Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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<
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>Sint quatuor magnitudines A prima, B ſecunda, C ter
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tia, & D quarta: quantacumque autem magnitudine propo
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ſita, ex infinitìs quæ proponi poſſunt eiuſdem generis cum
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A, C, vel vna tantum, ſi AC ſint eiuſdem generis: vel
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vna, & altera; ſi vna vnius, altera ſit alterius generis; ſemper
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aliæ duæ magnitudines vnà maiores, quàm AC, minori
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exceſsu magnitudine propoſita; eandem habeant proportio
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nem, maior quàm A ad B, & maior quàm C ad D. </
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<
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>Dico
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eſse vt A ad B, ita C ad D. </
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<
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>Poſita enim E ad D, vt
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A ad B, & F maiori quàm C vtcumque, ſint aliæ duæ ma
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gnitudines, G maior quàm A minori exceſsu magnitudine
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eiuſdem generis cum A, quam quis voluerit, & H maior
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quàm C minori exceſsu quàm
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quo F ſuperat C, ideſt, quæ ma
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ior ſit quàm C, & minor quàm
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F: ſit autem vt G ad B, ita H
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ad D. </
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<
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>Quoniam igitur F maior
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eſt, <34>H, maior erit proportio
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ipſius F quàm H ad D, hoc eſt
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quàm G ad B. </
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<
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>Sed
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G maior
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ſit quàm A, maior eſt proportio
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G ad B, quàm A ad B, multo igitur erit maior proportio F
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ad D, quàm A ad B. </
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<
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>Sed F ponitur maior quàm C, vtcum
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que; nulla igitur magnitudo maior quàm C eſt ad D, vt
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A ad B: ſed E ad D, eſt vt A ad B; non igitur eſt E ma
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ior quàm C; nec maior proportio E ad D, hoc eſt A ad
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B, quàm C ad D. </
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<
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>Eadem autem ratione nec maior erit
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proportio C ad D quàm A ad B, hoc eſt non minor A
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ad B, quàm C ad D; eadem igitur proportio A ad B,
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quæ C ad D. </
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<
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>Sed aliæ duæ magnitudines vnà minores quàm A, C
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minori defectu quantacumque magnitudine propoſita,
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eandem habeant proportionem, minor quàm A ad B, &
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minor quàm C, ad D. </
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<
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>Dico eſse vt A ad B, ita C ad D. </
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