Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
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to adjuſt the Ciſtern ſo, that the exceſs above the ordinary wa
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ter, diſcharge into the publick Fountains, that ſo the particular
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participants may have alwayes the ſame abundance of
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water.</
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>APPENDIX XI.</
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>Much more difficult is the diviſion of the waters which
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ſerve to water the fields, it not being poſſible to obſerve
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ſo commodiouſly, what quantity of water the whole
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Ditch ſends forth in one determinate time, as may be done in
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Fountains: Yet nevertheleſs, if the ſecond propoſition by us a
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little below demonſtrated, be well underſtood, there may be
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thence taken a very ſafe and juſt way to diſtribute ſuch waters.
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>The Propoſition therefore by us demonſtrated is this: If there
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be two Sections, (namely two mouths of Rivers) the quantity of
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the water which paſſeth by the firſt, hath a proportion to that
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which paſſeth by the ſecond, compounded of the proportions of
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the firſt Section to the ſecond, and of the velocity through
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the firſt, to the velocity through the ſecond: As I will declare
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for example by help of practice, that I may be underſtood by
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all, in a matter ſo important. </
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>Let the two mouths of the
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Rivers be A, and B, and let
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the mouth A be in meaſure
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and content thirty two feet,
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and the mouth B, eight feet.
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>Here you muſt take notice,
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that it is not alwayes true, that
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the Water which paſſeth by A,
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hath the ſame proportion to that which paſſeth by B, that the
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mouth A hath to the mouth B; but onely when the velocityes
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by each of thoſe paſſages are equal: But if the velocityes ſhall
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be unequal, it may be that the ſaid mouths may emit equal
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quantity of Water in equal times, though their meaſure be un
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equal; and it may be alſo, that the bigger doth diſcharge a great
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er quantity of Water: And laſtly, it may be, that the leſs mouth
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diſchargeth more Water than the greater; and all this is mani
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feſt by the things noted in the beginning of this diſcourſe, and
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by the ſaid ſecond Propoſition. </
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<
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>Now to examine the propor
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tion of the Water that paſſeth by one Ditch, to that which paſ
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ſeth by another, that this being known, the ſame Waters and
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mouths of Ditches may be then adjuſted; we are to keep ac
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count not onely of the greatneſs of the mouths or paſſages of the
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Water, but of the velocity alſo; which we will do, by firſt find
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ing two numbers that have the ſame proportion between them</
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