Galilei, Galileo, The systems of the world, 1661

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    <archimedes>
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            <p type="main">
              <s>
                <pb xlink:href="065/01/206.jpg" pagenum="198"/>
              may have erred in rehearſing his Argument, and to avoid running
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              into the ſame miſtakes for the future, I could wiſh I had his
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              Book; and if you had any body to ſend for it, I would take it
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              for a great favour.</s>
            </p>
            <p type="main">
              <s>SAGR. </s>
              <s>You ſhall not want a Lacquey that will runne for it
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              with all ſpeed: and he ſhall do it preſently, without loſing any
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              time; in the mean time
                <emph type="italics"/>
              Salviatus
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              may pleaſe to oblige us with his
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              computation.</s>
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            <p type="main">
              <s>SIMP. </s>
              <s>If he go, he ſhall finde it lie open upon my Desk,
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              together with that of the other Author, who alſo argueth
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              gainſt
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              Copernicus.
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              </s>
            </p>
            <p type="main">
              <s>SAGR. </s>
              <s>We will make him bring that alſo for the more
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              tainty: and in the interim
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              Salviatus
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              ſhall make his calculation: I
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              have diſpatch't away a meſſenger.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>Above all things it muſt be conſidered, that the motion
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              of deſcending grave bodies is not uniform, but departing from
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                <arrow.to.target n="marg394"/>
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              reſt they go continually accelerating: An effect known and
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              ſerved by all men, unleſſe it be by the forementioned modern
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              thour, who not ſpeaking of acceleration, maketh it even and
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              niforme. </s>
              <s>But this general notion is of no avail, if it be not known
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              according to what proportion this increaſe of velocity is made; a
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              concluſion that hath been until our times unknown to all
                <emph type="italics"/>
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              phers
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              ; and was firſt found out & demonſtrated by the ^{*}
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              Academick,
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                <arrow.to.target n="marg395"/>
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              our common friend, who in ſome of his ^{*} writings not yet
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                <arrow.to.target n="marg396"/>
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              ed, but in familiarity ſhewn to me, and ſome others of his
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              quaintance he proveth, how that the acceleration of the right
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              tion of grave bodies, is made according to the numbers uneven
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              beginning
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              ab unitate,
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              that is, any number of equal times being
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              ſigned, if in the firſt time the moveable departing from reſt ſhall
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                <arrow.to.target n="marg397"/>
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              have paſſed ſuch a certain ſpace, as for example, an ell, in the
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              cond time it ſhall have paſſed three ells, in the third five, in the
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              fourth ſeven, and ſo progreſſively, according to the following odd
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              numbers; which in ſhort is the ſame, as if I ſhould ſay, that the
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              ſpaces paſſed by the moveable departing from its reſt, are unto
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                <arrow.to.target n="marg398"/>
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              each other in proportion double to the proportion of the times,
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              in which thoſe ſpaces are meaſured; or we will ſay, that the
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              ſpaces paſſed are to each other, as the ſquares of their times.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg394"/>
                <emph type="italics"/>
              An exact
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              pute of the time of
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              the fall of the
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              non bullet from the
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              Moons concave to
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              the Earths centre.
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              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg395"/>
              * The Author.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg396"/>
              * By theſe
                <emph type="italics"/>
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              tings,
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              he every
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              where meanes his
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              Dialogues,
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              De
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              tu,
                <emph.end type="italics"/>
              which I promiſe
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              to give you in my
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              ſecond Volume.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg397"/>
                <emph type="italics"/>
              Acceleration of
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              the natural motion
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              of grave bodies is
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              made according to
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              the odde numbers
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              beginning at unity.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg398"/>
                <emph type="italics"/>
              The ſpaces paſt
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              by the falling
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              grave body are as
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              the ſquares of their
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              times.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>SAGR. </s>
              <s>This is truly admirable: and do you ſay that there is
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              a Mathematical demonſtration for it?</s>
            </p>
            <p type="main">
              <s>SALV. Yes, purely Mathematical; and not onely for this, but
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              for many other very admirable paſſions, pertaining to natural
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              tions, and to projects alſo, all invented, and demonſtrated by
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              Our
                <emph.end type="italics"/>
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                <arrow.to.target n="marg399"/>
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                <emph type="italics"/>
              Friend,
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              and I have ſeen and conſidered them all to my very great
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              content and admiration, ſeeing a new compleat Doctrine to ſpring
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              up touching a ſubject, upon which have been written hundreds of </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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