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

Table of figures

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              <s>
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              away a pretty big part towards the end with a notable alleviation
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              of the weight; which in Beams of great Rooms would be commo­
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              dious, and of no ſmall proſit. </s>
              <s>And it would be pretty, to find what
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              Figure that Solid ought to have, that it might have equal Reſi­
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              ſtance in all its parts; ſo as that it were not with more eaſe to be
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              broken by a weight that ſhould preſſe it in the midſt, than in any
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              other place.</s>
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              <s>SALV. </s>
              <s>I was juſt about to tell you a thing very notable and
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              pleaſant to this purpoſe. </s>
              <s>I will aſſume a brief Scheme for the bet­
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              ter explanation of my meaning. </s>
              <s>This Figure D B is a Priſm, whoſe
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              Reſiſtance againſt Fraction in the term A D by a Force preſſing
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              at the term B, is leſſe than the Reſiſtance that would be found in
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              the place C I, by how much the length C B is leſſer than B A; as
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              hath already been demon­
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              ſtrated. </s>
              <s>Now ſuppoſe the
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                <figure id="id.040.01.807.1.jpg" xlink:href="040/01/807/1.jpg" number="68"/>
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              ſaid Priſme to be ſawed
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              Diagonally according to the
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              Line FB, ſo that the oppo­
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              ſite Surfaces may be two
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              Triangles, one of which to­
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              wards us is F A B. </s>
              <s>This So­
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              lid obtains a quality contrary to the Priſme, to wit, that it leſſe re­
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              ſiſteth Fraction by the Force placed in B at the term C than at A,
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              by as much the Length C
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              B
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              is leſſe than
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              B
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              A; Which we will ea
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              ſily prove: For imagining the Section C N O parallel to the other
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              A F D, the Line
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              F
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              A ſhall be to C N in the Triangle F A
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              B
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              in the
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              ſame proportion, as the Line A
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              B
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              is to
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              B
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              C: and therefore if we
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              ſuppoſe the Fulciment of the two Leavers to be in the Points A
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              and C, whoſe Diſtances are
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              B
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              A, A F,
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              B
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              C, and C N, theſe, I ſay,
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              ſhall be like: and therefore that Moment which the
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              F
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              orce placed
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              at
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              B
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              hath at the Diſtance
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              B
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              A above the Reſiſtance placed at the
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              Diſtance A
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              F
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              , the ſaid
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              F
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              orce at
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              B
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              ſhall have at the Diſtance
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              B
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              C
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              above the ſame Reſiſtance, were it placed at the Diſtance C N:
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              B
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              ut the Reſiſtance to be overcome at the
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              F
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              ulciment C, being pla­
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              ced at the Diſtance C N, from the
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              F
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              orce in
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              B
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              is leſſer than the
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              Reſiſtance in A ſo much as the Rectangle C O is leſſe than the
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              Rectangle A D; that is, ſo much as the Line C N is leſs than A
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              F
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              ;
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              that is, C
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              B
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              than B A: Therefore the Reſiſtance of the part O C B
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              againſt
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              F
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              raction in C is ſo much leſs than the Reſiſtance of the
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              whole D A O againſt
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              F
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              racture in O, as the Length C B is leſs than
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              A B. </s>
              <s>We have therefore from the Beam or Priſme D B, taken
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              away a part, that is half, cutting it Diagonally, and left the Wedge
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              or triangular Priſm
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              F
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              B A; and they are two Solids of contrary
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              Qualities, namely, that more reſiſts the more it is ſhortned, and this
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              in ſhortning loſeth its toughneſs as faſt. </s>
              <s>Now this being granted, </s>
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