Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667

Table of figures

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              the leſſer; that is, to ſpeak more properly, The Water which
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              paſſeth through the greater Cock, hath alwaies a greater pro­
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              portion to that which paſſeth through the leſſer, than the greater
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              Cock hath to the leſſer. </s>
              <s>All which I will declare by an exam­
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              ple.</s>
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              <s>Let there be ſuppoſed for more plainneſs two Squares; (the
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              ſame may be underſtood of Circles, and other like Figures) The
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              firſt Square is, as we will ſuppoſe, quadruple to the other, and
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              theſe Squares are the mouths of two Cocks.; one of four inches,
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              the other of one: Now its manifeſt by what hath been ſaid, that
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              the Water which paſſeth by the leſs Cock, findeth its velocity
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              impeded in the circumference of the Cock; which impediment
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              is meaſured by the ſaid circumfe­
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              rence. </s>
              <s>Now it is to be conſider­
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              ed, that if we would have the Wa­
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              ter which paſſeth through the
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              greater Cock, to be onely qua­
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              druple to that which paſſeth
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              through the leſſe, in equal ſpaces of time, it would be neceſſary,
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              that not onely the capacity and the meaſure of the greater Cock
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              be quadruple to the leſſer Cock, but that alſo the impediment be
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              quadrupled. </s>
              <s>Now in our caſe it is true, That the belly and
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              mouth of the Cock is quadrupled, and yet the impediment is not
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              quadrupled, but is onely doubled; ſeeing that the circumference
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              of the greater Square, is onely double to the circumference of
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              the leſier Square; for the greater circumference containeth eight
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              of thoſe parts, of which the leſſer containeth but four, as is ma­
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              nifeſt by the deſcribed Figure; and for that cauſe there ſhall
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              paſs by the greater Cock, above four times as much Water, as
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              ſhall paſs by the leſſer Cock.</s>
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              <s>The like errour occurreth alſo in the other manner of meaſu­
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              ring the Water of a Fountain, as may eaſily be collected from
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              what hath been ſaid and obſerved above.</s>
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              <s>APPENDIX VIII.</s>
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              <s>The ſame contemplation diſcovereth the errour of thoſe
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              Architects, who being to erect a Bridge of ſundry Arches
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              over a River, conſider the ordinary breadth of the River;
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              which being
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              v. </s>
              <s>g.
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              fourty fathom, and the Bridge being to conſiſt
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              of four Arches, it ſufficeth them, that the breadth of all the four
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              Arches taken together, be fourty fathom; not conſidering that
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              in the ordinary Channel of the River, the Water hath onely
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              two impediments which retard its velocity; namely, the touching
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              and gliding along the two ſides or ſhores of the River: but </s>
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