eſt
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centrum grauitatis trianguli AED: & H, duorum trian
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gulorum ABE, ECD, ſimul; totius igitur trapezij AB
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CD, centrum grauitatis erit G. </
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<
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eſt æqualis GK, æqualium EH, HK; erit reliqua LH,
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æqualis reliquæ GH; tota igitur EG; erit bis GH, vna
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cum GK: eadem ratione quoniam FM, eſt æqualis GK,
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& MK, æqualis GH, erit FG, bis GK, vna cum GH:
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vt igitur HG, bis vna cum GK, ad GK, bis vna cum
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GH, ita erit EG, ad GF. </
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<
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GK, ad GK bis vna cum GH, ita eſt AD, bis vna cum
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BC, ad BC, bis vna cum AB, propterea quod eſt vt
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AD, ad BC, ita HG, ad GK; vt igitur eſt AD, bis vna
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cum BC, ad BC, bis vna cum AD, ita erit EG, ad GF.
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