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

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            <pb xlink:href="068/01/065.jpg" pagenum="51"/>
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              <s>PROPOSITION II. THEOREM I.</s>
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              <s>
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              If a River moving with ſuch a certain velocitie
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              through its Regulator, ſhall have a given quick
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              height, and afterwards by new water ſhall increaſe
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              to be double, it ſhall alſo increaſe double in ve­
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              locitie.
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              </s>
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              <s>Let the quick height of a River in the Regulator A B C D,
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              be the perpendicular F B, and afterwards, by new water that
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              is added to the River, let the water be ſuppoſed to be raiſ­
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              ed to G, ſo that G B may be double to E B. </s>
              <s>I ſay, that all the
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              water G C ſhall be double in velocity to
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                <figure id="id.068.01.065.1.jpg" xlink:href="068/01/065/1.jpg" number="13"/>
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              that of E C: For the water G F, having
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              for its bed the bottom E F, equally in­
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              clined as the bed B C, and its quick
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              height G E being equal to the quick
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              height E C, and having the ſame breadth
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              B C, it ſhall have of it ſelf a velocity e­
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              qual to the velocity of the firſt water
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              F C: but becauſe, beſides its own moti­
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              on, which is imparted to it by the motion of the water E C, it
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              hath alſo over and above its own motion, the motion of E C. </s>
              <s>And
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              becauſe the two waters G C, and E C, are alike in velocity, by
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              the third Suppoſition; therefore the whole water G C ſhall be
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              double in velocity to the water E C; which was that which we
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              were to demonſtrate.</s>
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              <s>
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              This demonſtration is not here inſerted, as perfect, the Authour ha­
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              ving by ſeveral letters to his friends confeſſed himſelf unſatisfi­
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              ed therewith; and that he intended not to publiſh the
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              Theorem
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                <emph type="italics"/>
              without a more ſolid demonſtration, which he was in hope to light
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              upon. </s>
              <s>But being overtaken by Death, he could not give the
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              finiſhing touch either to this, or to the rest of the ſecond Book. </s>
              <s>In
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              conſideration of which, it ſeemed good to the Publiſher of the
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              ſame, rather to omit it, than to do any thing contrary to the mind of
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              the Authour. </s>
              <s>And this he hints, by way of advertiſement, to
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              thoſe that have Manuſcript Copies of this Book, with the ſaid de­
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              monſtration. </s>
              <s>For this time let the Reader content himſelf with
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              the knowledge of ſo ingenious and profitable a Concluſion; of the
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              truth of which he may, with ſmall expence and much pleaſure, be
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              aſſured by means of the experiment to be made in the ſame man­
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              ner, with that which is laid down in the ſecond Corollary of
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              </s>
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          </chap>
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