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 contents

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        <div xml:id="echoid-div103" type="section" level="1" n="96">
          <pb o="[11]" file="0139" n="151"/>
          <p>
            <s xml:id="echoid-s3019" xml:space="preserve">148. </s>
            <s xml:id="echoid-s3020" xml:space="preserve">S. </s>
            <s xml:id="echoid-s3021" xml:space="preserve">s. </s>
            <s xml:id="echoid-s3022" xml:space="preserve">Line from V making an angle with S=A.</s>
            <s xml:id="echoid-s3023" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3024" xml:space="preserve">Diarian Repoſitory, qu. </s>
            <s xml:id="echoid-s3025" xml:space="preserve">197.</s>
            <s xml:id="echoid-s3026" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3027" xml:space="preserve">149. </s>
            <s xml:id="echoid-s3028" xml:space="preserve">S. </s>
            <s xml:id="echoid-s3029" xml:space="preserve">m. </s>
            <s xml:id="echoid-s3030" xml:space="preserve">n, theſe being ſegments of B by l from V making a given angle with S.</s>
            <s xml:id="echoid-s3031" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3032" xml:space="preserve">T. </s>
            <s xml:id="echoid-s3033" xml:space="preserve">and Country Mag. </s>
            <s xml:id="echoid-s3034" xml:space="preserve">1769, pag 662.</s>
            <s xml:id="echoid-s3035" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3036" xml:space="preserve">150. </s>
            <s xml:id="echoid-s3037" xml:space="preserve">One angle at the baſe. </s>
            <s xml:id="echoid-s3038" xml:space="preserve">The ſi le adjacent. </s>
            <s xml:id="echoid-s3039" xml:space="preserve">The ratio of the other ſide to a line
              <lb/>
            drawn from V to an unknown point in B, and the length of a line drawn from
              <lb/>
            the ſaid point parallel to the given ſide to terminate in the unknown ſide.</s>
            <s xml:id="echoid-s3040" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3041" xml:space="preserve">Hutton’s Miſc. </s>
            <s xml:id="echoid-s3042" xml:space="preserve">qu. </s>
            <s xml:id="echoid-s3043" xml:space="preserve">23.</s>
            <s xml:id="echoid-s3044" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3045" xml:space="preserve">151. </s>
            <s xml:id="echoid-s3046" xml:space="preserve">A - a. </s>
            <s xml:id="echoid-s3047" xml:space="preserve">R. </s>
            <s xml:id="echoid-s3048" xml:space="preserve">Line from centre of ins. </s>
            <s xml:id="echoid-s3049" xml:space="preserve">circle to middle of B.</s>
            <s xml:id="echoid-s3050" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3051" xml:space="preserve">Gent. </s>
            <s xml:id="echoid-s3052" xml:space="preserve">Diary, 1771 - 2, qu. </s>
            <s xml:id="echoid-s3053" xml:space="preserve">349.</s>
            <s xml:id="echoid-s3054" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3055" xml:space="preserve">152. </s>
            <s xml:id="echoid-s3056" xml:space="preserve">Three lines from the angles biſecting the oppoſite ſides.</s>
            <s xml:id="echoid-s3057" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3058" xml:space="preserve">Mathematician, pr. </s>
            <s xml:id="echoid-s3059" xml:space="preserve">48. </s>
            <s xml:id="echoid-s3060" xml:space="preserve">- Simp. </s>
            <s xml:id="echoid-s3061" xml:space="preserve">Sel. </s>
            <s xml:id="echoid-s3062" xml:space="preserve">Ex. </s>
            <s xml:id="echoid-s3063" xml:space="preserve">pr. </s>
            <s xml:id="echoid-s3064" xml:space="preserve">22. </s>
            <s xml:id="echoid-s3065" xml:space="preserve">\\ - Palladium, 1752. </s>
            <s xml:id="echoid-s3066" xml:space="preserve">qu. </s>
            <s xml:id="echoid-s3067" xml:space="preserve">43.</s>
            <s xml:id="echoid-s3068" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3069" xml:space="preserve">153. </s>
            <s xml:id="echoid-s3070" xml:space="preserve">Sxs: </s>
            <s xml:id="echoid-s3071" xml:space="preserve">mxn, ſegts by L. </s>
            <s xml:id="echoid-s3072" xml:space="preserve">m - n. </s>
            <s xml:id="echoid-s3073" xml:space="preserve">Angle made by L & </s>
            <s xml:id="echoid-s3074" xml:space="preserve">I biſecting the baſe.</s>
            <s xml:id="echoid-s3075" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3076" xml:space="preserve">Brit. </s>
            <s xml:id="echoid-s3077" xml:space="preserve">Oracle, qu. </s>
            <s xml:id="echoid-s3078" xml:space="preserve">93.</s>
            <s xml:id="echoid-s3079" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3080" xml:space="preserve">154. </s>
            <s xml:id="echoid-s3081" xml:space="preserve">The baſe of an iſoceles triangle, and the diſtance of the vertical angle from
              <lb/>
            the foot of a perpendicular from one of the equal angles upon the oppoſite ſide.</s>
            <s xml:id="echoid-s3082" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3083" xml:space="preserve">Brit. </s>
            <s xml:id="echoid-s3084" xml:space="preserve">Oracle, qu. </s>
            <s xml:id="echoid-s3085" xml:space="preserve">8.</s>
            <s xml:id="echoid-s3086" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3087" xml:space="preserve">155. </s>
