Galilei, Galileo, The systems of the world, 1661

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="065/01/023.jpg" pagenum="17"/>
              your incredulity; but for the knowledge of this, expect it at
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              ſome other time, namely, when you ſhall ſee the matters
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              ning local motion demonſtrated by our
                <emph type="italics"/>
              Academick
                <emph.end type="italics"/>
              ; at which
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              time you ſhall find it proved, that in the time that the one
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              ble falls all the ſpace C B, the other deſcendeth by C A as far
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              as the point T, in which falls the perpendicular drawn from the
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              point B: and to find where the ſame Cadent by the
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              cular would be when the other arriveth at the point A, draw from
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              A the perpendicular unto C A, continuing it, and C B unto the
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              interfection, and that ſhall be the point ſought. </s>
              <s>Whereby you
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              ſee how it is true, that the motion by C B is ſwifter than by the
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              inclination C A (ſuppoſing the term C for the beginning of the
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              motions compared) becauſe the line C B is greater than C T,
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              and the other from C unto the interſection of the perpendicular
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              drawn from A, unto the line C A, is greater than C A, and
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              therefore the motion by it is ſwifter than by C A But when we
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              compare the motion made by all C A, not with all the motion
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              made in the ſame time by the perpendicular continued, but with
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              that made in part of the time, by the ſole part C B, it hinders
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              not, that the motion by C A, continuing to deſcend beyond, may
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              arrive to A in ſuch a time as is in proportion to the other time,
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              as the line C A is to the line C B. </s>
              <s>Now returning to our firſt
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              purpoſe; which was to ſhew, that the grave moveable leaving
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              its quieſcence, paſſeth defcending by all the degrees of tardity,
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              precedent to any whatſoever degree of velocity that it aequireth,
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              re-aſſuming the ſame Figure which we uſed before, let us
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              ber that we did agree, that the Deſcendent by the inclination C
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              A, and the Cadent by the perpendicular C B, were found to have
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              acquired equal degrees of velocity in the terms B and A: now to
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              proceed, I ſuppoſe you will not ſcruple to grant, that upon
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              ther plane leſs ſteep than A C; as for example, A D [in
                <emph type="italics"/>
              Fig.
                <emph.end type="italics"/>
              5.]
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              the motion of the deſcendent would be yet more ſlow than in the
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              plane A C. </s>
              <s>So that it is not any whit dubitable, but that there
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              may be planes ſo little elevated above the Horizon A B, that the
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              moveable, namely the ſame ball, in any the longeſt time may
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              reach the point A, which being to move by the plane A B, an
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              nite time would not ſuffice: and the motion is made always more
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              ſlowly, by how much the declination is leſs. </s>
              <s>It muſt be therefore
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              confeſt, that there may be a point taken upon the term B, ſo near
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              to the ſaid B, that drawing from thence to the point A a plane,
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              the ball would not paſs it in a whole year. </s>
              <s>It is requiſite next
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              for you to know, that the
                <emph type="italics"/>
              impetus,
                <emph.end type="italics"/>
              namely the degree of
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              city the ball is found to have acquired when it arriveth at the
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              point A, is ſuch, that ſhould it continue to move with this ſelf-ſame
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              degree uniformly, that is to ſay, without accelerating or retarding; </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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