found by this Way, the Labour of doing then will moftly confift in fetting down the Numbers. Note, This Series is eafily deduced from that found out by Dr. Hally; and thofe who have a mind to be inform'd more in this Matter, let them confult his abovenam'd Treatife.

FINIS.

(which are many) affix'd to them, and fo the Reader's Progrefs very often retarded thereby,. for avoiding this, by carefully reading the Book, and examining the Demontrations over and over, we have found the following Errata, which the Reader is defir'd to correct.

ERRATA

Nthe Preface. Page i. line 14. for accufed read accufe ; p. iii. 1. 9. for Reformations. Reformation; p. vi. l. 17. for became r. become; ibidem

18. for Construction. Constructions; p. vii. l. 9. for Demonstrations r. Demonftration; ibid. l. 25. for Number r. Lumber.

3:

I

*

*

*

31.

Page 31.8. for which is r. and; p. 6. 1. 3. for Cr. G; p. 8. 1. 32. infert this Mark ; ibid. l. 33: dele ‡ p. 12. for * 1. of this in Margin, n 8. of this 3 p. 14. for # Def. 10. in Margin, r. + 8. of this; ibid. 1. 12. for r. Cs p. 18. i. 1. for BB r. CB'; p. 19. l. 29. for Part r. Points 21. 1. 21. this Mark houd be just after the Word TAKE; p. 33. l. 14. afer the Re iod must be inferted this. Again, because AC is parallel to BD, and B Calls upon them, the alternate Angles ACB, BCD are equal to one another sp364 36. for DCB. DCE; p. 39, 1. 17. for ECF. CEF; ibid. l. 25. for A Br. DB; p. 40. l. 35. for AMB F.ABM; p. 41. against 1.31. in Margin r. * 29. 1. Ibid. for 35. in Margins r. # 34 ; p. 48. for † 41. 1. r. † 31. 13 Ibid., against 1. 40. read in the Margin ± 29. 13. p. 49. L. 1. for GBC GCB; p So los. for KLG. KLO; Ibid. for † 43.1. in Margin 7. † 36. 13 page 5 againt Line 16. for † 36, 1. in the Margin, read t Ibid. 1. 20. for Fr. t. p. 52. against l. 27. in the Maigin r. Cor. 4. of this; p. 55. 1. 26. for EGB r. ECB; p. 57. 1. 23. for ‡ r. *; and against 1. 23 in Margin r. 29.15 p. 58. in Margin for 47 of this r... 47. p. 60., against 1. 25. in Margin r. * 12.13 p. 66. against 1. 23. in Margin r‡ Def. 8o. 1 ; p. 68. L. 1. for CBG, Y. ABC, p.69. L.33. for t. r. P. 70. against 1.11. in Margin r. † 4.15 p. 73. a gainst 1 34. in Margin r 10. I p. 75. for 12. I. r. 20. P. 77: in the Margin, for 4 of this r.3 of this; p 81. in Magin against 1. 12. for † 32. 1. Y. † 4. I; p. 83. l. 57. for EFCY. FEC p. 86. against 1. 23. in Marginer* 6.1 3. p. 89. 1. 18. for Bafe LF. Bale EF p. 984 1.21. for AEC r. ACE*; Ibid. 1.23. dele; p. 93. for † 19.1. r. +19.3; p. 94. for 4 of this, in Margin r. 4. 1; Ibid. in Margin for 31. r. 323 Ibid. 1. 23. for AEL . AEB; p. 97. L. 25. dele ibis Markt; Ib.L. 28. for this -Mark‡r. t; Ib. L. 34. for * r. † ; p. 98. 1. 16. for D Ar. DB; p. 100. l. 16. for Sides, r. Angles; p. 103. 1. 11. for i. t; p. 104. in the Margin for 6.3. r. 16.3. and 30. 1.7. 10.1; p. 105. 1. the last for AB r. DB; p. 106. for 31. I. r. 31.3; Ibid. 1.6. for equiangular 7. equilateral; p. 108. 1. 19. after the Word Distances 7. EA; p. 110. 1. 36. for Triangle r. Pentagon; p. III. for † 5.1. r. +8.1; p. 115. for * 18. 1. r. 15.13 p. 117. l [ 1. dele the; p. 120. l. 12. for trilicate r. triplicate; p. 132. for 6. r. 73 P.140. 1.7. for is r. is to; p. 142. l 3). inftead of reading, that Magnitude which has a greater Proportion to the fame Magnitude, . that Magnitude to which the fame Magnitude has a greater Proportion; p. 149. l. 11. for EF r. EC ; p. 151. 1. 16. fr ADE r. B DE; p. 152. for † 29.3. r. † 29. 13. p. 153 . 26. for CE r. CD; p. 162. l. 16 for BC v. BG; p. 166. 1. 36. for CDE. CDF; p. 168. after E F 1. 12. v. and as BC to BG, fo is the Triangle ABC to the Triangle ABG. Whence the Triangle ABC bears to the Triangle A BG a duplicate Proporcion to what BC doth to EF; Ibid. L. 15. for EA. r. BA; Ibid. in Margin, for 21. s. r. 22. 5; p. 172. in Margin for * 11.8. . *11.5; p. 175. in Margin, for ‡ Com. proceed, r. Lemma preceed; Ibid. in Margin, for ‡ 20. 5. r. £22. si p.

