Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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tiones, ita vt ſegmenta, quæ ad angulos, eo
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rum, quæ ad oppoſita triangula, ſint tripla; ex quo
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puncto tota pyramis diuiditur in quatuor pyrami
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des æquales. </
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<
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>Et in nullo alio puncto quatuor re
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ctæ lineæ ductæ ab angulis ad triangula oppoſita
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pyramidis ſecant ſeſe in eaſdem rationes. </
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>Vocetur
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autem punctum hoc centrum dictæ pyramidis. </
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>Sit pyramis ABCD, cuius vertex A, baſis autem
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triangulum BCD, axes AE, BM, CL, DN, vnde qua
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tuor triangulorum, quæ ſunt circa pyramidem ABCD,
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centra erunt grauitatis E, L, M, N. </
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>Dico quatuor li
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neas AE, BM, CL, DN, ſecare ſe ſe in vno puncto in
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eaſdem rationes, quas prædixi, & quæ ſequuntur. </
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<
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>Nam ex
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puncto A, ducatur recta ALH, quæ ob trianguli ABD,
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centrum L, ſecabit latus BD, bifariam in puncto H; iun
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cta igitur CE, & producta conueniet cum ALH, vt in
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puncto H. eadem ratione iunctæ AM, BE, & productæ
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conuenient in medio lateris CD, conueniant in puncto K,
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necnon AN, DE, in medio ipſius BC, vt in puncto G.
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>Quoniam igitur ob triangulorum centra, eſt vt CE ad EH,
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ita AL ad LH, dupla enim eſt vtraque vtriuſque, ſeca
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bunt ſeſe rectæ AE, CL, inter eaſdem parallelas; quare
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vt AF ad FE, ita erit CF ad FL, circum æquales angu
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los ad verticem: triangula igitur AFL, CFE; & reci
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proca, & æqualia inter ſe erunt. </
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>Cum igitur ſit vt AL ad
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LH, ita CE ad EH, hoc eſt vt triangulum AFL ad
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triangulum FLH, (ſi ducatur FH) ita triangulum CFE,
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ad triangulum FEH, erunt inter ſe æqualia triangula
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FEH, FLH. </
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<
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>Quare vt triangulum AFH, ad triangu
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lum FLH, hoc eſt vt AH ad HL, ita erit triangulum
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AFH ad triangulum FEH, hoc eſt AF ad FE: ſed re
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cta AH, eſt tripla ipſius LH; igitur & AF, erit ipſius FE, </
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