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

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              And becauſe that in the years paſt I had occaſion by Order of
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              our Lord Pope
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              Vrban
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              8. to apply my thoughts to the motion of
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              the Waters of Rivers, (a matter difficult, moſt important, and
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              little handled by others) having concerning the ſame obſerved
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              ſome particulars not well obſerved, or conſidered till now, but of
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              great moment both in publick and private affairs; I have thought
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              good to publiſh them, to the end that ingenious ſpirits might
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              have occaſion to diſcuſſe more exactly then hitherto hath been
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              done, ſo neceſſary and profitable a matter, and to ſupply alſo my
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              defects in this ſhort and difficult Tractate. </s>
              <s>Difficult I ſay, for
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              the truth is, theſe knowledges, though of things next our ſenſes,
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              are ſometimes more abſtruce and hidden, then the knowledge of
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              things more remote; and much better, and with greater exquiſit­
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              neſs are known the motions of the Planets, and Periods of the
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              Stars, than thoſe of Rivers and Seas: As that ſingular light of
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              Philoſophie of our times, and my Maſter
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              Signore Galileo Galilei
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              wiſely obſerveth in his Book concerning the Solar ſpots. </s>
              <s>And
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              to proceed with a due order in Sciences, I will take ſome ſuppo­
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              ſitions and cognitions ſufficiently clear; from which I will after­
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              wards proceed to the deducing of the principal concluſions. </s>
              <s>But
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              to the end that what I have written at the end of this diſcourſe in
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              a demonſtrative and Geometrical method, may alſo be under­
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              ſtood of thoſe which never have applyed their thoughts to the
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              ſtudy of Geometry; I have endeavoured to explain my conceit
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              by an example, and with the conſideration of the natural things
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              themſelves, muſt after the ſame order in which I began to doubt
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              in this matter; and have placed this particular Treatiſe here in
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              the beginning, adverting nevertheleſs, that he who deſires more
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              full and abſolute ſolidity of Reaſons, may overpaſs this prefatory
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              diſcourſe, and onely conſider what is treated of in the demonſtra­
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              tions placed towards the end, and return afterwards to the conſi­
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              deration of the things collected in the
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              Corollaries
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              and Appendices;
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              which demonſtrations notwithſtanding, may be pretermitted by
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              him that hath not ſeen at leaſt the firſt ſix Books of the Elements
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              of Euclid; ſo that he diligently obſerveth that which fol­
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              loweth.</s>
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              <s>I ſay therefore, that having in times paſt, on divers occaſi­
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              ons heard ſpeak of the meaſures of the waters of Rivers, and
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              Fountains, ſaying, ſuch a River is two or three thouſand feet of
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              water; ſuch a ſpring-water is twenty, thirty, or forty inches,
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              &c.
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              Although in ſuch manner I have found all to treat thereof in
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              word and writing, without variety, and as we are wont to ſay,
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              conſtanti ſermone,
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              yea even Artiſts and Ingeneers, as if it were
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              a thing that admitted not of any doubt, yet howſoever I re­
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              mained ſtill infolded in ſuch an obſcurity, that I well knew I un­</s>
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