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

Table of figures

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      <text>
        <body>
          <chap>
            <pb xlink:href="040/01/836.jpg" pagenum="143"/>
            <p type="head">
              <s>THEOR. I. PROP. I.</s>
            </p>
            <p type="main">
              <s>The time in which a Space is paſſed by a Movea­
                <lb/>
              ble with a Motion Vniformly Accelerate, out of
                <lb/>
              Reſt, is equal to the Time in which the ſame
                <lb/>
              Space would be paſt by the ſame Moveable
                <lb/>
              with an Equable Motion, the degree of whoſe
                <lb/>
              Velocity is ſubduple to the greateſt and ulti
                <lb/>
              mate degree of the Velocity of the former Vni­
                <lb/>
              formly Accelerate Motion.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              Let us by the extenſion A B repreſent the Time, in which the
                <lb/>
              Space
                <emph.end type="italics"/>
              C D
                <emph type="italics"/>
              is paſſed by a Moveable with a Motion Vniformly
                <lb/>
              Accelerate, out of Reſt in C: and let the greateſt and laſt de-
                <emph.end type="italics"/>
                <lb/>
                <figure id="id.040.01.836.1.jpg" xlink:href="040/01/836/1.jpg" number="83"/>
                <lb/>
                <emph type="italics"/>
              gree of Velocity acquired in the Inſtants of the Time
                <emph.end type="italics"/>
                <lb/>
              A B
                <emph type="italics"/>
              be repreſented by
                <emph.end type="italics"/>
              E B;
                <emph type="italics"/>
              and conſtitute at plea­
                <lb/>
              ſure upon
                <emph.end type="italics"/>
              A B
                <emph type="italics"/>
              any number of parts, and thorow the
                <lb/>
              points of diviſion draw as many Lines, continued
                <lb/>
              out unto the Line
                <emph.end type="italics"/>
              A E,
                <emph type="italics"/>
              and equidiſtant to
                <emph.end type="italics"/>
              B E,
                <lb/>
                <emph type="italics"/>
              which will repreſent the encreaſe of the degrees of
                <lb/>
              Velocity after the firſt Inſtant A. </s>
              <s>Then divide
                <emph.end type="italics"/>
              B E
                <lb/>
                <emph type="italics"/>
              into two equall parts in
                <emph.end type="italics"/>
              F,
                <emph type="italics"/>
              and draw
                <emph.end type="italics"/>
              F G
                <emph type="italics"/>
              and
                <emph.end type="italics"/>
              A G
                <lb/>
                <emph type="italics"/>
              parallel to B A and
                <emph.end type="italics"/>
              B F
                <emph type="italics"/>
              : The Parallelogram
                <emph.end type="italics"/>
              A G
                <lb/>
              F B
                <emph type="italics"/>
              ſhall be equall to the Triangle
                <emph.end type="italics"/>
              A E B,
                <emph type="italics"/>
              its Side
                <emph.end type="italics"/>
                <lb/>
              G F
                <emph type="italics"/>
              dividing
                <emph.end type="italics"/>
              A E
                <emph type="italics"/>
              into two equall parts in I: For
                <lb/>
              if the Parallels of the Triangle
                <emph.end type="italics"/>
              A E
                <emph type="italics"/>
              B be continued
                <lb/>
              out unto
                <emph.end type="italics"/>
              I G F,
                <emph type="italics"/>
              we ſhall have the Aggregate of all
                <lb/>
              the Parallels contained in the Quadrilatural Figure
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              equal to the Aggregate of all the Parallels compre­
                <lb/>
              hended in the Triangle
                <emph.end type="italics"/>
              A E
                <emph type="italics"/>
              B; For thoſe in the Triangle
                <emph.end type="italics"/>
              I E F
                <emph type="italics"/>
              are equal
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              to thoſe contained in the Triangle
                <emph.end type="italics"/>
              G I A,
                <emph type="italics"/>
              and thoſe that are in the
                <emph.end type="italics"/>
              Tra­
                <lb/>
              pezium
                <emph type="italics"/>
              are in common. </s>
              <s>Now ſince all and ſingular the Inſtants of Time
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              do anſwer to all and ſingular the Points of the Line A B; and ſince the
                <lb/>
              Parallels contained in the Triangle
                <emph.end type="italics"/>
              A E
                <emph type="italics"/>
              B do repreſent the degrees of Ac­
                <lb/>
              celeration or encreaſing Velocity, and the Parallels contained in the Pa­
                <lb/>
              rallelogram do likewiſe repreſent as many degrees of Equable Motion or
                <lb/>
              unencreaſing Velocity: It appeareth, that as many Moments of Velocity
                <lb/>
              paſſed in the Accelerate Motion according to the encreaſing Parallels of the
                <lb/>
              Triangle A E B, as in the Equable Motion according to the Parallels of
                <lb/>
              the Parallelogram G B: Becauſe what is wanting in the firſt half of the
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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