Galilei, Galileo, The systems of the world, 1661

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    <archimedes>
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            <p type="main">
              <s>
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              Moreover in the fourth Text; doth he not after ſome other Do­
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              ctrines, prove it by another demonſtration?
                <emph type="italics"/>
              Scilicet,
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              That no tran­
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              ſition is made but according to ſome defect (and ſo there is a tran­
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              ſition or paſſing from the line to the ſuperficies, becauſe the line is
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              defective in breadth) and that it is impoſſible for the perfect to
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              want any thing, it being every way ſo; therefore there is no tran­
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              ſition from the Solid or Body to any other magnitude. </s>
              <s>Now
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              think you not that by all theſe places he hath ſufficiently proved,
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              how that there's no going beyond the three dimenſions, Length,
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              Breadth, and Thickneſs, and that therefore the body or ſolid,
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              which hath them all, is perfect?</s>
            </p>
            <p type="margin">
              <s>
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              Ariſtotles
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              demon­
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              ſtrations to prove
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              the dimenſions to be
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              three and no more.
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              </s>
            </p>
            <p type="margin">
              <s>
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                <emph type="italics"/>
              The number three
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              celebrated among ſt
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              the
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              Pythagorians</s>
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            <p type="margin">
              <s>
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              Omne, Totum &
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              Perfectum.</s>
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            <p type="margin">
              <s>
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              Or Solid.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>To tell you true, I think not my ſelf bound by all theſe
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              reaſons to grant any more but onely this, That that which hath
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              beginning, middle, and end, may, and ought to be called perfect: But
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              that then, becauſe beginning, middle, and end, are Three, the num­
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              ber Three is a perfect number, and hath a faculty of conferring
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                <emph type="italics"/>
              Perfection
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              on thoſe things that have the ſame, I find no inducement
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              to grant; neither do I underſtand, nor believe that, for example,
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              of feet, the number three is more perfect then four or two, nor do
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              I conceive the number four to be any imperfection to the Ele­
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              ments: and that they would be more perfect if they were three.
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              </s>
              <s>Better therefore it had been to have left theſe ſubtleties to the
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                <emph type="italics"/>
              Rhetoricians,
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              and to have proved his intent, by neceſſary demonſtra­
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              tion; for ſo it behoves to do in demonſtrative ſciences.</s>
            </p>
            <p type="main">
              <s>SIMPL. </s>
              <s>You ſeem to ſcorn theſe reaſons, and yet it is all the
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              Doctrine of the
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              Pythagorians,
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              who attribute ſo much to numbers;
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              and you that be a
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              Mathematician,
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              and believe many opinions in
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              the
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              Pythagorick
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              Philoſophy, ſeem now to contemn their My­
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              ſteries.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>That the
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              Pythagorians
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              had the ſcience of numbers in
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              high eſteem, and that
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              Plato
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              himſelf admired humane underſtand­
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              ing, and thought that it pertook of Divinity, for that it under­
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                <arrow.to.target n="marg10"/>
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              ſtood the nature of numbers, I know very well, nor ſhould I be
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              far from being of the ſame opinion: But that the Myſteries for
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              which
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              Pythagoras
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              and his ſect, had the Science of numbers in ſuch
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              veneration, are the follies that abound in the mouths and writings
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                <arrow.to.target n="marg11"/>
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              of the vulgar, I no waies credit: but rather becauſe I know that they,
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              to the end admirable things might not be expoſed to the con­
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              tempt, and ſcorne of the vulgar, cenſured as ſacrilegious, the pub­
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                <arrow.to.target n="marg12"/>
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              liſhing of the abſtruce properties of Numbers, and incommen­
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              ſurable and irrational quantities, by them inveſtigated; and di­
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              vulged, that he who diſcovered them, was tormented in the other
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              World: I believe that ſome one of them to deter the common
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              ſort, and free himſelf from their inquiſitiveneſs, told them that the
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              myſteries of numbers were thoſe trifles, which afterwards did ſo </s>
            </p>
          </chap>
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    </archimedes>