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

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            <pb xlink:href="040/01/938.jpg" pagenum="245"/>
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              <s>SAGR. </s>
              <s>You argue very well, and make no ſeruple at all of
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              granting, that be the Force of the Mover never ſo ſmall it ſhall ſu­
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              perate any what ever great Reſiſtance at all times when that ſhall
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              more exceed in Velocity than this doth in Force and Gravity.
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              </s>
              <s>Now come we to the caſe of the Rope. </s>
              <s>And drawing a ſmall
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              Scheme be pleaſed to underſtand for once that this Line A B, reſt­
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              ing upon the two fixed and ſtanding points A and B, to have hang­
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              ing at its ends, as you ſee, two immenſe Weights C and D, which
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              drawing it with great Force make it to ſtand directly diſtended, it
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              being a ſimple Line without any gravity. </s>
              <s>And here I proceed, and
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              tell you, that if at the midſt of that which is the point E, you ſhould
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              hang any never ſo little a Weight, as is this H, the Line A B would
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              yield, and inclining towards the point F, and by conſequence
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              lengthening, will conſtrain the two great Weights C and D to
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              aſcend upwards: which I demonſtrate to you in this manner:
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              About the two points A and B as Centers I deſcribe two Quadrants
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              E F G, and E L M, and in regard that the two Semidiameters AI
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              and B L are equal to the two Semidiameters A E and E B, the exceſ­
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              ſes F I and F L ſhall be the quantity of the prolongations of the
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              parts A F and F B, above A E and E B; and of conſequence ſhall
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                <figure id="id.040.01.938.1.jpg" xlink:href="040/01/938/1.jpg" number="164"/>
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              determine the Aſcents
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              of the Weights C and
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              D, in caſe that the
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              Weight H had had a
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              power to deſcend to F:
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              which might then be
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              in caſe the Line E F,
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              which is the quantity
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              of the Deſcent of the
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              ſaid Weight H, had
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              greater proportion to
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              the Line F I which de­
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              termineth the Aſcent of
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              the two Weights C &
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              D, than the pondero­
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              ſity of both thoſe Weights hath to the ponderoſity of the Weight
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              H. </s>
              <s>But this will neceſſarily happen, be the ponderoſity of the
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              Weights C and D never ſo great, and that of H never ſo ſmall; for
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              the exceſs of the Weights C and D above the Weight His not ſo
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              great, but that the exceſs of the Tangent E F above the part of the
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              Secant F I may bear a greater proportion. </s>
              <s>Which we will prove
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              thus: Let there be a Circle whoſe Diameter is G A I; and look
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              what proportion the ponderoſity of the Weights C and D have to
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              the ponderoſity of H, let the Line B O have the ſame proportion to
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              another, which let be C, than which let D be leſſer: So that B O </s>
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