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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[71.] DETERMINATE SECTION. BOOK I. PROBLEM I. (Fig. 1.)
Page: 92 ([15])
[72.] PROBLEM II. (Fig. 2 and 3.)
Page: 93 ([16])
[73.] PROBLEM III. (Fig. 4. and 5.)
Page: 94 ([17])
[74.] PROBLEM IV. (Fig. 6. 7. and 8.)
Page: 95 ([18])
[75.] PROBLEM V. (Fig. 9. 10. 11. 12. 13. 14. 15. 16.)
Page: 96 ([19])
[76.] PROBLEM VI. (Fig. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26.)
Page: 98 ([21])
[77.] THE END OF BOOK I.
Page: 102 ([25])
[78.] DETERMINATE SECTION. BOOK II. LEMMA I.
Page: 103 ([26])
[79.] LEMMA II.
Page: 103 ([26])
[80.] LEMMA III.
Page: 104 ([27])
[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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            <s xml:id="echoid-s977" xml:space="preserve">
              <emph style="sc">Pappus</emph>
            , in his preface to the ſeventh Book of Matbematical
              <lb/>
            Collections, tells us that this Tract of
              <emph style="sc">Apollonius</emph>
            was divided into
              <lb/>
            two Books; </s>
            <s xml:id="echoid-s978" xml:space="preserve">that the firſt Book contained ſix Problems, and the
              <lb/>
            ſecond three: </s>
            <s xml:id="echoid-s979" xml:space="preserve">now
              <emph style="sc">Snellius'</emph>
            whole work contains but four; </s>
            <s xml:id="echoid-s980" xml:space="preserve">and
              <lb/>
            it ſeemed to me difficult to ſhew how thoſe could contain the ſub-
              <lb/>
            ſtance of nine, and yet the ſix firſt have ſixteen Epitagmas, or ge-
              <lb/>
            neral Caſes, and the three laſt nine. </s>
            <s xml:id="echoid-s981" xml:space="preserve">I firſt, therefore began with
              <lb/>
            inquiring whether, or no, other Problems could not be found,
              <lb/>
            wherein the ſection of an indefinite ſtraight line is propoſed to be
              <lb/>
            effected, “So, that of the ſegments contained between the point of
              <lb/>
            ſection ſought, and given points in the ſaid line, either the ſquare
              <lb/>
            on one of them, or the rectangle contained by two of them, may
              <lb/>
            have a given ratio to the rectangle contained by one of them and a
              <lb/>
            given external line, or to the rectangle contained by two of them;</s>
            <s xml:id="echoid-s982" xml:space="preserve">“
              <lb/>
            as is deſcribed by P
              <emph style="sc">APPUS.</emph>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s983" xml:space="preserve">In this inquiry it ſoon occurred to me, that the three problems
              <lb/>
            which make my firſt, ſecond and fourth, come within the account
              <lb/>
            given by P
              <emph style="sc">APPUS</emph>
            ;</s>
            <s xml:id="echoid-s984" xml:space="preserve">and therefore are properly Problems in Determi-
              <lb/>
            ate Section, to be added to the four given by
              <emph style="sc">Snellius</emph>
            : </s>
            <s xml:id="echoid-s985" xml:space="preserve">and it does
              <lb/>
            not appear to me that more can be found which ſhould. </s>
            <s xml:id="echoid-s986" xml:space="preserve">Hence I
              <lb/>
            concluded, that there were in theſe, ſome, more general than thoſe
              <lb/>
            of
              <emph style="sc">Apollonius</emph>
            , which ought therefore to be divided.</s>
            <s xml:id="echoid-s987" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s988" xml:space="preserve">My next buſineſs was, if poſſible, to find out the order in which
              <lb/>
              <emph style="sc">Apollonius</emph>
            had arranged them: </s>
            <s xml:id="echoid-s989" xml:space="preserve">and here, with reſpect to the
              <lb/>
            firſt Book, I had no other information to guide me, but what is </s>
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