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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      <text xml:lang="en" type="free">
        <div xml:id="echoid-div105" type="section" level="1" n="97">
          <pb o="[13]" file="0141" n="153"/>
          <note position="right" xml:space="preserve">
            <lb/>
          9. H
            <emph style="sub">2</emph>
          : S x s. Any other datum.
            <lb/>
          10. H
            <emph style="sub">2</emph>
          : S
            <emph style="sub">2</emph>
          + m
            <emph style="sub">2</emph>
          , or H
            <emph style="sub">2</emph>
          : s
            <emph style="sub">2</emph>
          + n
            <emph style="sub">2</emph>
          . any other.
            <lb/>
          11. H + P. H x P.
            <lb/>
          12. H + P. H x P + P
            <emph style="sub">2</emph>
          .
            <lb/>
          13. H + P. S
            <emph style="sub">2</emph>
          + n
            <emph style="sub">2</emph>
          .
            <lb/>
          14. H + P. m
            <emph style="sub">2</emph>
          + n
            <emph style="sub">2</emph>
          .
            <lb/>
          15. H x P + P
            <emph style="sub">2</emph>
          . P.
            <lb/>
          16. H x P: S
            <emph style="sub">2</emph>
          + n
            <emph style="sub">2</emph>
          . any other.
            <lb/>
          17. H x P + P
            <emph style="sub">2</emph>
          : S
            <emph style="sub">2</emph>
          + n
            <emph style="sub">2</emph>
          . any other.
            <lb/>
          18. {1/2}H - P. S - s. # Turner’s Math. Ex. pr. 37.
            <lb/>
          19. H±S. m, or H±s. n.
            <lb/>
          20. H + S. n, or H + s. m.
            <lb/>
          21. H
            <emph style="sub">2</emph>
          + S
            <emph style="sub">2</emph>
          : P
            <emph style="sub">2</emph>
          , or H
            <emph style="sub">2</emph>
          + s
            <emph style="sub">2</emph>
          : P
            <emph style="sub">2</emph>
          . any other.
            <lb/>
          22. H
            <emph style="sub">2</emph>
          + S
            <emph style="sub">2</emph>
          : S
            <emph style="sub">2</emph>
          + m
            <emph style="sub">2</emph>
          , or H
            <emph style="sub">2</emph>
          + s
            <emph style="sub">2</emph>
          : s
            <emph style="sub">2</emph>
          + n
            <emph style="sub">2</emph>
          . any other.
            <lb/>
          23. H
            <emph style="sub">2</emph>
          + S
            <emph style="sub">2</emph>
          . m, or H
            <emph style="sub">2</emph>
          + s
            <emph style="sub">2</emph>
          . n.
            <lb/>
          24. H
            <emph style="sub">2</emph>
          + S
            <emph style="sub">2</emph>
          . n, or H
            <emph style="sub">2</emph>
          + s
            <emph style="sub">2</emph>
          . m.
            <lb/>
          25. H
            <emph style="sub">2</emph>
          + S
            <emph style="sub">2</emph>
          : m
            <emph style="sub">2</emph>
          , or H
            <emph style="sub">2</emph>
          + s
            <emph style="sub">2</emph>
          : n
            <emph style="sub">2</emph>
          . any other.
            <lb/>
          26. H x S. s. or Hxs. S. # D’Omerique L. III. pr. 37. - Vieta Geo. \\ Eff. pr. 18. - Oughtred, ch. 19, pr. \\ 25. - Herigon Geo. planæ, pr. 9. - \\ Schooten, pr. 38.
            <lb/>
          27. H x S: s
            <emph style="sub">2</emph>
          , or H x s: S
            <emph style="sub">2</emph>
          . any other
            <lb/>
          28. H + S + m. H
            <emph style="sub">2</emph>
          + S
            <emph style="sub">2</emph>
          + m
            <emph style="sub">2</emph>
          .
            <lb/>
          29. H + S + m. H x S + S x m + S
            <emph style="sub">2</emph>
          .
            <lb/>
          30. H + S + m. H x S + S x m.
            <lb/>
          31. H + S + m. H
            <emph style="sub">2</emph>
          + m
            <emph style="sub">2</emph>
          .
            <lb/>
          32. H
            <emph style="sub">2</emph>
          + S
            <emph style="sub">2</emph>
          + m
            <emph style="sub">2</emph>
          : H x S + S x m. any other.
            <lb/>
          33. H
            <emph style="sub">2</emph>
          + S
            <emph style="sub">2</emph>
          + m
            <emph style="sub">2</emph>
          : H x S + S x m + S
            <emph style="sub">2</emph>
          . any other.
            <lb/>
          </note>
        </div>
      </text>
    </echo>
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