Castelli, Benedetto
,
Of the mensuration of running waters
,
1661
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not give me a certain and ſtable meaſure and quantity of Water,
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began deſervedly to be ſuſpected by me, as difficult and defective,
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being alwayes various, and the meaſure, on the contrary, being
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to be alwayes determinate, and the ſame; it is therefore written,
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that
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Pondus & Pondus, Menſura & Menſura, utrumque abomi
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nabile eſt apud Deum,
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Exod. </
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>I conſidered that in the Terri
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tory of
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Breſcia,
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my native Countrey, and in other places, where
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Waters are divided to overflow the Grounds, by the like way of
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meaſuring them, there were committed grievous and moſt impor
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tant errours, to the great prejudice of the Publique and of Pri
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vate perſons, neither they that ſell, nor they that buy under
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ſtanding the true quantity of that which is ſold and bought: In
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regard that the ſame ſquare meaſure, as is accuſtomed in thoſe
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parts, aſſigned one particular perſon, carried to ſometimes above
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twice or thrice as much water, as did the ſame ſquare meaſure aſ
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ſigned to another. </
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>Which thing proveth to be the ſame incon
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venience, as if the meaſure wherewith Wine and Oil is bought
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and ſold, ſhould hold twice or thrice as much Wine or Oil at one
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time as at another. </
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>Now this Conſideration invited my minde
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and curioſity to the finding out of the true meaſure of Running
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Waters. </
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>And in the end, by occaſion of a moſt important bu
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ſineſſe that I was imployed in ſome years ſince, with great in
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tenſeneſſe of minde, and with the ſure direction of
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Geometry,
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I
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have diſcovered the miſtake, which was, that we being upon the
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buſineſſe of taking the meaſure of the Waters that move, do make
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uſe of two dimenſions onely, namely, breadth and depth, keep
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ing no account of the length. </
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>And yet the Water being, though
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running, a Body, it is neceſſary in forming a conceit of its quan
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tity, in relation to another, to keep account of all the three Di
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menſions, that is of length, breadth, and depth.</
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>Here an objection hath been put to me, in behalf of the ordi
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nary way of meaſuring Running Waters, in oppoſition to what
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I have above conſidered and propoſed: and I was told, Its true,
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that in meaſuring a Body that ſtands ſtill, one ought to take all
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the three Dimenſions; but in meaſuring a Body that continually
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moveth, as the Water, the caſe is not the ſame: For the length
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is not to be had, the length of the water that moveth being infi
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nite, as never finiſhing its running; and conſequently is incom
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prehenſible by humane underſtanding, and therefore with reaſon,
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nay upon neceſſity it cometh to be omitted.</
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>In anſwer to this, I ſay, that in the aboveſaid Diſcourſe, two
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things are to be conſidered diſtinctly; Firſt, whether it be poſſible
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to frame any conceit of the quantity of the Body of the Water
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with two Dimenſions onely. </
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>And ſecondly, whether this length
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be to be found. </
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>As to the firſt, I am very certain that no man, let </
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