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

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              Regulator 6. of thoſe parts high; of which it ran before but 5. let
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              6 be found in the row of heights, and let the number 11. ſtand­
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              ing under the ſame be taken and added to the number 25.
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              that is placed under the number 9. in the Additions, and 5. in
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              the heights, and you ſhall have 36; which is the quantity of the
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              water that runneth with the height of the River, when it is high
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              6 of thoſe parts, whereof it was before but 5.</s>
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              <s>3. But if it ſhould be deſired, to know how much water it is
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              requiſite to add to make the River riſe ſo, as that it may run in
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              height 8. of thoſe parts of which before it ran but 5; one
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              ought to take the ſum of the number of the Series of Additions
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              ſtanding under 8. 7. and 6, which are 15. 13. and 11. that is, 39.
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              and this ſhall be the ſumme that muſt be added to 25: So that
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              to make the River to run 8. of thoſe parts in height, of which it
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              before did run 5, it will be neceſſary to add 39. of thoſe parts,
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              of which the River before was 25.</s>
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              <s>4. Likewiſe the ſame Table giveth the quantity of water
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              that runneth from time to time through a River, that increaſeth
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              by the addition of new water to the ſame in one of its heights, the
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              quantity of its water be known. </s>
              <s>As for example: If we knew that
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              the River in one minute of an hour diſchargeth 2500. of thoſe mea­
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              ſures of water, and runneth in height 5. parts in the Regulator, and
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              afterwards ſhould ſee that it runneth 8 Palms high, finding in the
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              row of quantity the number placed under 8. which is 64. we would
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              ſay that the River heightned, carrieth of water 64. of thoſe parts
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              whereof it carried before but 25; and becauſe before it carried
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              2500. meaſures, by the Golden Rule we will ſay, that the River
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              carrieth 6400. of thoſe meaſures, of which before it carried 2500.</s>
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              <s>In this progreſs of Nature, is one thing really curious, and that
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              at firſt ſight ſeemeth to be ſomewhat Paradoxal, that we pro­
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              ceeding ordinately in the diverſions and additions, with additi­
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              ons and diverſions ſo unequal, the abatings do notwithſtanding
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              alwaies prove equal, and ſo do the riſings: And who would ever
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              think that a River in height,
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              v. </s>
              <s>g.
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              10. Palms, running and carry­
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              ing an hundred meaſures in a minute of an hour, is to abate but
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              one Palm, onely by the diverſion of 19. of thoſe meaſures; and
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              then again, that the buiſineſs cometh to that paſs, that it abateth
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              likewiſe a Palm by the diverſion of three onely of thoſe meaſures,
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              nay, by the diverſion of but one meaſure? </s>
              <s>and yet it is moſt
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              certain: And this truth meets with ſo manifeſt proofs in experi­
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              ence, that it is very admirable! And for the full ſatisfaction of
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              thoſe, who not being able to comprehend ſubtil demonſtrati­
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              ons, desire to be clearly inform'd by the matters of fact, and to
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              ſee with their bobily eyes, and touch with their hands, what their
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              underſtanding and reaſon cannot reach unto: I will hear add
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              another very eaſie way to reduce all to an experiment, the </s>
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