Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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PROPOSITIO II.
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<
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>In omni triangulo vnum dumtaxat punctum
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eſt, in quo rectæ ab angulis ad latera incidentes
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ſecant ſeſe in eaſdem rationes. </
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>& ſegmenta, quæ
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ad angulos, ſunt reliquorum dupla. </
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>& prædictæ
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incidentes ſecant trianguli latera bifariam. </
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<
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>Sit triangulum ABC, cuius duo quælibet latera AB,
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AC, ſint bifariam ſecta in punctis D, E, & ductæ rectæ
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lineæ BE, CFD, AFG. </
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>Dico CF duplam eſſe ipſius
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FD, & AF, ipſius FG, & BF, ipſius FE. </
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>Et in nullo alio
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puncto à puncto F tres rectas ab angulis ad latera inciden
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tes ſecare ſe ſe in eaſdem rationes. </
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<
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>Et reliquum latus BC
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ſectum eſſe bifariam in puncto G. </
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<
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>Quoniam enim eſt vt BA
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ad AD, ita CA ad AE: hoc eſt, vt triangulum ABC ad
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triangulum ADC, ita triangulum idem ABC ad trian
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gulum AEB; æqualia
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erunt triangula ADC,
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AEB, & ablato trape
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zio DE communi re
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liquum triangulum BD
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F reliquo triangulo C
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EF æquale erit: ſed
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triangulum ADF eſt
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æquale triangulo BDF;
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& triangulum AFE
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triangulo EFC, pro
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pter æquales baſes, &
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communes altitudines; totum igitur triangulum AFB
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toti AFC, triangulo æquale erit: ſed vt triangulum AFB </
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