*

*

*

187

1. 12.

for CD. 187. 1.33. for B L, and GBL, . GB, GBC; p. 193. . CB; p. 194. L. 17. for GH r. GE; p. 199. 7. 16. for Right r. Right 7. 3. 1. and Angles; p. 200. in Magin, for 31. 2. and ‡ 14. of this, t4. of this; p.202. 1.6. dele can; p. 206. 1. 1. for Place r. Planes p. 210. 1. the last but two. for LE r. LX; f. 216. 1. 22. for LT r. 1 Y ; p. 221. l. 37. før & Y ́r. ¥Y; p.2.2. 1.8. and r. ¥Y; p. 223. l. 37. for EH v. FH ; p. 224. 1. 17. for EK r. &* p. 227. in Margin, for 30. of this, r

EK;

T.

*

12. for

Y

to

31. of this; p. 228. ̄l. 25. for BIr. BT; p. 234. 1. 20. for plane Angle r. only plane; p. 235. 1.6. after the Word Diameter, dele Commia, and r. of; p. 236. l. 11. for which 7. which is; Ibid. in Margin, for * 14. I. Y. 41.1; p. 238. in Margin, for 22.1. r. †.0.6; p. 241. L.31. for fo is r. o is; Ib. in Margin, for 14.5. *11.53 p. 242. 1. 10. for into r. into two; p. 259. 4. 5. for PE r. PF; p. 263. 1. 1. for EMON r. FMON; p. 268. 1. 23. dele not; p. 270. l. 16. for is to, r. is equal to; Ibid. in Margin, for † 23. 1. 7. † 33.43 Ibid. 1. 38. for RBOS . KBOS; P. 282. for the of r. the Sine of; p. 283. 1. 5. for beging the r. beginning of the; p. 28 1. 29. for (by 13-1) r. (by 22-3); Ibid. 1.31. for (by 22. 3) Y. (13, 1) ;. p. 285, L.:13, for GLAB r. GL➡AE; Ibid. L. 22, for Prop. 5.r. Prop. 4; p. 286. 1. 10. for Prop. 5. r. Prop. 6; •

z1

I. 2.

&c.

74 287. read the last Line thus, Or, 2a X 1.2.3.4. 1.2.3.4.5.6.0 2288. L. 12. for a c r. a=0; Ibid. 1. 14. for 6. r. b; p. 291. 1. 14. dele from; p. 294. in the Title (and in the Titles afterwards) for Sphe rical Triangles 7. Spherical Trigonometry; p. 296. 1. 26. for comprehending r. comprehended by; p. 31. 1. 9. for nnarer r. nearers Ibid. l. 22. for RS rRSq; p. 302. 1. 22. for the fame r. a Different; b. 1. 23. for 2 Different, the fame p. 316. l. 32. for or r. and; Ibid. L. 35. for BL T. BD; p. 317. l. 16. for CD r. BD; Ibid. in the Column under the Word fought against Number 7. for the Side DC r. the Angle C; Ibid. is the Column under the Word given, against Number 8. for the Angle BC Dr. the Angles B CD, and B Ibid. in the Column under the Word fought, againt Number 8, for Angles BCD r. the Side DC; p. 318. T. 4. for DB r. DC; page 319. L. 10. for PTR 7. STR; p. 320. 1. 28. for another v. of another; p. 334. l. 18. for 12 r. 12 › P. 335. for ZALM 4. ILM; p. 337. 15. for therefore 7. thereof; p. 343. l. 16. for if r. it tos p. 346. 1. 29. for. Tabōōi Ib. l. 34. for Tob! Tröði P. 348. 1. 1. for triplate 7. triple; p. 350. 1. 23. for and r. of.

T

I

over - against St. Dunstan's

the Half-Moon, overChurch in Fleet-Street.

