Castelli, Benedetto
,
Of the mensuration of running waters
,
1661
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Book^{*} of the meaſure of Running Watets;) but yet doth not
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run thorowout with the ſame velocity: Hence it is, that the vul
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gar meaſures of the ſaid River, in divers parts of its Chanel, are
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alwaies divers; inſomuch, that if a River paſſing through its cha
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nel had ſuch velocity, that it ran 100 Braces in the 1/60 of an hour
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and afterwards the ſaid River ſhould be reduced to ſo much tardi,
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ty of motion, as that in the ſame time it ſhould not run more than
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one Brace, it would be neceſſary that that ſame River ſhould be
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come 100. times bigger in that place where it was retarded; I
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mean, 100. times bigger than it was in the place where it was
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ſwifter. </
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>And let it be kept well in mind, that this point rightly
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underſtood, will clear the underſtanding to diſcover very many
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accidents worthy to be known. </
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>But for this time let it ſuffice,
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that we have onely declared that which makes for our purpoſe,
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referring apprehenſive and ſtudious Wits to the peruſal of my
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aforenamed Treatiſe; for therein he ſhall finde profit and delight
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both together.</
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* He here intends
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the Demonſtrati
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ons following, at
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the end of the firſt
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Book</
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>Now applying all to our principal intent, I ſay, That by what
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hath been declared it is manifeſt, that if the
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Brent
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were 40. Bra
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ces broad, and 2 1/2 high, in ſome one part of its Chanel, that after
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wards the ſame Water of the
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Brent
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falling into the Lake, andpaſ
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ſing thorow the ſame to the Sea, it ſhould loſe ſo much of its ve
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locity, that it ſhould run but one Brace, in the time wherein
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whilſt it was in its Chanel at the place aforeſaid, it ran 100. Bra
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ces. </
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>It would be abſolutely neceſſary, that increaſing in mea
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ſure, it ſhould become an hundred times ^{*} thicker; and therefore
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if we ſhould ſuppoſe that the Lake were 20000. Braces, the
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Brent
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that already hath been ſuppoſed in its Chanel 100. Braces,
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being brought into the Lake, ſhould be 100. times 100. Brates;
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that is, ſhall be 10000. Braces in thickneſs, and conſequently ſhall
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be in height half a Brace; that is, 100/200 of a Brace, and not 1/2. of a
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Brace, as was concluded in the Argument.</
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* Deeper.</
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>Now one may ſee into what a groſs errour of 99. in 100. one
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may fall through the not well underſtanding the true quantity
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of Running Water, which being well underſtood, doth open a
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direct way to our judging aright in this moſt conſiderable affair.</
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>And therefore admitting that wich hath been demonſtrated,
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I fay, that I would (if it did concern me) greatly encline to con
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ſult upon the returning of the
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Brent
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again into the Lake: For it
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being moſt evident, that the
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Brent
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in the Chanel of its mouth, is
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much ſwifter than the
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Brent
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being brought into the Lake, it will
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certainly follow thereupon, that the thickneſs of the Water of
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Brent
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in the Lake, ſhall be ſo much greater than that of
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Brent
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in
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Brent,
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by how much the
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Bront
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in
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Brent
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is ſwifter than thh
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Brent
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in the Lake.</
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