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