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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            <s xml:id="echoid-s989" xml:space="preserve">
              <pb o="[vii]" file="0065" n="72"/>
            be met with in the above mentioned Preface of
              <emph style="sc">Pappus</emph>
            ; </s>
            <s xml:id="echoid-s990" xml:space="preserve">where he
              <lb/>
            tells us that in the ſix Problems of Book I. </s>
            <s xml:id="echoid-s991" xml:space="preserve">there were “Sixteen
              <lb/>
            Epitagmas, or general Caſes, five Determinations; </s>
            <s xml:id="echoid-s992" xml:space="preserve">and of theſe,
              <lb/>
            four were Maxima, and one a minimum: </s>
            <s xml:id="echoid-s993" xml:space="preserve">That the maxima are at the
              <lb/>
            ſecond Epitagma of the ſecond Problem, at the third of the fourth,
              <lb/>
            the third of the fifth, and the third of the ſixth; </s>
            <s xml:id="echoid-s994" xml:space="preserve">but that the minimum
              <lb/>
            was at the third Epitagma of the third problem.</s>
            <s xml:id="echoid-s995" xml:space="preserve">” It moreover ſeem- ed reaſonable to me, that theſe Problems wherein the feweſt points
              <lb/>
            are given, would be antecedent to thoſe wherein there were more;
              <lb/>
            </s>
            <s xml:id="echoid-s996" xml:space="preserve">and of theſe wherein the number of given points are the ſame, that
              <lb/>
            thoſe would be prior to the others, wherein there was a given ex-
              <lb/>
            ternal line concerned: </s>
            <s xml:id="echoid-s997" xml:space="preserve">and laſtly, that when the number of given
              <lb/>
            points were two, the ſecond Caſe, or Epitagma, would naturally
              <lb/>
            be when the required point O is ſought between the two given
              <lb/>
            ones.</s>
            <s xml:id="echoid-s998" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s999" xml:space="preserve">Now the three new Problems, together with the three firſt of
              <lb/>
              <emph style="sc">Snellius</emph>
            , making exactly ſixteen Epitagmas, viz. </s>
            <s xml:id="echoid-s1000" xml:space="preserve">one in the firſt,
              <lb/>
            and three in each of the others; </s>
            <s xml:id="echoid-s1001" xml:space="preserve">it ſeemed highly probable, that
              <lb/>
            theſe compoſed the firſt book. </s>
            <s xml:id="echoid-s1002" xml:space="preserve">Alſo that the Problem, wherein
              <lb/>
            only one point was given, would be the firſt; </s>
            <s xml:id="echoid-s1003" xml:space="preserve">and it ſeemed eaſy
              <lb/>
            to aſſign the ſecond, becauſe it is the only one wherein the limita-
              <lb/>
              <note symbol="*" position="foot" xlink:label="note-0065-01" xlink:href="note-0065-01a" xml:space="preserve">The words which are in Italics were entirely omitted in
                <emph style="sc">Snellius's</emph>
              Extract
                <lb/>
              from Pappus, both in the Greek and Latin, and are read with ſome variation in
                <lb/>
                <emph style="sc">Commandine's</emph>
              tranſlation; but are here printed according to Dr.
                <emph style="sc">Halley</emph>
              : and
                <lb/>
              though I know not whether in this particular place he had the Authority of either
                <lb/>
              of the Savilian MSS, yet I hope I run no great riſk in ſubſcribing to the opinion
                <lb/>
              of ſo excellent a Geometer.</note>
            </s>
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