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

Table of figures

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      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="040/01/917.jpg" pagenum="224"/>
              Quantities, that is to ſay, of Spaces, of Times, and of
                <emph type="italics"/>
              Impetus's,
                <emph.end type="italics"/>
              let
                <lb/>
              it be required to determine in the aſſigned Space, and at the height
                <lb/>
              A C, how much the Time of the Fall of the Moveable from A to
                <lb/>
              C is to be, and what the
                <emph type="italics"/>
              Impetus
                <emph.end type="italics"/>
              is that ſhall be found to have been
                <lb/>
              acquired in the ſaid Term C, in relation to the Time and to the
                <lb/>
                <emph type="italics"/>
              Impetus
                <emph.end type="italics"/>
              meaſured by A B. </s>
              <s>Both theſe queſtions ſhall be reſolved
                <lb/>
              taking A D the Mean-proportional betwixt the two Lines A C
                <lb/>
              and A B; affirming the Time of the Fall along the whole Space
                <lb/>
              A C to be as the Time A D is in relation to A B, aſſigned in the
                <lb/>
              beginning for the Quantity of the Time in the Fall A B. </s>
              <s>And like­
                <lb/>
              wiſe we will ſay that the
                <emph type="italics"/>
              Impetus,
                <emph.end type="italics"/>
              or degree of Velocity that the
                <lb/>
              Cadent Moveable ſhall obtain in the Term C, in relation to the
                <lb/>
                <emph type="italics"/>
              Impetus
                <emph.end type="italics"/>
              that it had in B, is as the ſame Line A D is in relation to
                <lb/>
              A B, being that the Velocity encreaſeth with the ſame proportion
                <lb/>
              as the Time doth: Which Concluſion although it was aſſumed as
                <lb/>
              a
                <emph type="italics"/>
              Poſtulatum,
                <emph.end type="italics"/>
              yet the Author was pleaſed to explain the Applicati­
                <lb/>
              on thereof above in the third Propoſition.</s>
            </p>
            <p type="main">
              <s>This point being well underſtood and proved, we come to the
                <lb/>
              Conſideration of the
                <emph type="italics"/>
              Impetus
                <emph.end type="italics"/>
              derived from two compound Moti­
                <lb/>
              ons: whereof let one be compounded of the Horizontal and alwaies
                <lb/>
              Equable, and of the Perpendicular unto the Horizon, and it alſo
                <lb/>
              Equable: but let the other be compounded of the Horizontal like­
                <lb/>
              wiſe alwaies Equable, and of the Perpendicular Naturally-Accele­
                <lb/>
              rate. </s>
              <s>If both ſhall be Equable, it hath been ſeen already that the
                <lb/>
                <emph type="italics"/>
              Impetus
                <emph.end type="italics"/>
              emerging from the compoſition of both is
                <emph type="italics"/>
              potentia
                <emph.end type="italics"/>
              equal to
                <lb/>
              both, as for more plainneſs we will thus Exemplifie. </s>
              <s>Let the Move­
                <lb/>
              able deſcending along the Perpendicular A B be ſuppoſed to have,
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              for example, three degrees of Equable
                <emph type="italics"/>
              Impetus,
                <emph.end type="italics"/>
              but being tranſ­
                <lb/>
              ported along A B towards C, let the ſaid Velocity and
                <emph type="italics"/>
              Impetus
                <emph.end type="italics"/>
              be
                <lb/>
              ſuppoſed four degrees, ſo that in the ſame Time that falling it would
                <lb/>
              paſs along the Perpendicular,
                <emph type="italics"/>
              v. </s>
              <s>gr.
                <emph.end type="italics"/>
              three yards,
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                <figure id="id.040.01.917.1.jpg" xlink:href="040/01/917/1.jpg" number="152"/>
                <lb/>
              it would in the Horizontal paſs four, but in
                <lb/>
              that compounded of both the Velocities it
                <lb/>
              cometh in the ſame Timefrom the point A un­
                <lb/>
              to the Term C, deſcending all the way along the Diagonal Line
                <lb/>
              A C, which is not ſeven yards long, as that ſhould be which is com­
                <lb/>
              pounded of the two Lines A B, 3, and B C, 4, but is 5; which 5 is
                <lb/>
                <emph type="italics"/>
              potentia
                <emph.end type="italics"/>
              equal to the two others, 3 and 4: For having found the
                <lb/>
              Squares of 3 and 4, which are 9 and 16, and joyning theſe together,
                <lb/>
              they make 25 for the Square of A C, which is equal to the two
                <lb/>
              Squares of A B and B C: whereupon A C ſhall be as much as is the
                <lb/>
              Side, or, if you will, Root of the Square 25, which is 5. For a conſtant
                <lb/>
              and certain Rule therefore, when it is required to aſſign the
                <lb/>
              Quantity of the
                <emph type="italics"/>
              Impetus
                <emph.end type="italics"/>
              reſulting from two
                <emph type="italics"/>
              Impetus's
                <emph.end type="italics"/>
              given, the
                <lb/>
              one Horizontal, and the other Perpendicular, and both Equable, </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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