Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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Poſita enim rurſus E ad D, vt A ad B, & F minori quàm
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C vtcumque, ſit G minor quam A, minori defectu magni
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tudine eiuſdem generis cum A, quam quis voluerit, & H
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minor quàm C, & maior quàm F: ſit autem vt G ad B, ita
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H ad D. </
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>Quoniam igitur F minor eſt quàm H, minor erit
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proportio ipſius F
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H ad D,
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hoc eſt <34>G ad B: ſed cum G ſit
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minor <34>A, minor eſt propor
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tio G ad B, quàm A ad B; mul
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to ergo minor proportio F ad
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D, quàm A ad B: ſed F poni
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tur minor quàm C vtcumque;
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nulla igitur magnitudo minor
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quàm C eſt ad D, vt A ad B: ſed E eſt ad D, vt A ad B:
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non igitur eſt E minor quàm C, nec minor proportio E ad
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D, hoc eſt A ad B, quàm C ad D. eadem autem ratione
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non minor erit proportio C ad D, quàm A ad B; hoc eſt
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non maior A ad B, quàm C ad D; vt igitur A ad B, ita
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eſt C ad D. </
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ALITE R.
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<
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>Dico eſse vt A ad B, ita C ad
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D. </
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>Si enim fieri poteſt, ſit minor
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proportio A ad B quàm C ad D.
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alia igitur aliqua magnitudo G
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maior quàm A, eandem habebit
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proportionem ad B, quam C ad
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D. </
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<
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>Sit autem F maior quam C
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minori exceſsu magnitudine,
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quis voluerit, & E maior quàm
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A, & minor quàm G: vt autem
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E ad B, ita F ad D. </
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<
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>Quoniamigitur F maior eſt quàm
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C, maior erit proportio F ad D, quàm C ad D. </
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<
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F ad D, ità eſt E ad B: & vt C ad D, ita G ad B; maior </
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