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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              </s>
              <s>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. </s>
              <s>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. </s>
              <s>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. </s>
              <s>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. </s>
              <s>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. </s>
              <s>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.</s>
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              <s>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.</s>
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              <s>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. </s>
              <s>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 </s>
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