Castelli, Benedetto
,
Of the mensuration of running waters
,
1661
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the fourth
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Theorem
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of this, with its Table, and the uſe there
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of annexed.
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COROLLARIE
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>Hence it followeth, that when a River increaſeth in quick
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height by the addition of new water, it alſo increaſeth in ve
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locity; ſo that the velocity hath the ſame proportion to the velo
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city that the quick height hath to the quick height; as may be
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demonſtrated in the ſame manner.</
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>PROPOS. III. PROBLEME II.</
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Achanel of Water being given whoſe breadth exceeds not
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twenty Palms, or thereabouts, and whoſe quick beight
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is leſs than five Palms, to meaſure the quantity of the
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Water that runneth thorow the Chanel in a time
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given.
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>Place in the Chanel a Regulator, and obſerve the quick
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height in the ſaid Regulator; then let the water be turned
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away from the Chanel by a Chanellet of three or four Palms
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in breadth, or thereabouts: And that being done, meaſure the
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quantity of the water which paſſeth thorow the ſaid Chanellet,
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as hath been taught in the ſecond Propoſition; and at the ſame
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time obſerve exactly how much the quick height ſhall be abated
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in the greater Chanel, by means of the diverſion of the Chancl
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let; and all theſe particulars being performed, multiply the quick
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height of the greater Chanel into it ſelf, and likewiſe multiply
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into it ſelf the leſſer height of the ſaid bigger Chanel, and the
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leſſer ſquare being taken, from the greater, the remainder ſhall
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have the ſame proportion to the whole greater ſquare, as the wa
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ter of the Chanellet diverted, hath to the water of the bigger
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Chanel: And becauſe the water of the Chanellet is known by
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the Method laid down in the firſt Theorem, and the terms of the
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Theorem being alſo known, the quantity of the water which run
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neth thorow the bigger Chanel, ſhall be alſo known by the Gol
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den
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R
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ule, which was that that was deſired to be known. </
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will explain the whole buſineſs by an example.</
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>Let a Chanel be, for example, 15 Palms broad, its quick height
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before its diverſion by the Chanellet ſhall be ſuppoſed to be 24
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inches; but after the diverſion, let the quick height of the Chanel
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be onely 22 inches. </
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<
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>Therefore the greater height to the leſſer,
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is as the number 11. to 12. But the ſquare of 11. is 121, and the
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ſquare of 12. is 144, the difference between the ſaid leſſer </
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