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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[Item 1.]
[2.] THE TWO BOOKS OF APOLLONIUS PERGÆUS, CONCERNING TANGENCIES, As they have been Reſtored by FRANCISCUSVIET A and MARINUSGHETALDUS. WITH A SUPPLEMENT.
[3.] THE SECOND EDITION. TO WHICH IS NOW ADDED, A SECOND SUPPLEMENT, BEING Monſ. FERMAT’S Treatiſe on Spherical Tangencies. 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. MDCCLXXI.
[4.] PREFACE.
[5.] EXTRACT from PAPPUS’s Preſace to his Seventh Book in Dr. HALLEY’s Tranſlation. DE TACTIONIBUS II.
[6.] Synopsis of the PROBLEMS.
[7.] PROBLEMS CONCERNING TANGENCIES. PROBLEM I.
[8.] PROBLEM II.
[9.] PROBLEM III.
[10.] The GENERAL Solution.
[11.] PROBLEM IV.
[12.] PROBLEM V.
[13.] The general Solution.
[14.] PROBLEM VI.
[15.] The general Solution.
[16.] PROBLEM VII.
[17.] LEMMA I.
[18.] PROBLEM VIII.
[19.] Mr. Simpſon conſtructs the Problem thus.
[20.] PROBLEM IX.
[21.] LEMMA II.
[22.] LEMMA III.
[23.] PROBLEM X.
[24.] PROBLEM XI.
[25.] PROBLEM XII .
[26.] LEMMA IV.
[27.] LEMMA V.
[28.] PROBLEM XIII.
[29.] PROBLEM XIV.
[30.] SUPPLEMENT. PROBLEM I.
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          <head xml:id="echoid-head8" xml:space="preserve">EXTRACT from PAPPUS’s Preſace to his Seventh Book
            <lb/>
          in Dr. HALLEY’s Tranſlation.</head>
          <head xml:id="echoid-head9" xml:space="preserve">DE TACTIONIBUS II.</head>
          <p>
            <s xml:id="echoid-s28" xml:space="preserve">HIS ordine ſubnexi ſunt libri duo
              <emph style="sc">DE</emph>
              <emph style="sc">Tactionibus</emph>
            , in
              <lb/>
            quibus plures ineſſe propoſitiones videntur; </s>
            <s xml:id="echoid-s29" xml:space="preserve">ſed & </s>
            <s xml:id="echoid-s30" xml:space="preserve">ex
              <lb/>
            his unam etiam faciemus, ad hunc modum ſe habentem. </s>
            <s xml:id="echoid-s31" xml:space="preserve">“ E
              <lb/>
            punctis rectis & </s>
            <s xml:id="echoid-s32" xml:space="preserve">circulis, quibuſcunque tribus poſitione
              <lb/>
            datis, circulum ducere per ſingula data puncta, qui, ſi fieri
              <lb/>
            poſſit, contingat etiam datas lineas.</s>
            <s xml:id="echoid-s33" xml:space="preserve">” Ex hac autem ob mul-
              <lb/>
            titudinem in Hypotheſibus datorum, tam ſimilium quam diſſi-
              <lb/>
            milium
              <emph style="sc">GENERUM</emph>
            , fiunt neceſſario decem propoſitiones di-
              <lb/>
            verſæ; </s>
            <s xml:id="echoid-s34" xml:space="preserve">quia ex tribus diſſimilibus generibus fiunt diverſæ
              <lb/>
            triades inordinatæ numero decem. </s>
            <s xml:id="echoid-s35" xml:space="preserve">Data etenim eſſe poſſunt
              <lb/>
            vel tria puncta; </s>
            <s xml:id="echoid-s36" xml:space="preserve">vel tres rectæ; </s>
            <s xml:id="echoid-s37" xml:space="preserve">vel duo puncta & </s>
            <s xml:id="echoid-s38" xml:space="preserve">recta; </s>
            <s xml:id="echoid-s39" xml:space="preserve">vel
              <lb/>
            duæ rectæ & </s>
            <s xml:id="echoid-s40" xml:space="preserve">punctum; </s>
            <s xml:id="echoid-s41" xml:space="preserve">vel duo puncta & </s>
            <s xml:id="echoid-s42" xml:space="preserve">circulus; </s>
            <s xml:id="echoid-s43" xml:space="preserve">vel duo
              <lb/>
            circuli & </s>
            <s xml:id="echoid-s44" xml:space="preserve">punctum; </s>
            <s xml:id="echoid-s45" xml:space="preserve">vel duo circuli & </s>
            <s xml:id="echoid-s46" xml:space="preserve">recta; </s>
            <s xml:id="echoid-s47" xml:space="preserve">vel punctum,
              <lb/>
            recta & </s>
            <s xml:id="echoid-s48" xml:space="preserve">circulus; </s>
            <s xml:id="echoid-s49" xml:space="preserve">vel duæ rectæ & </s>
            <s xml:id="echoid-s50" xml:space="preserve">circulus; </s>
            <s xml:id="echoid-s51" xml:space="preserve">vel tres circuli.
              <lb/>
            </s>
            <s xml:id="echoid-s52" xml:space="preserve">Horum duo quidem prima problemata oſtenduntur in libro
              <lb/>
            quarto primorum Elementorum. </s>
            <s xml:id="echoid-s53" xml:space="preserve">Nam per tria data puncta,
              <lb/>
            quæ non ſint in linea recta, circulum ducere, idem eſt ac
              <lb/>
            circa datum triangulum circumſcribere. </s>
            <s xml:id="echoid-s54" xml:space="preserve">Problema autem in
              <lb/>
            tribus datis rectis non parallelis, ſed inter ſe occurrentibus,
              <lb/>
            idem eſt ac dato triangulo circulum inſcribere. </s>
            <s xml:id="echoid-s55" xml:space="preserve">Caſus vero
              <lb/>
            duarum rectarum parallelarum cum tertiâ occurrente, </s>
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