Apollonius <Pergaeus>; Lawson, John, The two books of Apollonius Pergaeus, concerning tangencies, as they have been restored by Franciscus Vieta and Marinus Ghetaldus : with a supplement to which is now added, a second supplement, being Mons. Fermat's Treatise on spherical tangencies

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          <head xml:id="echoid-head43" xml:space="preserve">A SECOND
            <lb/>
          SUPPLEMENT,
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          BEING
            <lb/>
          Monſ. DE FERMAT’S Treatiſe on
            <lb/>
          Spherical Tangencies.</head>
          <head xml:id="echoid-head44" xml:space="preserve">PROBLEM I.</head>
          <p>
            <s xml:id="echoid-s694" xml:space="preserve">HAVING four points N, O, M, F, given, to deſcribe a ſphere which
              <lb/>
            ſhall paſs through them all.</s>
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            <s xml:id="echoid-s696" xml:space="preserve">
              <emph style="sc">Taking</emph>
            any three of them N, O, M, ad libitum, they will form a triangle,
              <lb/>
            about which a circle ANOM may be circumſcribed, which will be given in
              <lb/>
            magnitude and poſition. </s>
            <s xml:id="echoid-s697" xml:space="preserve">That this circle is in the ſurface of the ſphere
              <lb/>
            ſought appears from hence; </s>
            <s xml:id="echoid-s698" xml:space="preserve">becauſe if a ſphere be cut by any plane, the
              <lb/>
            ſection will be a circle; </s>
            <s xml:id="echoid-s699" xml:space="preserve">but only one circle can be drawn to paſs through the
              <lb/>
            three given points N, O, M; </s>
            <s xml:id="echoid-s700" xml:space="preserve">therefore this circle muſt be in the ſurface of
              <lb/>
            the ſphere. </s>
            <s xml:id="echoid-s701" xml:space="preserve">Let the center of this circle be C, from whence let CB be
              <lb/>
            erected perpendicular to it’s plane; </s>
            <s xml:id="echoid-s702" xml:space="preserve">it is evident that the center of the ſphere
              <lb/>
            ſought will be in this line CB. </s>
            <s xml:id="echoid-s703" xml:space="preserve">From the fourth given point F let FB be
              <lb/>
            drawn perpendicular to CB, which FB will be alſo given in magnitude and
              <lb/>
            poſition. </s>
            <s xml:id="echoid-s704" xml:space="preserve">Through C draw ACD parallel to FB, and this line will be </s>
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