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

Table of figures

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            <p type="main">
              <s>
                <pb xlink:href="040/01/837.jpg" pagenum="144"/>
                <emph type="italics"/>
              Accelerate Motion of the Velocity of the Equable Motion (which defi­
                <lb/>
              cient Moments are repreſented by the Parallels of the Triangle A
                <emph.end type="italics"/>
              G I)
                <lb/>
                <emph type="italics"/>
              is made up by the moments repreſented by the Parallels of the Triangle
                <emph.end type="italics"/>
                <lb/>
              I E F.
                <emph type="italics"/>
              It is manifeſt, therefore, that thoſe Spaces are equal which are
                <lb/>
              in the ſame Time by two Moveables, one whereof is moved with a Mo­
                <lb/>
              tion uniformly Accelerated from Reſt, the other with a Motion Equable
                <lb/>
              according to the Moment ſubduple of that of the greateſt Velocity of the
                <lb/>
              Accelerated Motion: Which was to be demonſtrated.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="head">
              <s>THEOR. II. PROP. II.</s>
            </p>
            <p type="main">
              <s>If a
                <emph type="italics"/>
              M
                <emph.end type="italics"/>
              oveable deſcend out of Reſt with a
                <emph type="italics"/>
              M
                <emph.end type="italics"/>
              oti­
                <lb/>
              on uniformly Accelerate, the Spaces which it
                <lb/>
              paſſeth in any whatſoever Times are to each
                <lb/>
              other in a proportion Duplicate of the ſame
                <lb/>
              Times; that is, they are as the Squares of
                <lb/>
              them.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              Let
                <emph.end type="italics"/>
              A B
                <emph type="italics"/>
              repreſent a length of Time beginning at the firſt Inſtant A;
                <lb/>
              and let
                <emph.end type="italics"/>
              A D
                <emph type="italics"/>
              and
                <emph.end type="italics"/>
              A E
                <emph type="italics"/>
              repreſent any two parts of the ſaid Time;
                <lb/>
              and let
                <emph.end type="italics"/>
              H I
                <emph type="italics"/>
              be a Line in which the Moveable out of H, (as the firſt
                <lb/>
              beginning of the Motion) deſcendeth uniformly accelerating; and let the
                <emph.end type="italics"/>
                <lb/>
                <figure id="id.040.01.837.1.jpg" xlink:href="040/01/837/1.jpg" number="84"/>
                <lb/>
                <emph type="italics"/>
              Space
                <emph.end type="italics"/>
              H L
                <emph type="italics"/>
              be paſſed in the firſt Time
                <emph.end type="italics"/>
              A D;
                <emph type="italics"/>
              and let
                <emph.end type="italics"/>
              H M
                <lb/>
                <emph type="italics"/>
              be the Space that it ſhall deſcend in the Time
                <emph.end type="italics"/>
              A E.
                <emph type="italics"/>
              I ſay,
                <lb/>
              the Space
                <emph.end type="italics"/>
              M H
                <emph type="italics"/>
              is to the Space
                <emph.end type="italics"/>
              H L
                <emph type="italics"/>
              in duplicate propor­
                <lb/>
              tion of that which the Time
                <emph.end type="italics"/>
              E A
                <emph type="italics"/>
              hath to the Time
                <emph.end type="italics"/>
              A D
                <emph type="italics"/>
              :
                <lb/>
              Or, if you will, that the Spaces
                <emph.end type="italics"/>
              M H
                <emph type="italics"/>
              and
                <emph.end type="italics"/>
              H L
                <emph type="italics"/>
              are to one
                <lb/>
              another in the ſame proportion as the Squares
                <emph.end type="italics"/>
              E A
                <emph type="italics"/>
              and
                <emph.end type="italics"/>
                <lb/>
              A D.
                <emph type="italics"/>
              Draw the Line
                <emph.end type="italics"/>
              A C
                <emph type="italics"/>
              at any Angle with
                <emph.end type="italics"/>
              A B,
                <emph type="italics"/>
              and
                <lb/>
              from the points D and E draw the Parallels
                <emph.end type="italics"/>
              D O
                <emph type="italics"/>
              and
                <emph.end type="italics"/>
                <lb/>
              P E
                <emph type="italics"/>
              : of which
                <emph.end type="italics"/>
              D O
                <emph type="italics"/>
              will repreſent the greateſt degree
                <lb/>
              of Velocity acquired in the Inſtant D of the Time
                <emph.end type="italics"/>
              A D;
                <lb/>
                <emph type="italics"/>
              and
                <emph.end type="italics"/>
              P
                <emph type="italics"/>
              the greateſt degree of Velocity acquired in the In­
                <lb/>
              ſtant E of the Time
                <emph.end type="italics"/>
              A E.
                <emph type="italics"/>
              And becauſe we have de­
                <lb/>
              monſtrated in the laſt Propoſition concerning Spaces, that
                <lb/>
              thoſe are equal to one another, of which two Moveables
                <lb/>
              have paſt in the ſame Time, the one by a Moveable out
                <lb/>
              of Reſt with a Motion uniformly Accelerate, and the
                <lb/>
              other by the ſame Moveable with an Equable Motion,
                <lb/>
              whoſe Velocity is ſubduple to the greateſt acquired by the
                <lb/>
              Accelerate Motion: Therefore
                <emph.end type="italics"/>
              M H
                <emph type="italics"/>
              and
                <emph.end type="italics"/>
              H L
                <emph type="italics"/>
              are the Spaces that two
                <lb/>
              Lquable Motions, whoſe Velocities ſhould be as the half of
                <emph.end type="italics"/>
              P E,
                <emph type="italics"/>
              and
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
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