Castelli, Benedetto
,
Of the mensuration of running waters
,
1661
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>PROPOSITION I.</
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The Sections of the ſame River diſcharge equal quan
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tities of Water in equal times, although the Secti
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ons themſelves he unequal.
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>Let the two Sections be A and B, in the River C, running
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from A, towards B; I ſay, that they diſcharge equal quan
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tity of Water in equal times; for if greater quantity of Wa
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ter ſhould paſs through A, than paſſeth through B, it would
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follow that the Water in the intermediate ſpace of the River C,
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would increaſe continually, which is manifeſtly falſe, but if
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more Water ſhould iſſue through the Section B, than entreth at
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the Section A, the Water in the intermediate ſpace C, would
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grow continually leſs, and alwaies ebb, which is likewiſe falſe;
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therefore the quantity of Water that paſſeth through the Secti
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on B, is equal to the quantity of Water which paſſeth through
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the Section A, and therefore the Sections of the ſame River diſ
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charge,
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&c.
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Which w s to be demonſtrated.</
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<
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>PROPOSITION II.</
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In two Sections of Rivers, the quantity of the Water
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which paſſeth by one Section, is to that which paſ
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ſeth by the ſecond, in a Proportion compounded of
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the proportions of the firſt Section to the ſecond, and
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of the velocitie through the first, to the velocitie
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of the ſecond.
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<
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>I Et A, and B be two Sections of a River; I ſay, that the
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quantity of Water which paſſeth through A, is to that which
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paſſeth through B, in a proportion compounded of the pro
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portions of the firſt Section A, to the Section B; and of the velo
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city through A, to the velocity through B: Let a Section be </
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