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

List of thumbnails

< >
21
21 ((9)) 		22
22 ((10))
23
23 ((11)) 		24
24 ((12))
25
25 ((13)) 		26
26 ((14))
27
27 ((15)) 		28
28 ((16))
29
29 ((17)) 		30
30
< >
page |< < ((13)) of 161 > >|
    <echo version="1.0RC">
      <text xml:lang="en" type="free">
        <div xml:id="echoid-div29" type="section" level="1" n="29">
          <p>
            <s xml:id="echoid-s581" xml:space="preserve">
              <pb o="(13)" file="0025" n="25"/>
            and DF = the Difference of the ſemidiameters of the 1ſt and 3d, and through A
              <lb/>
            deſcribe a circle which ſhall touch the two auxiliary ones externally.</s>
            <s xml:id="echoid-s582" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s583" xml:space="preserve">
              <emph style="sc">Case</emph>
            2d. </s>
            <s xml:id="echoid-s584" xml:space="preserve">If it be required that the circle ſhould touch all the other three
              <lb/>
            externally; </s>
            <s xml:id="echoid-s585" xml:space="preserve">then the circles being the ſame as before in reſpect to their magnitude,
              <lb/>
            let BG and DF be alſo the ſame as in the 1ſt Caſe, but through A deſcribe a circle
              <lb/>
            which ſhall touch and include the two auxiliary ones.</s>
            <s xml:id="echoid-s586" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s587" xml:space="preserve">
              <emph style="sc">Case</emph>
            3d. </s>
            <s xml:id="echoid-s588" xml:space="preserve">If it be required that the circle ſhould touch and include one of the
              <lb/>
            given circles A, and touch the other two externally; </s>
            <s xml:id="echoid-s589" xml:space="preserve">then let BG and DF = the
              <lb/>
            the ſum of the ſemidiameters of the 1ſt and 2d, and ſum of the ſemidiameters of
              <lb/>
            of the 1ſt and 3d reſpectively; </s>
            <s xml:id="echoid-s590" xml:space="preserve">and through A deſcribe a circle which ſhall touch
              <lb/>
            the two auxiliary ones externally.</s>
            <s xml:id="echoid-s591" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s592" xml:space="preserve">
              <emph style="sc">Case</emph>
            4th. </s>
            <s xml:id="echoid-s593" xml:space="preserve">If it be required that the circle ſhould touch externally one of the
              <lb/>
            given circles A, and ſhould touch and include the other two; </s>
            <s xml:id="echoid-s594" xml:space="preserve">then let BG and
              <lb/>
            DF = the ſums as in Caſe 3d, but through A deſcribe a circle which ſhall touch
              <lb/>
            and include the two auxiliary ones.</s>
            <s xml:id="echoid-s595" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum