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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          <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>
          </p>
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