Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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<
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>Sed eſto polygonum æquilaterum, & æquiangulum,
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ABCDEF, cuius laterum numerus ſit par, & centrum
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eſto G. </
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<
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>Dico idem G, eſse centrum grauitatis polygoni
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ABCDEF. </
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<
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>Iungantur enim angulorum oppoſitorum
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puncta rectis lineis AD, BE, CF. </
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<
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>Ex quarto igitur
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Elem. ſecabunt ſeſe hæ rectæ omnes bifariam in vno pun
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cto, quod talis figuræ centrum definiuimus: ſed G poni
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tur centrum; in puncto igitur G. </
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<
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>Quoniam igitur duo
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rum triangulorum CBG, GFE, anguli ad verticem
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BGC, FGE, ſunt æquales; & vterlibet angulorum CBG,
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GCB, æqualis eſt vtrilibet ipſorum EFG, GEF; ex
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quarto Elem. & circa æquales angulos latera proportio
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nalia horum triangu
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lorum ſunt æqualia;
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ſimilia, & æqualia
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erunt triangula BC
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G, GFE: poſitis
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igitur centris graui
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tatis K, H, duorum
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triangulorum EFG,
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GBC, iunctifque
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KG, GH, erit v
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terlibet angulorum
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BGH, HGC, æ
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qualis vtrilibet an
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gulorum CGK, KGE, propter ſimilitudinem poſitio
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nis centrorum K, H, in iſoſcelijs triangulis CBG,
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GFE: (nam GH, ſi produceretur latus BC, bifariam
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ſecaret: ſimiliter GK, latus EF) ſed CG, eſt in directum
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poſita ipſi GF; igitur & GH ipſi GK: & ſunt æquales,
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vtpote lateribus triangulorum BCG, GFE, æqualibus
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homologæ; cum igitur eorundem triangulorum centra
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grauitatis ſint K, H; centrum grauitatis duorum triangu
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lorum CBG, GFE, ſimul, erit punctum G. </
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<
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>Eadem </
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