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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            and DF = the Difference of the ſemidiameters of the 1ſt and 3d, and through A
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            deſcribe a circle which ſhall touch the two auxiliary ones externally.</s>
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          <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,
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            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>
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          <p>
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              <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
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            of the 1ſt and 3d reſpectively; </s>
            <s xml:id="echoid-s590" xml:space="preserve">and through A deſcribe a circle which ſhall touch
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            the two auxiliary ones externally.</s>
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              <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
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            DF = the ſums as in Caſe 3d, but through A deſcribe a circle which ſhall touch
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            and include the two auxiliary ones.</s>
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