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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        <div xml:id="echoid-div102" type="section" level="1" n="95">
          <pb o="[9]" file="0137" n="149"/>
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        <div xml:id="echoid-div103" type="section" level="1" n="96">
          <head xml:id="echoid-head115" xml:space="preserve">Continuation of the
            <emph style="sc">Synopsis</emph>
          ,
            <lb/>
          Containing ſuch Data as cannot readily be expreſſed by the
            <lb/>
          Symbols before uſed without more words at length.</head>
          <p>
            <s xml:id="echoid-s2773" xml:space="preserve">124. </s>
            <s xml:id="echoid-s2774" xml:space="preserve">IT is required to conſtruct an iſoceles triangle ſuch, as to have its equal legs
              <lb/>
            to a given line, and moreover ſuppoſing a circle inſcribed therein, and a di-
              <lb/>
            ameter thereof drawn parallel to the baſe, and continued to meet the equal legs;
              <lb/>
            </s>
            <s xml:id="echoid-s2775" xml:space="preserve">ſuch line ſhall divide the area in a given ratio.</s>
            <s xml:id="echoid-s2776" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2777" xml:space="preserve">Rudd’s Prac. </s>
            <s xml:id="echoid-s2778" xml:space="preserve">Geom. </s>
            <s xml:id="echoid-s2779" xml:space="preserve">part 2d, qu. </s>
            <s xml:id="echoid-s2780" xml:space="preserve">4
              <emph style="sub">6</emph>
            . </s>
            <s xml:id="echoid-s2781" xml:space="preserve">- Supp. </s>
            <s xml:id="echoid-s2782" xml:space="preserve">to Gent. </s>
            <s xml:id="echoid-s2783" xml:space="preserve">Diary, 1741, 1742, qu. </s>
            <s xml:id="echoid-s2784" xml:space="preserve">II.</s>
            <s xml:id="echoid-s2785" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2786" xml:space="preserve">125. </s>
            <s xml:id="echoid-s2787" xml:space="preserve">In a plane triangle, ABC, there is given the angle
              <lb/>
              <figure xlink:label="fig-0137-01" xlink:href="fig-0137-01a" number="26">
                <image file="0137-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0137-01"/>
              </figure>
            at C, and the parts or ſegments of the baſe AD, AE;
              <lb/>
            </s>
            <s xml:id="echoid-s2788" xml:space="preserve">to conſtruct the triangle ſo, that if BD be drawn, the
              <lb/>
            angle ABD may be a maximum, and BC to EC in
              <lb/>
            a given ratio.</s>
            <s xml:id="echoid-s2789" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2790" xml:space="preserve">L. </s>
            <s xml:id="echoid-s2791" xml:space="preserve">Diary, 1773, qu. </s>
            <s xml:id="echoid-s2792" xml:space="preserve">659.</s>
            <s xml:id="echoid-s2793" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2794" xml:space="preserve">126. </s>
            <s xml:id="echoid-s2795" xml:space="preserve">V. </s>
            <s xml:id="echoid-s2796" xml:space="preserve">B. </s>
            <s xml:id="echoid-s2797" xml:space="preserve">Line from A or a to divide S or s in a given ratio.</s>
            <s xml:id="echoid-s2798" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2799" xml:space="preserve">Town and Coun. </s>
            <s xml:id="echoid-s2800" xml:space="preserve">Mag. </s>
            <s xml:id="echoid-s2801" xml:space="preserve">Dec. </s>
            <s xml:id="echoid-s2802" xml:space="preserve">1772.</s>
            <s xml:id="echoid-s2803" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2804" xml:space="preserve">127. </s>
            <s xml:id="echoid-s2805" xml:space="preserve">V. </s>
            <s xml:id="echoid-s2806" xml:space="preserve">B. </s>
            <s xml:id="echoid-s2807" xml:space="preserve">Difference of two lines from the angles at the baſe to the centre of the
              <lb/>
            inſcribed ☉(sun).</s>
            <s xml:id="echoid-s2808" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2809" xml:space="preserve">*Simpſon’s Sel. </s>
            <s xml:id="echoid-s2810" xml:space="preserve">Ex. </s>
            <s xml:id="echoid-s2811" xml:space="preserve">pr. </s>
            <s xml:id="echoid-s2812" xml:space="preserve">18.</s>
