Castelli, Benedetto
,
Of the mensuration of running waters
,
1661
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him be never ſo great a Wit, can never promiſe to frame a con
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ceit of the quantity of the Body of Water, without the third
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Dimenſion of length: and hereupon I return to affirm, that the
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vulgar Rule of meaſuring Running water is vain and erroneous.
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<
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>This point being agreed on, I come to the ſecond, which is, Whe
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ther the third Dimenſion of length may be meaſured. </
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<
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>And I ſay,
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that if one would know the whole length of the water of a
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Fountain or River, thereby to come to know the quantity of all
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the Water, it would prove an impoſſible enterprize, nay the
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knowing of it would not be uſeful. </
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>But if one would know how
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much water a Fountain, or a River carrieth in a determinate time
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of an hour, of a day, or of a moneth, &c. </
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<
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>I ſay, that it is a very
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poſſible and profitable enquiry, by reaſon of the innumerable
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benefits that may be derived thence, it much importing to know
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how much Water a Chanel carrieth in a time given; and I have
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demonſtrated the ſame above in the beginning of this Book; and
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of this we ſtand in need in the buſineſſe of the Lake, that ſo we
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may be able to determine how much ſhall be the height of the
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Brent,
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when it is ſpread all over the Lake: For the three dimen
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ſions of a Body being given, the Body is known; and the quan
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tity of a Body being given, if you have but two dimenſions, the
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third ſhall be known. </
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>And thus diving farther and farther into
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this Conſideration, I found that the Velocity of the courſe of the
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water may be an hundred times greater or leſſer in one part of
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its Chanel than in another. </
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>And therefore although there ſhould
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be two mouths of Waters equal in bigneſſe; yet nevertheleſs it
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might come to paſſe, that one might diſcharge an hundred or a
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thouſand times more water than another: and this would be, if
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the water in one of the mouths ſhould run with an hundred or a
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thouſand times greater velocity, than the other; for that it
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would be the ſame as to ſay, that the ſwifter was an hundred or
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a thouſand times longer, than the ſlower: and in this manner I
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diſcovered that to keep account of the velocity, was the keeping
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account of the Length.</
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>And therefore it is manifeſt, that when two Mouths diſcharge
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the ſame quantity of Wa r in an equal velocity, it is neceſſary
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that the leſs ſwift Mouth be ſo much bigger than the more ſwift;
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as the more ſwift exceedeth in velocity the leſs ſwift; as for
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example.</
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>In caſe two Rivers ſhould carry equal quantity of water in
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equal times, but that one of them ſhould be four times more
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ſwift than the other, the more ſlow ſhould of neceſſity be four
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times more large. </
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<
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>And becauſe the ſame River in any part
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thereof alwaies diſchargeth the ſame quantity of Water in equal
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times (as is demonſtrated in the firſt Propoſition of the firſt </
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