Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
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ſuppoſed equal to the Section A, in magnitude; but of velocity
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equal to the Section B, and let it be G, and as the Section A is
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to the Section B, ſo let the line F be to the line D; and as the
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velocity A, is to the velocity by B, ſo let the line D be to the
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line R: Therefore the Water which paſſeth thorow A, ſhall be
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to that which paſſeth through G (in regard the Sections A and
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G are of equal bigneſs, but of unequal velocity) as the velocity
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through A, to the velocity through G; But as the velocity
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through A, is to the velocity through G, ſo is the velocity through
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A, to the velocity through B; namely, as the line D, to the
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line R: therefore the quantity of the Water which paſſe the
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through A, ſhall be to the quantity which paſſeth through G, as
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the line D is to the line R; but the quantity which paſſeth
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through G, is to that which paſſeth through B, (in regard the
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Sections G, and B, are equally ſwift) as the Section G to the Se
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ction B; that is, as the Section A, to the Section B; that is, as
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the line F, to the line D: Therefore by the equal and perturbed
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proportionality, the quantity of the Water which paſſeth through
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A, hath the ſame proportion to that which paſſeth through B,
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that the line F hath to the line R; but F to R, hath a proportion
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compounded of the proportions of F to D, and of D to R; that
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is, of the Section A to the Section B; and of the velocity through
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A, to the velocity through B. </
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>Therefore alſo the quantity of
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Water which paſſeth through the Section A, ſhall have a propor
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tion to that which paſſeth through the Section B, compounded of
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the proportions of the Section A, to the Section B; and of
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the velocity through A, to the velocity through B: And
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therefore in two Sections of Rivers, the quantity of Water which
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paſſeth by the firſt,
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&c.
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which was to be demonſtrated.</
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COROLLARIE.
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<
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>The ſame followeth, though the quantity of the Water which
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paſſeth through the Section A, be equal to the quantity of
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Water which paſſeth through the Section B, as is manifeſt by the
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ſame demonſtration.</
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