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

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="040/01/201.jpg" pagenum="183"/>
              But the curve-line A C B, is greater than the two right-lines A C,
                <lb/>
              and C B; therefore,
                <emph type="italics"/>
              à fortiori,
                <emph.end type="italics"/>
              the curve-line A C B, is much
                <lb/>
              greater than the right line A B, which was to be
                <lb/>
                <arrow.to.target n="marg372"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg371"/>
                <emph type="italics"/>
              The
                <lb/>
              tion of a
                <lb/>
              tick, to prove the
                <lb/>
              right line to be the
                <lb/>
              ſhorteſt of all lines.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg372"/>
                <emph type="italics"/>
              The Paralogiſm
                <lb/>
              of the ſame
                <lb/>
              tetick, which
                <lb/>
              veth
                <emph.end type="italics"/>
              ignotum per
                <lb/>
              ignotius.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>I do not think that if one ſhould ranſack all the
                <lb/>
              logiſms of the world, there could be found one more commodious
                <lb/>
              than this, to give an example of the moſt ſolemn fallacy of all
                <lb/>
              fallacies, namely, than that which proveth
                <emph type="italics"/>
              ignotum per ignotius.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>SIMP. </s>
              <s>How ſo?</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>Do you ask me how ſo? </s>
              <s>The unknown concluſion
                <lb/>
              which you deſire to prove, is it not, that the curved line A C B, is
                <lb/>
              longer than the right line A B; the middle term which is taken
                <lb/>
              for known, is that the curve-line A C B, is greater than the two
                <lb/>
              lines A C and C B, the which are known to be greater than A B;
                <lb/>
              And if it be unknown whether the curve-line be greater than the
                <lb/>
              ſingle right-line A B, ſhall it not be much more unknown whether
                <lb/>
              it be greater than the two right lines A C & C B, which are known
                <lb/>
              to be greater than the ſole line A B, & yet you aſſume it as known?</s>
            </p>
            <p type="main">
              <s>SIMP. </s>
              <s>I do not yet very well perceive wherein lyeth the
                <lb/>
              lacy.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>As the two right lines are greater than A B, (as may be
                <lb/>
              known by
                <emph type="italics"/>
              Euclid
                <emph.end type="italics"/>
              ) and in as much as the curve line is longer than
                <lb/>
              the two right lines A C and B C, ſhall it not not be much greater
                <lb/>
              than the ſole right line A B?</s>
            </p>
            <p type="main">
              <s>SIMP. </s>
              <s>It ſhall ſo.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>That the curve-line A C B, is greater than the right
                <lb/>
              line A B, is the concluſion more known than the middle term,
                <lb/>
              which is, that the ſame curve-line is greater than the two
                <lb/>
              lines A C and C B. </s>
              <s>Now when the middle term is leſs known
                <lb/>
              than the concluſion, it is called a proving
                <emph type="italics"/>
              ignotum per ignotius.
                <emph.end type="italics"/>
                <lb/>
              But to return to our purpoſe, it is ſufficient that you know the
                <lb/>
              right line to be the ſhorteſt of all the lines that can be drawn
                <lb/>
              tween two points. </s>
              <s>And as to the principal concluſion, you ſay,
                <lb/>
              that the material ſphere doth not touch the ſphere in one ſole
                <lb/>
              point. </s>
              <s>What then is its contact?</s>
            </p>
            <p type="main">
              <s>SIMP. </s>
              <s>It ſhall be a part of its ſuperficies.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>And the contact likewiſe of another ſphere equal to the
                <lb/>
              firſt, ſhall be alſo a like particle of its ſuperficies?</s>
            </p>
            <p type="main">
              <s>SIMP. </s>
              <s>There is no reaſon vvhy it ſhould be othervviſe.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>Then the tvvo ſpheres vvhich touch each other, ſhall
                <lb/>
              touch vvith the tvvo ſame particles of a ſuperficies, for each of them
                <lb/>
              agreeing to one and the ſame plane, they muſt of neceſſity agree
                <lb/>
              in like manner to each other. </s>
              <s>Imagine now that the two ſpheres </s>
            </p>
            <p type="main">
              <s>
                <arrow.to.target n="marg373"/>
                <lb/>
              [
                <emph type="italics"/>
              in Fig.
                <emph.end type="italics"/>
              6.] whoſe centres are A and B, do touch one another:
                <lb/>
              and let their centres be conjoyned by the right line A B, which
                <lb/>
              paſſeth through the contact. </s>
              <s>It paſſeth thorow the point C, and </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>