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

Table of figures

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              Velocity encreaſed in the manner aforeſaid would be equal to the
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              Space that the ſaid Moveable would paſſe, in caſe it were in the
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              ſame Time
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              A
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              C, moved with an Uniform Motion, whoſe degree of
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              Velocity ſhould be equal to E C, the half of B C. </s>
              <s>I now proceed
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              farther, and imagine the Moveable; having deſcended with an
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              A
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              ccelerate Motion, to have in the Inſtant
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              C the degree of Velocity B C: It is ma­
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              nifeſt, that if it did continue to move
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              with the ſame degree of Velocity B C,
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              without farther
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              A
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              cceleration, it would
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              paſſe in the following Time C I, a Space
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              double to that which it paſſed in the equal
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              Time
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              A
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              C, with the degree of Uniform
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              Velocity E C, the half of the Degree B C.
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              <s>But becauſe the Moveable deſcendeth
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              with a Velocity encreaſed alwaies Uni­
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              formly in all equal Times; it will add to
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              the degree C B in the following Time
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              C I, thoſe Tame Moments of Velocity
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              that encreaſe according to the Parallels of
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              the Triangle B F G, equal to the Triangle
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              A
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              B C. </s>
              <s>So that adding to the degree of
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              Velocity G I, the half of the degree F G, the greateſt of thoſe ac­
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              quired in the
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              A
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              ccelerate Motion, and regulated by the Parallels of
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              the Triangle B F G, we ſhall have the degree of Velocity I N, with
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              which, with an Uniform Motion, it would have moved in the
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              Time C I: Which degree I N, being triple the degree E C, pro­
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              veth that the Space paſſed in the ſecond Time C I ought to be tri­
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              ple to that of the firſt Time C
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              A. A
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              nd if we ſhould ſuppoſe to be
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              added to
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              A
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              I another equal part of Time I O, and the Triangle to
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              be enlarged unto
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              A
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              P O; it is manifeſt, that if the Motion ſhould
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              continue for all the Time I O with the degree of Velocity I F,
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              acquired in the
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              A
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              ccelerate Motion in the Time
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              A
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              I, that degree
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              I F being Quadruple to E C, the Space paſſed would be Quadruple
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              to that paſſed in the equal firſt Time
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              A
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              C: But continuing the
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              encreaſe of the Uniform
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              A
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              cceleration in the Triangle F P Q like
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              to that of the Triangle
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              A
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              B C, which being reduced to equable
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              Motion addeth the degree equal to E C, Q R being added, equal
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              to E C, we ſhall have the whole Equable Velocity exerciſed in the
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              Time I O, quintuple to the Equable Velocity of the firſt Time
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              A
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              C,
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              and therefore the Space paſſed quintuple to that paſt in the firſt
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              Time
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              A
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              C. </s>
              <s>We ſee therefore, even by this familiar computation,
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              That the Spaces paſſed in equal Times by a Moveable which
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              departing from Reſt goeth acquiring Velocity, according to the
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              encreaſe of the Time, are to one another as the odd Numbers
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              ab
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