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

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              for that amongſt ſo many tryals as have been made, that alſo
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              was light upon, on which the improvement and remedy to the
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              diſorder did depend. </s>
              <s>And to us my fore-named Treatiſe ſhall
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              ſerve for a Rule, which being well underſtood, ſhall make us to
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              know wherein conſiſteth, and whereon dependeth this miſcarri­
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              age, and conſequently it will be eaſie to apply thereunto a ſeaſo­
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              nable remedy.</s>
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              <s>And firſt I ſay, That there is no doubt but that the waters
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              continue ſo high on thoſe Plains becauſe they are ſo high in the
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              principal River, which ought to receive them, and carry them
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              into the Sea. </s>
              <s>Now the Cauſes of the height of the River, may
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              in my judgement be reduced to one alone; which is that by me
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              ſo often mentioned for the moſt Potent one, and declared in my
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              afore-named Tractate; to wit, The tardity of the motion of the
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              waters, which doth alwayes infallibly, and preciſely cauſe the
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              ſelf ſame Running Water to change the meaſure of its thickneſs
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              at ſuch a rate, that the more it encreaſeth in velocity, the more
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              it decreaſeth in meaſure; and the more it decreaſeth in velocity,
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              the more it encreaſeth in meaſure: As for example; If a River
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              run in ſuch a place with the velocity of moving a mile in the
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              ſpace of an hour, and afterwards the ſame River in another place
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              doth encreaſe in velocity, ſo as to make three miles an hour;
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              that ſame River ſhall diminiſh in thickneſs two thirds: And on
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              the contrary, If it ſhall diminiſh in velocity ſo, as that it runneth
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              but half a mile in the ſame time, it ſhall encreaſe the double in
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              thickneſs and meaſure. </s>
              <s>And in a word, look what proportion
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              the velocity in the firſt place, hath to the velocity in the ſecond,
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              and ſuch hath reciprocally the meaſure of the thickneſs in the
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              ſecond place, to the meaſure in the firſt; as I have clearly demon­
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              ſtrated in my Treatiſe: Which I repeat ſo frequently, that I
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              fear the Profeſſors of Polite Learning will charge me with Tua­
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              tologie, and vain Repetition. </s>
              <s>But I am ſo deſirous in this moſt
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              important point to be well underſtood, becauſe it will then be
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              eaſie to comprehend all the reſt; and without this it is impoſſible
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              (I will not ſay difficult, but abſolutely impoſſible) to underſtand,
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              or ever to effect any thing to purpoſe. </s>
              <s>And the better to ex­
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              plain the example, let it be ſuppoſed,
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              That the water of a River A D,
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              runneth high at the level of A F,
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              with ſuch a certain velocity; and let
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              it, by the ſame water, be velocitated
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              three times more; I ſay, that it will
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              abate 1/3, and ſhall ſtand at the level
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              in B E; and if it ſhall more veloci­
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              tate, it will abate the more at the Sea; But if it ſhould retard </s>
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