            <s xml:id="echoid-s3088" xml:space="preserve">P - n. </s>
            <s xml:id="echoid-s3089" xml:space="preserve">m of an iſoceles triangle, m and n being ſegts. </s>
            <s xml:id="echoid-s3090" xml:space="preserve">by a perpendicular from
              <lb/>
            one of the angles at the baſe on one of the equal ſides.</s>
            <s xml:id="echoid-s3091" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3092" xml:space="preserve">Court Mag. </s>
            <s xml:id="echoid-s3093" xml:space="preserve">Sep. </s>
            <s xml:id="echoid-s3094" xml:space="preserve">1761.</s>
            <s xml:id="echoid-s3095" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3096" xml:space="preserve">156. </s>
            <s xml:id="echoid-s3097" xml:space="preserve">V. </s>
            <s xml:id="echoid-s3098" xml:space="preserve">Line biſecting A or a. </s>
            <s xml:id="echoid-s3099" xml:space="preserve">Neareſt diſtance from V to periphery of ins. </s>
            <s xml:id="echoid-s3100" xml:space="preserve">☉(sun).</s>
            <s xml:id="echoid-s3101" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3102" xml:space="preserve">*Gent. </s>
            <s xml:id="echoid-s3103" xml:space="preserve">Diary, qu. </s>
            <s xml:id="echoid-s3104" xml:space="preserve">129.</s>
            <s xml:id="echoid-s3105" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3106" xml:space="preserve">157. </s>
            <s xml:id="echoid-s3107" xml:space="preserve">V. </s>
            <s xml:id="echoid-s3108" xml:space="preserve">The ſegments of S made by a line drawn from A to make a given angle
              <lb/>
            with B.</s>
            <s xml:id="echoid-s3109" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3110" xml:space="preserve">*Mis. </s>
            <s xml:id="echoid-s3111" xml:space="preserve">Cur. </s>
            <s xml:id="echoid-s3112" xml:space="preserve">Math. </s>
            <s xml:id="echoid-s3113" xml:space="preserve">Vol. </s>
            <s xml:id="echoid-s3114" xml:space="preserve">I. </s>
            <s xml:id="echoid-s3115" xml:space="preserve">qu. </s>
            <s xml:id="echoid-s3116" xml:space="preserve">79.</s>
            <s xml:id="echoid-s3117" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3118" xml:space="preserve">158. </s>
            <s xml:id="echoid-s3119" xml:space="preserve">V. </s>
            <s xml:id="echoid-s3120" xml:space="preserve">B. </s>
            <s xml:id="echoid-s3121" xml:space="preserve">Line from A or a to the centre of inſcribed circle.</s>
            <s xml:id="echoid-s3122" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3123" xml:space="preserve">Mis. </s>
            <s xml:id="echoid-s3124" xml:space="preserve">Sci. </s>
            <s xml:id="echoid-s3125" xml:space="preserve">Cur. </s>
            <s xml:id="echoid-s3126" xml:space="preserve">qu. </s>
            <s xml:id="echoid-s3127" xml:space="preserve">53.</s>
            <s xml:id="echoid-s3128" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3129" xml:space="preserve">159. </s>
            <s xml:id="echoid-s3130" xml:space="preserve">B. </s>
            <s xml:id="echoid-s3131" xml:space="preserve">L. </s>
            <s xml:id="echoid-s3132" xml:space="preserve">Line from extremity of L parallel to S or s.</s>
            <s xml:id="echoid-s3133" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3134" xml:space="preserve">Math. </s>
            <s xml:id="echoid-s3135" xml:space="preserve">Mag. </s>
            <s xml:id="echoid-s3136" xml:space="preserve">No. </s>
            <s xml:id="echoid-s3137" xml:space="preserve">III. </s>
            <s xml:id="echoid-s3138" xml:space="preserve">prob. </s>
            <s xml:id="echoid-s3139" xml:space="preserve">7.</s>
            <s xml:id="echoid-s3140" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3141" xml:space="preserve">160. </s>
            <s xml:id="echoid-s3142" xml:space="preserve">V. </s>
            <s xml:id="echoid-s3143" xml:space="preserve">The ſegments of B made by a line dividing V into given angles.</s>
            <s xml:id="echoid-s3144" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3145" xml:space="preserve">Mis. </s>
            <s xml:id="echoid-s3146" xml:space="preserve">Cur. </s>
            <s xml:id="echoid-s3147" xml:space="preserve">Math. </s>
            <s xml:id="echoid-s3148" xml:space="preserve">Vol. </s>
            <s xml:id="echoid-s3149" xml:space="preserve">II. </s>
            <s xml:id="echoid-s3150" xml:space="preserve">qu. </s>
            <s xml:id="echoid-s3151" xml:space="preserve">48.</s>
            <s xml:id="echoid-s3152" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3153" xml:space="preserve">161. </s>
            <s xml:id="echoid-s3154" xml:space="preserve">V. </s>
            <s xml:id="echoid-s3155" xml:space="preserve">One ſide. </s>
            <s xml:id="echoid-s3156" xml:space="preserve">Ratio of the ſegments of the baſe made by a line dividing V
              <lb/>
            into given angles.</s>
            <s xml:id="echoid-s3157" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3158" xml:space="preserve">Palladium, 1756, pa: </s>
            <s xml:id="echoid-s3159" xml:space="preserve">43.</s>
            <s xml:id="echoid-s3160" xml:space="preserve"/>
          </p>
        </div>
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