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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[51.] PROBLEM X.
Page: 39 ((27))
[52.] PROBLEM XI.
Page: 39 ((27))
[53.] PROBLEM XII.
Page: 40 ((28))
[54.] PROBLEM XIII.
Page: 40 ((28))
[55.] PROBLEM XIV.
Page: 40 ((28))
[56.] PROBLEM XV.
Page: 40 ((28))
[57.] Synopſis of the PROBLEMS.
Page: 41 ((29))
[58.] THE TWO BOOKS OF APOLLONIUS PERGÆUS, CONCERNING DETERMINATE SECTION, As they have been Reſtored by WILLEBRORDUS SNELLIUS. By JOHN LAWSON, B. D. Rector of Swanſcombe, Kent. TO WHICH ARE ADDED, THE SAME TWO BOOKS, BY WILLIAM WALES, BEING AN ENTIRE NEW WORK. LONDON: Printed by G. BIGG, Succeſſor to D. LEACH. And ſold by B. White, in Fleet-Street; L. Davis, in Holborne; J. Nourse, in the Strand; and T. Payne, near the Mews-Gate. MDCC LXXII.
Page: 64
[59.] ADVERTISEMENT.
Page: 66 ([i])
[60.] EXTRACT from PAPPUS's Preface to his Seventh Book in Dr. HALLEY's Tranſlation. DE SECTIONE DETERMINATA II.
Page: 68 ([iii])
[61.] THE PREFACE.
Page: 70 ([v])
[62.] PROBLEMS CONCERNING DETERMINATE SECTION. PROBLEM I.
Page: 78
[63.] LEMMA I.
Page: 79 ([2])
[64.] LEMMA II.
Page: 80 ([3])
[65.] LEMMA III.
Page: 80 ([3])
[66.] PROBLEM II.
Page: 80 ([3])
[67.] LEMMA IV.
Page: 83 ([6])
[68.] LEMMA V.
Page: 83 ([6])
[69.] PROBLEM III.
Page: 84 ([7])
[70.] PROBLEM IV.
Page: 86 ([9])
[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])
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150[10]
133. V. The ſquare of the baſe equal to the rectangle of one ſide and a given line.
General Mag. qu. 61.
134. V. P. The angle of two lines from extremes of B to middle of P.
Mathematician, pr. 65.
135. V. B. The angle of two lines from extremes of B to the middle of P.
Brit. Oracle, qu. 91.
136. V. S. The ratio of the ſquare of a line, drawn in a given direction from V to B,
to the rectangle of the ſegments of B made thereby.
Anderſoni Exercitationes Math. No. 8.
137. V. S or s. m: n, theſe being ſegts. by a line from V to B dividing V into
given angles.
Hutton’s La. Diary, qu. 139.
138. V. A line from V to B dividing V in a given ratio. Area a minimum.
L. Diary, 1761, qu. 479.
139. V. Line from A biſecting S. Line from a biſecting s.
*Simpſon’s Sel. Ex. pr. 15.
140. V. Per. Line parallel to B biſecting the area.
*Gent. Di. 1750, qu. 98. - Reducible to V. B. S + s.
141. S. s. Line from V to centre of ins. ☉(sun).
L. Diary, 1771, qu. 635.
142. Baſe. One ſide. Ratio of a line from V, making a given angle with ſaid ſide,
to alternate part of B.
Hutton’s Mis. pag. 63, Cor.
143. B. Point of contact therein of ins. ☉(sun). mxn.
Hutton’s L. Diaries, 1722, qu. 94.
144. L. A perpendicular thereto from one of the angles at the baſe. The other
angle at the baſe.
L. Diary, 1769, 1770, qu. 604.
145. L. A perpendicular thereto from A. Another from a.
L. Diary 1768, 1769, qu. 588.
146. One of the angles at the baſe. Perpendicular therefrom to oppoſite ſide a max-
imum. A line from the other angle at the baſe biſecting its oppoſite ſide.
*L. Diary, 1769, 1770, qu. 607.
147. S. s. m: n, theſe being ſegts. by a line from V to B, and the ratio of this line to
m or n.
Rudd’s Prac. Geom. part 2d, qu. 40.

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