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

Table of Notes

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            <lb/>
          84. S
            <emph style="sub">2</emph>
          + n
            <emph style="sub">2</emph>
          . m - n.
            <lb/>
          85. S
            <emph style="sub">2</emph>
          + n
            <emph style="sub">2</emph>
          : m
            <emph style="sub">2</emph>
          - n
            <emph style="sub">2</emph>
          . any other.
            <lb/>
          86. S
            <emph style="sub">2</emph>
          + n
            <emph style="sub">2</emph>
          : m
            <emph style="sub">2</emph>
          + 2n
            <emph style="sub">2</emph>
          . any other.
            <lb/>
          87. s
            <emph style="sub">2</emph>
          + n
            <emph style="sub">2</emph>
          : m
            <emph style="sub">2</emph>
          - n
            <emph style="sub">2</emph>
          . any other.
            <lb/>
          88. m - n. m
            <emph style="sub">2</emph>
          - n
            <emph style="sub">2</emph>
          .
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s3166" xml:space="preserve">89. </s>
            <s xml:id="echoid-s3167" xml:space="preserve">Ar. </s>
            <s xml:id="echoid-s3168" xml:space="preserve">Sides in arithmetical progreſſion.</s>
            <s xml:id="echoid-s3169" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3170" xml:space="preserve">Simp. </s>
            <s xml:id="echoid-s3171" xml:space="preserve">Alg. </s>
            <s xml:id="echoid-s3172" xml:space="preserve">pr. </s>
            <s xml:id="echoid-s3173" xml:space="preserve">36. </s>
            <s xml:id="echoid-s3174" xml:space="preserve">- Simp. </s>
            <s xml:id="echoid-s3175" xml:space="preserve">Sel. </s>
            <s xml:id="echoid-s3176" xml:space="preserve">Ex. </s>
            <s xml:id="echoid-s3177" xml:space="preserve">pr. </s>
            <s xml:id="echoid-s3178" xml:space="preserve">45.</s>
            <s xml:id="echoid-s3179" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3180" xml:space="preserve">90. </s>
            <s xml:id="echoid-s3181" xml:space="preserve">Ar. </s>
            <s xml:id="echoid-s3182" xml:space="preserve">Sides in geom. </s>
            <s xml:id="echoid-s3183" xml:space="preserve">progreffion.</s>
            <s xml:id="echoid-s3184" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3185" xml:space="preserve">Wolfiu’s Alg. </s>
            <s xml:id="echoid-s3186" xml:space="preserve">pr. </s>
            <s xml:id="echoid-s3187" xml:space="preserve">114. </s>
            <s xml:id="echoid-s3188" xml:space="preserve">- Simps. </s>
            <s xml:id="echoid-s3189" xml:space="preserve">Sel. </s>
            <s xml:id="echoid-s3190" xml:space="preserve">Ex. </s>
            <s xml:id="echoid-s3191" xml:space="preserve">pr.
              <lb/>
            </s>
            <s xml:id="echoid-s3192" xml:space="preserve">46. </s>
            <s xml:id="echoid-s3193" xml:space="preserve">- Vieta Iſt. </s>
            <s xml:id="echoid-s3194" xml:space="preserve">App. </s>
            <s xml:id="echoid-s3195" xml:space="preserve">to Apoll. </s>
            <s xml:id="echoid-s3196" xml:space="preserve">Gallus, pr. </s>
            <s xml:id="echoid-s3197" xml:space="preserve">7.</s>
            <s xml:id="echoid-s3198" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3199" xml:space="preserve">91. </s>
            <s xml:id="echoid-s3200" xml:space="preserve">Per. </s>
            <s xml:id="echoid-s3201" xml:space="preserve">Sides in geom. </s>
            <s xml:id="echoid-s3202" xml:space="preserve">progreſſion.</s>
            <s xml:id="echoid-s3203" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3204" xml:space="preserve">Simps. </s>
            <s xml:id="echoid-s3205" xml:space="preserve">Alg. </s>
            <s xml:id="echoid-s3206" xml:space="preserve">pr. </s>
            <s xml:id="echoid-s3207" xml:space="preserve">39.</s>
            <s xml:id="echoid-s3208" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3209" xml:space="preserve">92. </s>
            <s xml:id="echoid-s3210" xml:space="preserve">I biſecting an acute angle. </s>
            <s xml:id="echoid-s3211" xml:space="preserve">I from right angle biſecting the foregoing given line.</s>
            <s xml:id="echoid-s3212" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3213" xml:space="preserve">Gent. </s>
            <s xml:id="echoid-s3214" xml:space="preserve">Diary, qu. </s>
            <s xml:id="echoid-s3215" xml:space="preserve">266.</s>
            <s xml:id="echoid-s3216" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3217" xml:space="preserve">93. </s>
            <s xml:id="echoid-s3218" xml:space="preserve">H. </s>
            <s xml:id="echoid-s3219" xml:space="preserve">Part of S adjacent to the right angle intercepted by a perpendicular to H
              <lb/>
            from middle of H.</s>
            <s xml:id="echoid-s3220" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3221" xml:space="preserve">L. </s>
            <s xml:id="echoid-s3222" xml:space="preserve">Diary, qu. </s>
            <s xml:id="echoid-s3223" xml:space="preserve">633.</s>
            <s xml:id="echoid-s3224" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3225" xml:space="preserve">94. </s>
            <s xml:id="echoid-s3226" xml:space="preserve">One leg and a line parallel thereto intercepted by the hypothenuſe and
              <lb/>
            the other leg being given; </s>
            <s xml:id="echoid-s3227" xml:space="preserve">to determine the triangle ſuch, that the rectangle un-
              <lb/>
            der the hypothenuſe and a line from the acute angle, adjacent to the given leg,
              <lb/>
            to the point of interſection of the parallel and the other leg may be of a given
              <lb/>
            magnitude.</s>
            <s xml:id="echoid-s3228" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3229" xml:space="preserve">L. </s>
            <s xml:id="echoid-s3230" xml:space="preserve">Diary. </s>
            <s xml:id="echoid-s3231" xml:space="preserve">qu. </s>
            <s xml:id="echoid-s3232" xml:space="preserve">648.</s>
            <s xml:id="echoid-s3233" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3234" xml:space="preserve">N. </s>
            <s xml:id="echoid-s3235" xml:space="preserve">B. </s>
            <s xml:id="echoid-s3236" xml:space="preserve">In all the Nos. </s>
            <s xml:id="echoid-s3237" xml:space="preserve">from 28 to 52 incluſive, S may be changed for s, and m
              <lb/>
            for n, though this be not expreſſed as in others.</s>
            <s xml:id="echoid-s3238" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div106" type="section" level="1" n="98">
          <head xml:id="echoid-head117" style="it" xml:space="preserve">FINIS.</head>
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