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

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            <p type="main">
              <s>
                <pb xlink:href="040/01/211.jpg" pagenum="193"/>
              round upon their centres with equal velocities, ſo as that two
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              veables, which ſuppoſe for example to be two ſtones placed in the
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              points B and C, come to be carried along the circumferences B G
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              and C E, with equal velocities; ſo that in the ſame time that the
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              ſtone B ſhall have run the arch B G, the ſtone C will have paſt the
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              arch C E. </s>
              <s>I ſay now, that the whirl or
                <emph type="italics"/>
              vertigo
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              of the leſſer wheel
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              is much more potent to make the projection of the ſtone B, than
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              the
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              vertigo
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              of the bigger wheel to make that of the ſtone C.
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              </s>
              <s>Therefore the projection, as we have already declared, being to be
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              made along the tangent, when the ſtones B and C are to ſeparate
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              from their wheels, and to begin the motion of projection from the
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              points B and C, then ſhall they be extruded by the
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              impetus
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              ceived from the
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              vertigo
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              by (or along) the tangents B F and C D.
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              </s>
              <s>The two ſtones therefore have equal impetuoſities of running
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              long the tangents B F and C D, and would run along the ſame, if
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              they were not turn'd aſide by ſome other force: is it not ſo
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              gredus
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              ?</s>
            </p>
            <p type="main">
              <s>SAGR. </s>
              <s>In my opinion the buſineſſe is as you ſay.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>But what force, think you, ſhould that be which averts
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              the ſtones from moving by the tangents, along which they are
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              tainly driven by the
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              impetus
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              of the
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              vertigo.
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              </s>
            </p>
            <p type="main">
              <s>SAGR. </s>
              <s>It is either their own gravity, or elſe ſome glutinous
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              matter that holdeth them faſt and cloſe to the wheels.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>But for the diverting of a moveable from the motion
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              to which nature inciteth it, is there not required greater or leſſer
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              force, according as the deviation is intended to be greater or
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              ſer? </s>
              <s>that is, according as the ſaid moveable in its deviation hath a
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              greater or leſſer ſpace to move in the ſame time?</s>
            </p>
            <p type="main">
              <s>SAGR. </s>
              <s>Yes certainly: for it was concluded even now, that to
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              make a moveable to move; the movent vertue muſt be increaſed
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              in proportion to the velocity wherewith it is to move.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>Now conſider, that for the deviating the ſtone upon
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              the leſſe wheel from the motion of projection, which it would
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              make by the tangent B F, and for the holding of it faſt to the
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              wheel, it is required, that its own gravity draw it back the whole
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              length of the ſecant F G, or of the perpendicular raiſed from the
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              point G, to the line B F, whereas in the greater wheel the
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              on needs to be no more than the ſecant D E, or the
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              lar let fall from the tangent D G to the point E, leſſe by much
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              than F G, and alwayes leſſer and leſſer according as the wheel is
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              made bigger. </s>
              <s>And foraſmuch as theſe retractions (as I may call
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              them) are required to be made in equal times, that is, whil'ſt the
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              wheels paſſe the two equal arches B G and C E, that of the ſtone
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              B, that is, the retraction F G ought to be more ſwift than the
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              ther D E; and therefore much greater force will be required for </s>
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