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

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              <s>
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              Parabola G D. </s>
              <s>Let G M be a Mean-proportional betwixt A B and
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              G L; G M ſhall be the Time, and the Moment or
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              Impetus
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              in G of the
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              Project falling from L, (for it hath been ſuppoſed that A B is the Mea­
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              ſure of the Time and
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              Impetus.)
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              Again, let G N be a Mean-propor­
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              tional betwixt B C and C G: this G N ſhall be the Meaſure of the
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              Time and the
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              Impetus
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              of the
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                <figure id="id.040.01.924.1.jpg" xlink:href="040/01/924/1.jpg" number="156"/>
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              Project falling
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              from G to C.
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              </s>
              <s>If therefore a
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              Line be drawn
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              from M to N
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              it ſhall be the
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              the Meaſure of
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              the
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              Impetus
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              of
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              the Project a­
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              long the Para­
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              bola B D, ſcri­
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              king in the
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              term D. Which
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                <lb/>
              Impetus,
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              I ſay,
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              is greater than the
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              Impetus
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              of the Project along the Parabola B D,
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              whoſe quantity was A E. </s>
              <s>For becauſe G N is ſuppoſed the Mean-pro­
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              portional betwixt B C and C G, and B C is equal to B E, that is to H G;
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              (for they are each of them ſubduple to D C:) Therefore as C G is to
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              G N, ſo ſhall N G be to G K: and, as C G or H G is to G K, ſo ſhall the
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              Square N G be to the Square of G K: But as H G is to G K, ſo was
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              K G ſuppoſed to be to G L: Therefore as N G is to the Square G K, ſo
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              is K G to G L: But as K G is to G L, ſo is the Square K G unto the
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              Square G M, (for G M is the Mean between K G and G L:) Therefore
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              the three Squares N G, K G, and G M are continual proportionals: And
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              the two extream ones N G and G M taken together, that is the Square
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              M N is greater than double the Square K G, to which the Square A E
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              is double: Therefore the Square M N is greater than the Square A E:
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              and the Line M N greater than the Line A E: Which was to be de­
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              monſtrated.
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            <p type="head">
              <s>CORROLLARY I.</s>
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            <p type="main">
              <s>Hence it appeareth, that on the contrary, in the Project out of D
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              along the Semiparabola D B, leſs
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              Impetus
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              is required than
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              along any other according to the greater or leſſer Elevation
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              of the Semiparabola B D, which is according to the Tan­
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              gent A D, containing half a Right-Angle upon the Hori­
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              zon.</s>
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          </chap>
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