A

N exact Survey of the Tide; explicating its Production and Propagation, Variety, and Anomaly, in all Parts of the World, especially near the Coafts of Great Britain and Ireland; with a Preliminary Treatife concerning the Origine of Springs, Generation of Rain, and Production of Wind. With Fifteen curious Maps. The Second Edition. To which is added, A clear and fuccinct Defcription of an Engine, which fetcheth Water out of the Deep, and raifeth it to the Height defign'd, progreffively, by the fame Motion. By E. Barlow, Gent.

II. The Compleat Surveyor: Or, The whole Art of Surveying of Land. By a new Inftrument lately invented; as alfo by the Plain Table, Circumferentor, the Theodolite, as now improv'd, or by the Chain only. Containing plain and eafy Directions in feveral Kinds. of Menfuration, and other Things neceffary to be known in a Work of this Nature. By William Leybourn. The Whole alter'd and amended, and two entire Books added by the Author long before his Death. The Fifth Edition. In Nine Books. Every Operation, both Geometrical and Arithmetical, examin'd; and an Appendix added to the Whole, confifting of Practical Obfervations in Land-Surveying. By S.Cunn.

III. Mathematical Elements of Phyficks, prov'd by Experiments. Being an Introduction to Sir Ifaac Newton's Philofophy. By Dr. William-James Gravefande, Profeffor of Mathematicks and Aftronomy. in the University of Leyden, and Fellow of the Royal Society of London. Made English, and illuftrated with 33 Copper-Plates. Revis'd and corrected by Dr. John Keil, F. R.S. Profeffor of Aftronomy in Oxford.

The Second Edition of

IV. A new and COMPLEAT TREATISE of the DOCTRINE of FRACTIONS, Vulgar and Decimal: Containing not only all that hath hitherto been publifh'd on this Subject; but also many other compendious Ufages and Applications of them. Never before extant. Together with a Compleat Management of Circulating Numbers, which is entirely new, and abfolutely neceffary to the right using of Fractions. To which is added, an Epitome of Duodecimals, and an Idea of Measuring. The Whole is adapted to the meaneft Capacity, and very ufeful to Book-keepers, Gaugers, Surveyors, and all Perfons whose Business requires Skill in Arithmetick. By SAMUEL CUNN, Teacher of the Mathematicks in Litchfield-Street, near Newport-Market. V. Chriftiani Hugenii Libellus de Ratiociniis in Ludo Alex: Or, the Value of all Chances in Games of Fortune, Cards, Dice, Wagers, Lotteries, &c. Mathematically demonstrated.

7

T

ADVERTISEMENT.

HOMAS HEATH, at the Hercules, next Door to the Fountain Tavern in the Strand, Makes and Sells, wholefale and retale, all Sorts of Mathematical Inftruments in Silver, Brafs,

Ivory, Wood, &c,

Perform'd according to the latest Obfervations of Philofophers, and Practifers of the feveral Mathematical Arts; whereby they are render'd. most neat, portable, accurate, and expeditious.

Whether they be for Geometry, Surveying, Navigation, Gauging, Measuring, (of Timber, Stone, Workmanship, &c.) Dialling, Geogra phy, Aftronomy, &c.

As Sectors, Scales, Compaffes, Drawing-Pens, Land-Quadrants, Theodolites, Semicircles, Circumferentors, Plane Tables, Water-Levels, Meafuring-Wheels, Dials (Portable, or to be fix'd,) Sea-Quadrants, Foreftaffs, Nocturnals, Gunter's, Sea-Compaffes (Meridian, or Azimuth ones,) Charts, Maps, Spheres, Weather-Glaffes, Load-Stones, Telescopes, Reading-Glaffes, Burning-Glaffes, Prifms, Sky-Opticks, Drawing-Boards, Sliding-Rules of all Sorts, Parallel-Rulers, &c. Toge-. ther with Books of their Ufes.

Alfo Globes moft neatly fitted up in Brafs Frames, and Horizons moved by two Wrack-Works; the one elevating the Poles; the other carrying the whole Body horizontally; with Levels and Needles in Boxes divided and fitted to the Frames, for the placing readily and fpeedily their Horizons parallel to the real one, and their Meridians in the Plane of the Celeftial one: Alfo Quadrants for taking the Altitudes of celeftial Phænomena contriv'd to move round on the Horizon. Together with Quadrants of Altitude, and other Appurte nances neceffary to render them moft Compleat.

He likewife makes the new Invented Architectonick Sector, and Sliding-Plates; whereby Scales of all Sizes are more readily and univerfally obtain'd, for Fluting Pillafters and Columns, and drawing the Geometrical Planes and Uprights, in any of the five Orders, according to the given Diameter of a Column. With feveral other Scales very convenient and ready for the Ingenious Defigners of Buildings.. By T. CARWITHAM Painter of Twickenham. Together with a Tract of their Ufes.