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

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              <s>
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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. </s>
              <s>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. </s>
              <s>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. </s>
              <s>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. </s>
              <s>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. </s>
              <s>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.</s>
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              <s>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.</s>
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              <s>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. </s>
              <s>And ſecondly, whether this length
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              be to be found. </s>
              <s>As to the firſt, I am very certain that no man, let </s>
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          </chap>
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