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

Table of figures

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              <s>PROP. XIII. PROBL. IV.</s>
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              <s>
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              There being given the greateſt Weight that can be ſup­
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              ported at the middle of a Cylinder or Priſme, where
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              the Reſiſtance is leafl; and there being given a
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              Weight greater than that, to find in the ſaid Cylin­
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              der, the point at which the given greater Weight may
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              be ſupporited as the greateſt Weight.
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              <s>Let the given weight greater than the greateſt weight that
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              can be ſupported at the middle of the Cylinder A B, have
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              unto the ſaid greateſt weight, the proportion of the line E
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              to F: it is required to find the point in the Cylinder at which the
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              ſaid given weight commeth to be ſupported as the biggeſt. </s>
              <s>Be­
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              tween E and F let G be a Mean-Proportional; and as E is to G,
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              ſo let A D be to S, S ſhall be leſſer than A D. </s>
              <s>Let A D be the
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              Diameter of the Semicircle A H D: in which ſuppoſe A H equal
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              to S; and joyn together H and D, and take D R equal to it.
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              <s>I ſay that R is the point ſought, at which the given weight,
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              greater than the greateſt that can be ſupported at the middle of the
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              Cylinder D, would become as the greateſt weight. </s>
              <s>On the length
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              B
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              A deſcribe the Semicircle A N B, and raiſe the Perpendicular
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              RN, and conjoyn N and
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              D: And becauſe the two
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                <figure id="id.040.01.806.1.jpg" xlink:href="040/01/806/1.jpg" number="67"/>
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              Squares N R and R D are
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              equal to the Square N D;
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              that is, to the Square A D;
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              that is, to the two A H and
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              and H D; and H D is equal
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              to the Square D R: There­
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              fore the Square N R, that
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              is, the Rectangle A R B
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              ſhall be equal to the Square A H; that is, to the Square S: But
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              the Square S is to the Square A D, as F to E; that is, as the
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              greateſt ſupportable Weight at D to the given greater Weight:
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              Therefore this greater ſhall be ſupported at R, as the greateſt
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              that can be there ſuſtained. </s>
              <s>Which is that that we ſought.</s>
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              <s>SAGR. </s>
              <s>I underſtand you very well, and am conſidering that
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              the Priſme A B having alwayes more ſtrength and reſiſtance a­
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              gainſt Preſſion in the parts that more and more recede from the
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              middle, whether in very great and heavy Beams one may take </s>
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