Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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MG, & angulus ABM, angulo AGM, ſed totus ABC,
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toti AGF, eſt æqualis; reliquus igitur angulus CBG,
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reliquo BGF, æqualis erit: ſed circa hos æquales an
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gulos recta BM, oſtenſa eſt æqualis rectæ MG, & CB,
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eſt æqualis GF; baſis igitur CM, baſi GF, & angulus
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CMB, angulo FMG, æqualis erit; ſed totus BMN,
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æqualis eſt toti GMN; quia vterque rectus; reliquus
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igitur CMN, reliquo NMF, æqualis erit, quos circa
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recta CM, eſt æqualis MF, & MN, communis; baſis
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igitur CN, baſi NF, & anguli, qui ad N, æquales erunt,
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atque ideo recti: ſed & qui ad M, ſunt recti, & BM, eſt
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æqualis GM; parallelæ igitur ſunt BG, CF, & trape
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zij CBGF, centrum grauitatis eſt in linea MN: ſed &
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trianguli ABG, centrum grauitatis eſt in linea AM; to
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tius igitur figuræ ABCFG, centrum grauitatis eſt in li
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nea AN; hoc eſt in linea AH. </
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>Rurſus quoniam omnis
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quadrilateri quatuor anguli ſunt æquales quatuor rectis:
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& tres anguli ABM, BMN, MNC, ſunt æquales tri
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bus angulis FGM, GMN, MNF, reliquus angulus
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BCF, reliquo CFG, æqualis erit: ſed totus angulus
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BCD, eſt æqualis toti angulo GFE; reliquus ergo
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DCF, reliquo CFE, æqualis erit: ſed linea CN, eſt
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æqualis NF, & anguli, qui ad N, ſunt recti; ſimiliter
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ergo vt antea, centrum grauitatis trapezij CDEF, erit
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in linea AH: ſed & totius figuræ ABCFG, eſt in li
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nea AH; totius igitur polygoni ABCDEFG, in li
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nea AH, eſt centrum grauitatis, quod idem ſimiliter in
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linea CK, eſse oftenderemus; in communi igitur ſectione
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puncto L, eſt centrum grauitatis polygoni ABCDEFG.
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<
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>Similiter quotcumque plurium laterum numero impa
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rium eſset polygonum æquilaterum, & æquiangulum,
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ſemper deueniendo ab vno triangulo ad quotcumque eius
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trapezia; propoſitum concluderemus. </
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