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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[81.] LEMMA IV.
Page: 105 ([28])
[82.] LEMMA V.
Page: 106 ([29])
[83.] PROBLEM VII. (Fig. 32, 33, 34, &c.)
Page: 108 ([31])
[84.] PROBLEM I. (Fig. 32 to 45.)
Page: 109 ([32])
[85.] PROBLEM II. (Fig. 46 to 57.)
Page: 113 ([36])
[86.] PROBLEM III.
Page: 116 ([39])
[87.] THE END.
Page: 117 ([40])
[88.] A SYNOPSIS OF ALL THE DATA FOR THE Conſtruction of Triangles, FROM WHICH GEOMETRICAL SOLUTIONS Have hitherto been in Print.
Page: 133
[89.] By JOHN LAWSON, B. D. Rector of Swanscombe, in KENT. ROCHESTER:
Page: 133
[90.] MDCCLXXIII. [Price One Shilling.]
Page: 133
[91.] ADVERTISEMENT.
Page: 135
[92.] AN EXPLANATION OF THE SYMBOLS made uſe of in this SYNOPSIS.
Page: 137
[93.] INDEX OF THE Authors refered to in the SYNOPSIS.
Page: 139 ([i])
[94.] Lately was publiſhed by the ſame Author; [Price Six Shillings in Boards.]
Page: 140 ([ii])
[95.] SYNOPSIS.
Page: 141 ([1])
[96.] Continuation of the Synopsis, Containing ſuch Data as cannot readily be expreſſed by the Symbols before uſed without more words at length.
Page: 149 ([9])
[97.] SYNOPSIS
Page: 152 ([12])
[98.] FINIS.
Page: 156 ([16])
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            tion is at the ſecond Epitagma; </s>
            <s xml:id="echoid-s1004" xml:space="preserve">and farther, the Limiting Ratio is
              <lb/>
            therein a maximum, as it ought. </s>
            <s xml:id="echoid-s1005" xml:space="preserve">Again, the Problem, wherein
              <lb/>
            it is propoſed to make the ſquare on AO in a given ratio to the rect-
              <lb/>
            angle contained by EO and P, has its limiting ratio a minimum
              <lb/>
            when the required point is ſought beyond (E) that of the given ones
              <lb/>
            which bounds the ſegment concerned in the conſequent term of
              <lb/>
            the ratio; </s>
            <s xml:id="echoid-s1006" xml:space="preserve">which, therefore, I apprehend muſt have been the third
              <lb/>
            Epitagma, and if ſo, this of courſe muſt have been the third Pro-
              <lb/>
            blem: </s>
            <s xml:id="echoid-s1007" xml:space="preserve">and as there remains only one wherein the number of given
              <lb/>
            pointsare two, I make that the fourth. </s>
            <s xml:id="echoid-s1008" xml:space="preserve">With reſpect to the fifth and
              <lb/>
            ſixth Problems, in which three points are given, it ſhould ſeem
              <lb/>
            that that would be the firſt in order, wherein there is a given ex-
              <lb/>
            ternal line concerned.</s>
            <s xml:id="echoid-s1009" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1010" xml:space="preserve">But it ſhould, by no means, be diſſembled that objections may be
              <lb/>
            brought againſt the identity, and arrangment of ſome of theſe Pro-
              <lb/>
            blems. </s>
            <s xml:id="echoid-s1011" xml:space="preserve">For firſt,
              <emph style="sc">Pappus</emph>
            no where expreſsly ſays that
              <emph style="sc">Apollo</emph>
            -
              <lb/>
              <emph style="sc">NIUS</emph>
            compared together two ſquares, wherefore, if this cannot be
              <lb/>
            implied, the identity of the fourth Problem is deeply ſtruck at:
              <lb/>
            </s>
            <s xml:id="echoid-s1012" xml:space="preserve">and moreover, this fourth Problem perhaps cannot with propriety,
              <lb/>
            be ſaid to have its limiting ratio either maximum or minimum, un-
              <lb/>
            leſs the ratio of equality, can be admitted as ſuch. </s>
            <s xml:id="echoid-s1013" xml:space="preserve">Laſtly, in the
              <lb/>
            fifth Problem, the ſaid limiting ratio is a minimum, and not a maxi-
              <lb/>
            mum as it is ſaid to have been by
              <emph style="sc">Pappus</emph>
            : </s>
            <s xml:id="echoid-s1014" xml:space="preserve">either, therefore, </s>
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