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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[31.] PROBLEM II.
[32.] PROBLEM III.
[33.] PROBLEM IV.
[34.] PROBLEM V.
[35.] PROBLEM VI.
[36.] General Solution.
[37.] A SECOND SUPPLEMENT, BEING Monſ. DE FERMAT’S Treatiſe on Spherical Tangencies. PROBLEM I.
[38.] PROBLEM II.
[39.] PROBLEM III.
[40.] PROBLEM IV.
[41.] PROBLEM V.
[42.] PROBLEM VI.
[43.] PROBLEM VII.
[44.] LEMMA I.
[45.] LEMMA II.
[46.] LEMMA III.
[47.] LEMMA IV.
[48.] LEMMA V.
[49.] PROBLEM VIII.
[50.] PROBLEM IX.
[51.] PROBLEM X.
[52.] PROBLEM XI.
[53.] PROBLEM XII.
[54.] PROBLEM XIII.
[55.] PROBLEM XIV.
[56.] PROBLEM XV.
[57.] Synopſis of the PROBLEMS.
[58.] THE TWO BOOKS OF APOLLONIUS PERGÆUS, CONCERNING DETERMINATE SECTION, As they have been Reſtored by WILLEBRORDUS SNELLIUS. By JOHN LAWSON, B. D. Rector of Swanſcombe, Kent. TO WHICH ARE ADDED, THE SAME TWO BOOKS, BY WILLIAM WALES, BEING AN ENTIRE NEW WORK. LONDON: Printed by G. BIGG, Succeſſor to D. LEACH. And ſold by B. White, in Fleet-Street; L. Davis, in Holborne; J. Nourse, in the Strand; and T. Payne, near the Mews-Gate. MDCC LXXII.
[59.] ADVERTISEMENT.
[60.] EXTRACT from PAPPUS's Preface to his Seventh Book in Dr. HALLEY's Tranſlation. DE SECTIONE DETERMINATA II.
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          <head xml:id="echoid-head71" xml:space="preserve">EXTRACT from PAPPUS's Preface to his Seventh Book
            <lb/>
          in Dr. HALLEY's Tranſlation.</head>
          <head xml:id="echoid-head72" xml:space="preserve">DE SECTIONE DETERMINATA II.</head>
          <p>
            <s xml:id="echoid-s943" xml:space="preserve">HIS ſubjiciuntur libri duo de Sectione Determinatâ,
              <lb/>
            quas etiam ad modum præcedentium unam pro-
              <lb/>
            poſitionem dicere liceat, ſed disjunctam: </s>
            <s xml:id="echoid-s944" xml:space="preserve">quæ hujuſ-
              <lb/>
            modi eſt. </s>
            <s xml:id="echoid-s945" xml:space="preserve">“ Datam rectam infinitam in uno puncto ſe-
              <lb/>
            care, ita, ut è rectis interceptis inter illud & </s>
            <s xml:id="echoid-s946" xml:space="preserve">puncta
              <lb/>
            in illâ data, vel quadratum ex unâ, vel rectangulum
              <lb/>
            ex duabus interceptis, datam habeat rationem, vel ad
              <lb/>
            contentum ſub aliâ unâ interceptâ & </s>
            <s xml:id="echoid-s947" xml:space="preserve">datá quâdum;
              <lb/>
            </s>
            <s xml:id="echoid-s948" xml:space="preserve">vel etiam ad contentum ſub duabus aliis interceptis: </s>
            <s xml:id="echoid-s949" xml:space="preserve">
              <lb/>
            idque ad quam partem velis punctorum datorum.</s>
            <s xml:id="echoid-s950" xml:space="preserve">”
              <lb/>
            Hujus autem, quaſi bis disjunctæ, & </s>
            <s xml:id="echoid-s951" xml:space="preserve">intricatos Dio-
              <lb/>
            riſmos habentis, per plura neceſſario facta eſt demon-
              <lb/>
            ſtratio. </s>
            <s xml:id="echoid-s952" xml:space="preserve">Hanc autem dedit Apollonius communi methodo
              <lb/>
            tentamen faciens, ac ſolis rectis lineis uſus, ad exemplum
              <lb/>
            ſecundi libri Elementorum primorum Euclidis: </s>
            <s xml:id="echoid-s953" xml:space="preserve">ac rur- ſus idem demonſtravit ingenioſe quidem, & </s>
            <s xml:id="echoid-s954" xml:space="preserve">magis ad
              <lb/>
            inſtitutionem accomodate, per ſemicirculos. </s>
            <s xml:id="echoid-s955" xml:space="preserve">Habet
              <lb/>
              <note symbol="*" position="foot" xlink:label="note-0061-01" xlink:href="note-0061-01a" xml:space="preserve">From hence it appears that
                <emph style="sc">Euclid's</emph>
              were called the firſt Elements,
                <lb/>
              and that the other Analytical Tracts, recited by
                <emph style="sc">Pappus,</emph>
              were called the
                <lb/>
              ſecond Elements.</note>
            </s>
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