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-s1024" xml:space="preserve">
              <pb o="[x]" file="0068" n="75"/>
            The Limitations of the two former are ſaid by
              <emph style="sc">Pappus</emph>
            to have
              <lb/>
            been minimums, and that of the third a maximum, in conformity,
              <lb/>
            to which, I have here made them ſo; </s>
            <s xml:id="echoid-s1025" xml:space="preserve">although I cannot ſee with
              <lb/>
            what propriety: </s>
            <s xml:id="echoid-s1026" xml:space="preserve">each of them admitting, in ſome Caſes, of a maxi-
              <lb/>
            mum and in others of minimum, as I have intimated in a ſcbolium at
              <lb/>
            the end of each Problem. </s>
            <s xml:id="echoid-s1027" xml:space="preserve">But notwithſtanding I have conformed to
              <lb/>
            the manner of
              <emph style="sc">Apollonius</emph>
            in dividing this Problem into three,
              <lb/>
            which it muſt be confeſſed contributes much to order in enumera-
              <lb/>
            ting ſuch a multitude of Caſes, yet have I previouſly ſhewn how
              <lb/>
            the whole may be generally conſtructed at once; </s>
            <s xml:id="echoid-s1028" xml:space="preserve">and that by a me-
              <lb/>
            thod, which I flatter myſelf will not be found inferior to any that
              <lb/>
            hath heretofore been given of this very intricate and general
              <lb/>
            Problem.</s>
            <s xml:id="echoid-s1029" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1030" xml:space="preserve">Such are the things that I have attempted, and ſuch the reaſons
              <lb/>
            for what I have done in the following little Tract. </s>
            <s xml:id="echoid-s1031" xml:space="preserve">The merit due
              <lb/>
            to each of them I chearfully ſubmit (where every one ought) to
              <lb/>
            the deciſion of the impartial Reader. </s>
            <s xml:id="echoid-s1032" xml:space="preserve">In the Conſtructions, my
              <lb/>
            chief Aim was novelty and uniformity: </s>
            <s xml:id="echoid-s1033" xml:space="preserve">I could have given more
              <lb/>
            ſimple conſtructions to one or two of them; </s>
            <s xml:id="echoid-s1034" xml:space="preserve">in particular the ſixth
              <lb/>
            of Book I: </s>
            <s xml:id="echoid-s1035" xml:space="preserve">but it was not my intention to give any thing that I
              <lb/>
            knew had been done before. </s>
            <s xml:id="echoid-s1036" xml:space="preserve">I know of many imperfections, but
              <lb/>
            no falſe reaſonings, and hope none will be found; </s>
            <s xml:id="echoid-s1037" xml:space="preserve">but if there
              <lb/>
            ſhould, I hope the candid Geometer will be more inclined to ex-
              <lb/>
            cuſe than exult, when I aſſure him the greateſt part of the work
              <lb/>
            has been executed at different times, amidſt the hurry and perplexi-
              <lb/>
            ties which it may eaſily be conceived attend the fitting out for a
              <lb/>
            three years Voyage to the ſouth ſeas.</s>
            <s xml:id="echoid-s1038" xml:space="preserve"/>
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