Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667
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              <s>PROBL. IV. PROP. XI.</s>
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              <s>The
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              Impetus
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              and Amplitude of a Semiparabola be­
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              ing given, to find its Altitude, and conſequently
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              its Sublimity.</s>
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              <s>
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              Let the
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              Impetus
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              given be defined by the Perpendicular to the Ho­
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              rizon A B; and let the Amplitude along the Horizontal Line be
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              B C. </s>
              <s>It is required to find the Altitude and Sublimity of the
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              Parabola whoſe
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              Impetus
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              is A B, and Amplitude B C. </s>
              <s>It is manifeſt,
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              from what hath been already demonſtrated, that half the Amplitude B C
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              will be a Mean-proportional betwixt the Altitude and the Sublimity of
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              the ſaid Semiparabola, whoſe
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              Impetus,
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              by the precedent Propoſition, is
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              the ſame with the
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              Impetus
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              of the Moveable falling from Reſt in A along
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              the whole Perpendicular A B: Wherefore B A is ſo to be cut that the
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              Rectangle contained by its parts may be equal to the Square of half of
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              B C, which let be B D. </s>
              <s>Hence it appeareth
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              to be neceſſary that D B do not exceed the
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                <figure id="id.040.01.929.1.jpg" xlink:href="040/01/929/1.jpg" number="161"/>
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              half of B A; for of Rectangles contained by
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              the parts the greateſt is when the whole
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              Line is cut into two equal parts. </s>
              <s>Therefore
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              let B A be divided into two equal parts in E.
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              </s>
              <s>And if B D be equal to B E the work is
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              done; and the Altitude of the Semipara­
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              bola ſhall be B E, and its Sublimity E A:
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              (and ſee here by the way that the Amplitude
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              of the Parabola of a Semi-right Elevation,
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              as was demonſtrated above, is the greateſt of
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              all thoſe deſcribed with the ſame
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              Impetus.)
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              But let B D be leſs than the half of B A,
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              which is ſo to be cut that the Rectangle under the parts may be equal to
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              the Square B D. </s>
              <s>Upon E A deſcribe a Semicircle, upon which out of A
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              ſet off A F equal to B D, and draw a Line from F to E, to which cut
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              a part equal E G. </s>
              <s>Now the Rectangle B G A, together with the Square
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              E G, ſhall be equal to the Square E A; to which the two Squares A F
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              and F E are alſo equal: Therefore the equal Squares G E and F E be­
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              ing ſubſtracted, there remaineth the Rectangle B G A equal to the
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              Square A F,
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              ſcilicet,
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              to B D; and the Line B D is a Mean-proportional
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              betwixt B G and G A. </s>
              <s>Whence it appeareth, that of the Semipa­
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              rabola whoſe Amplitude is B C, and
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              Impetus
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              A B, the Altitude is
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              B G, and the Sublimity G A. </s>
              <s>And if we ſet off B I below equal to G A,
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              this ſhall be the Altitude, and I A the Sublimity of the Semiparabola
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              I C. </s>
              <s>From what hath been already demonſtrated we are able,
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              </s>
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