Castelli, Benedetto, Of the mensuration of running waters, 1661

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              <s>
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              velocity of the parts of the thread paſſed the hole, than the volo­
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              city of the parts before the hole: Inſomuch that if
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              verbi gratia
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              the thickneſſe of the thread before the hole, were double to the
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              thickneſſe after the hole, in ſuch caſe the velocity of the parts of
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              the thread paſſed the hole, ſhould be double to the velocity of the
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              parts of the thread before the hole; and thus the thickneſſe
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              compenſates the velocity, and the velocity compenſates the thick­
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              neſſe. </s>
              <s>So that the ſame occurreth in the ſolid Metals of Gold,
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              Silver, Braſs, Iron, &c. </s>
              <s>that eveneth alſo in the fluid Element of
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              Water, and other liquids, namely, That the velocity beareth the
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              ſame proportion to the velocity, that the thickneſſe of the Me­
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              tal, or Water, hath to the thickneſſe.</s>
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              <s>And therefore granting this diſcourſe, we may ſay, that as of­
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              ten as two Taps with different velocity diſcharge equal quanti­
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              ties of Water in equal times, it will be neceſſary that the Tap
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              leſſe ſwift be ſo much greater, and larger, than the Tap more
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              ſwift, by how much the ſwifter ſuperates in velocity the ſlower;
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              and to pronounce the Propoſition in more proper terms, we ſay;
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              That if two Taps of unequal velocity, diſcharge in equal times
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              equal quantities of Water, the greatneſſe of the firſt ſhall be to
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              the greatneſſe of the ſecond, in reciprocal proportion, as the ve­
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              locity of the ſecond to the velocity of the firſt. </s>
              <s>As for example,
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              if the firſt Tap ſhall be ten times ſwifter than the ſecond Tap, it
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              will be neceſſary, that the ſecond be ten times bigger and larger
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              than the firſt; and in ſuch caſe the Taps ſhall diſcharge equall
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              quantities of water in equal times; and this is the principal and
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              moſt important point, which ought to be kept alwayes in minde,
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              for that on it well underſtood depend many things profitable,
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              and worthy of our knowledge.</s>
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              <s>Now applying all that hath been ſaid neerer to our purpoſe, I
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              conſider, that it being moſt true, that in divers parts of the ſame
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              River or Current of running water, there doth always paſſe equal
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              quantity of Water in equal time (which thing is alſo demon­
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              ſtrated in out firſt Propoſition) and it being alſo true, that in di­
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              vers parts the ſame River may have various and different veloci­
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              ty; it follows of neceſſary conſequence, that where the River
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              hath leſſe velocity, it ſhall be of greater meaſure, and in thoſe
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              parts, in which it hath greater velocity, it ſhall be of leſſe mea­
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              ſure; and in ſum, the velocity of ſeveral parts of the ſaid River,
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              ſhall have eternally reciprocall and like proportion with
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              their meaſures. </s>
              <s>This principle and fundamental well eſtabliſh­
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              ed, that the ſame Current of Water changeth meaſure, accor­
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              ding to its varying of velocity; that is, leſſening the meaſure,
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              when the velocity encreaſeth, and encreaſing the meaſure, when
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              the velocity decreaſeth; I paſſe to the conſideration of many </s>
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