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

Page concordance

< >
Scan Original
31 (19)
32 (20)
33 (21)
34 (22)
35 (23)
36 (24)
37 (25)
38 (26)
39 (27)
40 (28)
41 (29)
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
< >
page |< < ((19)) of 161 > >|
    <echo version="1.0RC">
      <text xml:lang="en" type="free">
        <div xml:id="echoid-div36" type="section" level="1" n="36">
          <pb o="(19)" file="0031" n="31"/>
        </div>
        <div xml:id="echoid-div37" type="section" level="1" n="37">
          <head xml:id="echoid-head43" xml:space="preserve">A SECOND
            <lb/>
          SUPPLEMENT,
            <lb/>
          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>
            <s xml:id="echoid-s695" xml:space="preserve"/>
          </p>
          <p>
            <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>
          </p>
        </div>
      </text>
    </echo>
Impressum