            <s xml:id="echoid-s2813" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2814" xml:space="preserve">128. </s>
            <s xml:id="echoid-s2815" xml:space="preserve">V. </s>
            <s xml:id="echoid-s2816" xml:space="preserve">B. </s>
            <s xml:id="echoid-s2817" xml:space="preserve">Two lines from A and a meeting in a point O given in poſition, as alſo
              <lb/>
            the angle of a line from V to O with either of the ſides about the vertical angle.</s>
            <s xml:id="echoid-s2818" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2819" xml:space="preserve">Mis. </s>
            <s xml:id="echoid-s2820" xml:space="preserve">Cur. </s>
            <s xml:id="echoid-s2821" xml:space="preserve">Math. </s>
            <s xml:id="echoid-s2822" xml:space="preserve">qu. </s>
            <s xml:id="echoid-s2823" xml:space="preserve">107.</s>
            <s xml:id="echoid-s2824" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2825" xml:space="preserve">129. </s>
            <s xml:id="echoid-s2826" xml:space="preserve">V. </s>
            <s xml:id="echoid-s2827" xml:space="preserve">A point in B. </s>
            <s xml:id="echoid-s2828" xml:space="preserve">Rect. </s>
            <s xml:id="echoid-s2829" xml:space="preserve">of the ſegments of B made by that point.</s>
            <s xml:id="echoid-s2830" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2831" xml:space="preserve">Simp. </s>
            <s xml:id="echoid-s2832" xml:space="preserve">Sel. </s>
            <s xml:id="echoid-s2833" xml:space="preserve">Ex. </s>
            <s xml:id="echoid-s2834" xml:space="preserve">pr. </s>
            <s xml:id="echoid-s2835" xml:space="preserve">44.</s>
            <s xml:id="echoid-s2836" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2837" xml:space="preserve">130. </s>
            <s xml:id="echoid-s2838" xml:space="preserve">Poſition of a line through V. </s>
            <s xml:id="echoid-s2839" xml:space="preserve">B. </s>
            <s xml:id="echoid-s2840" xml:space="preserve">S - s.</s>
            <s xml:id="echoid-s2841" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2842" xml:space="preserve">Simp. </s>
            <s xml:id="echoid-s2843" xml:space="preserve">Sel. </s>
            <s xml:id="echoid-s2844" xml:space="preserve">Ex. </s>
            <s xml:id="echoid-s2845" xml:space="preserve">pr. </s>
            <s xml:id="echoid-s2846" xml:space="preserve">49.</s>
            <s xml:id="echoid-s2847" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2848" xml:space="preserve">131. </s>
            <s xml:id="echoid-s2849" xml:space="preserve">Poſition of a line through V. </s>
            <s xml:id="echoid-s2850" xml:space="preserve">B. </s>
            <s xml:id="echoid-s2851" xml:space="preserve">S, line biſect. </s>
            <s xml:id="echoid-s2852" xml:space="preserve">B, & </s>
            <s xml:id="echoid-s2853" xml:space="preserve">s in geometrical progreſſion.</s>
            <s xml:id="echoid-s2854" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2855" xml:space="preserve">Simp. </s>
            <s xml:id="echoid-s2856" xml:space="preserve">Sel. </s>
            <s xml:id="echoid-s2857" xml:space="preserve">Ex. </s>
            <s xml:id="echoid-s2858" xml:space="preserve">pr. </s>
            <s xml:id="echoid-s2859" xml:space="preserve">51.</s>
            <s xml:id="echoid-s2860" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2861" xml:space="preserve">132. </s>
            <s xml:id="echoid-s2862" xml:space="preserve">V. </s>
            <s xml:id="echoid-s2863" xml:space="preserve">S. </s>
            <s xml:id="echoid-s2864" xml:space="preserve">The angle of a line from extreme of S with the baſe, and ſegment of
              <lb/>
            s cut off thereby adjacent to the baſe.</s>
            <s xml:id="echoid-s2865" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2866" xml:space="preserve">*Mis. </s>
            <s xml:id="echoid-s2867" xml:space="preserve">Cur. </s>
            <s xml:id="echoid-s2868" xml:space="preserve">Math. </s>
            <s xml:id="echoid-s2869" xml:space="preserve">Vol. </s>
            <s xml:id="echoid-s2870" xml:space="preserve">II. </s>
            <s xml:id="echoid-s2871" xml:space="preserve">qu. </s>
            <s xml:id="echoid-s2872" xml:space="preserve">30.</s>
            <s xml:id="echoid-s2873" xml:space="preserve"/>
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