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

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              <s>I will declare my ſelf by another example. </s>
              <s>If we ſhould ima­
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              gine, that two cords or lines of equal thickneſs, be drawn through
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              two holes of equal bore; but ſo that the firſt paſs with quadruple
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              velocity to the ſecond: It is manifeſt, that if in a determinate
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              time, we ſhall by the firſt bore have drawn four Ells of the line,
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              in the ſame time, by the ſecond hole we ſhall have drawn but one
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              Ell of cord onely; and if by the firſt there paſſe twelve Ells, then
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              through the ſecond there ſhall paſſe onely three Ells; and in
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              ſhort the quantity of cord ſhall have the ſame proportion to the
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              cord, that the volocity hath to the velocity. </s>
              <s>And therefore we
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              deſiring to compenſate the tardity of the ſecond cord, and main­
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              taining the ſame tardity to draw through the ſecond hole as much
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              cord as through the firſt, it will be neceſſary to draw through the
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              ſecond bore four ends of cord; ſo that the thickneſs of all the
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              cords by the ſecond hole, have the ſame proportion to the thick­
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              neſs of the cord which paſſeth onely by the firſt, as the velocity
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              of the cord by the firſt hole hath reciprocally to the velocity of
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              the codrs by the ſecond hole. </s>
              <s>And thus its clear, that when
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              there is drawn through two holes equal quantity of cords in
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              equal time, but with unequal velocity, it will be neceſſary, that
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              the thickneſs of all the four cords ſhall have the ſame reciprocal
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              proportion to the thickneſs of the ſwifter cord, that the velo­
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              city of the ſwifter cord hath to the velocity of the ſlower. </s>
              <s>The
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              which is verified likewiſe in the fluid Element of Water.</s>
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              <s>And to the end that this principal fundamental be well under­
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              ſtood, I will alſo note a certain obſervation made my me in the
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              Art of Wyer-drawing, or ſpinning Gold, Silver, Braſs, and Iron,
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              and it is this; That ſuch Artificers deſiring more and more to
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              diſgroſſe and ſubtillize the ſaid Metals, having would about a
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                <emph type="italics"/>
              R
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              ocket or Barrel, the thread of the Metal, they place the Roc­
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              ket in a frame upon a ſtedfaſt Axis, in ſuch ſort that the Rocket
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              may turn about in it ſelf; then making one end of the thread to
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              paſſe by force through a Plate of Steel pierced with divers holes,
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              greater and leſſer, as need requireth, faſtning the ſame end of the
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              thread to another Rocket, they wind up the thread, which paſ­
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              ſing through a bore leſs than the thickneſſe of the thread, is of
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              force conſtrained to diſgroſſe and ſubtillize. </s>
              <s>Now that which is
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              intenſly to be obſerved in this buſineſs, is this, That the parts of
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              the thread before the hole, are of ſuch a thickneſſe, but the parts
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              of the ſame thread after it is paſſed the hole, are of a leſſer thick­
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              neſſe: and yet nevertheleſſe the maſſe and weight of the thread
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              which is drawn forth, is ever equal to the maſſe and weight of the
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              thread which is winded up. </s>
              <s>But if we ſhould well conſider the mat­
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              ter, we ſhould finde, that the thicker the thread before the hole is,
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              than the thread paſſed the hole, the greater reciprocally is the </s>
            </p>
          </chap>
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      </text>
    </archimedes>
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