Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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PROPOSITIO III.
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<
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>In ſimilibus triangulis rectæ lineæ, quæ inter
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centra, & alia in ijs ſimiliter poſita puncta in
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terijciuntur, proportionales ſunt in proportione
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laterum homologorum. </
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<
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>Sint triangula ſimilia, & ſimiliter poſita ABC, DEF,
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quorum ſint centra O, P, in ijs autem triangulis ſint pun
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cta ſimiliter poſita K, L, quæ cadant primum in rectis
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BG, EH, quæ ab angulis æqualibus B, E, baſes bifa
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riam diuidunt. </
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<
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>Dico eſſe OK ad PL, vt eſt latus AB,
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ad latus DE. iunctis enim AK, KC, DL, LF, quo
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niam angulus KAC, æqualis eſt angulo LDF, & angu
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lus KCA, angulo LFD, ob ſimiliter poſita puncta K,
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L, triangulum AKC, triangulo LDF ſimile erit, & vt
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KA ad AC, ita LD ad DF: ſed vt CA ad AG, ita
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eſt FD ad DH, expræcedenti; vt igitur KA, ad AG
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ita erit LD, ad DH, circa æquales angulos: ſimilia igi
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tur ſunt triangula AGK, DHL, & angulus AGK, </
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