Prop: I 14 1 1.17 2 18---Cor. 3. 14• 15. I.20 to the is. 2.21 29, 30 and 20 21 to 19. 28} Cor.2.of 3.119 24 12. 22 BOOK I. ,Prop. Theo. Prop: Theo.. Prop. Thea Theo: 5 & 6 Ax. 3. 24-Cor: to 3.113 C.coProb. 2. i Prob. 11. 7 5.125 6. 2 Prob. 2. 8 6. 15 3 Prob. 3: 9-Cor. to 5.1 BOOK VI. 16 8. 4 8. 10 Ax. 4. IO. 5. 9. 1 and 12 7. 2. 18 9. 6-Cor. 3. 9.113 Ax. 6. 3 3. 19-Cor. 1. 9: 8 7:14 3. 4 4. 20 and 22. - 13. C9 Prob. 9. 15 4:1 5 Cor. 1. 4.121 10 Prob. 8. 16 8. 6 time 5.23 fee NB. 2d. 11 Prob. 6. 17. Prob. 42. 8 724 12 Prob. 7. 8. 3. 25 13 1.19-Cor. 2. 8. 10 Prob. 36. 26 | fee N B. 14-Cor. 1. 9. u Prob. 31. 27 15 10.12 Prob. 32. 28 16. 16 and 17 1022 11.13 Prob. 30. 18 1223 and 24 are 14 and 15.-.8 31 are in the 17. igiCor. 11, 12 useless. 16 9. 32 Cor. 1. 57. 13 25. Prob. 40. 18. 14 26 and 27—10.18. Prob. 16. 34 22 Prob. 14. 19 12035 22. 23 Prob. f. 20:13:36 - 23. 24 and 25 are 30 Prob. 8. 21 Axiom. 37 in Cor. to 8.31 15.38-Cor: 2. 9. 26.com - 13.23. 11. 27 and 28—4.33 Proß. 44. 24 17. BOOK VIII. 29 Cor. 1&2. 4. 34 Prob. 43. 25 Prob. 38. 12 of Euclid. 30 5.35 14.26-Cor. to 17. I 14. 6. 31 Prob. 5. 16.27. - 18. 2 Cor. 1.14.6. 32 1o. 37 Converse. 28 and 29 are 3 and 4 are 33-Cor. to 15. useless and pro- wholly ornit34 15. BOOK V. lix Problems. ted, as useless. Those which are 30 Prob. 35. and 6 5 18 -6. 37 & 38. noi numbered 31 16. 4. 39 and 40. are whoily 0-32 - is useless: 8 7: Cor. to 18. mitted, as use-33 19:1:9 8. 41 17 5. 42 BOOK VII. Cor. 1 & 2.0. 43 Ax. 11.of Euclid. (12 Cor. 1 & 2.7. 44 Prob. 23. į Ax. I. 13 is an Axiom; 45 Prob. 22. 10 Ax. 6. 2 Ax. 4. and the same 24, 20 & 21. 11 Ax. 13. 3 as 15 of B. 7. "246 Prob. 17 -Cor. 3. 20.14 Ax. 12. 5-Cor. to 2.15-Cor. to 8. 48—Cor. to 20.15 Ax. 7 & 8. 6 3. 16 & 17 are use. 16 4. 7 Ax. 3. less, and proBOOK III. 17 7: lix Problems, 1 Prob. 39. 18 6. 4.18-Cor. to 9. 2 Ax. si 19 5. 3 9. 11 Prob. 1. 4 10.'12 Prob. 2. 3.10 1.22 2.123 Article Page Į. How the Area of a Square is obtained. 3 4 } s 7 7 8 any other Figure, having equal circuit. 14 suring or delineating ; in Decimals and Duodecimals. 16 17 18 19 10 } IZ 23 1, How the Area of a Cube is obtained. -47 Euclid. 27 ? 67. Practical Geometry, Page. Line. 240.- 7. B. for equality of Ratios, Page. Line. read, Ratio of Equality. 23.-9. Art. 4. for, Circles, reag, 244.- 2 and 4. B. for, Ratio, read, Circumferences. Increase. 38. 8. for, CDAB, read, CDbB. 244.10. B. for, A &C,r. A&B. 41.-10. read, intersecting at F. 5. B. read, if A be 3. 42.- -. B. far, A, read, H. 257.711. for, Def. 6. read Ax. 6. 47.- 7. for., CDG, read, CDG. -19. for, A:B, read, if A:B. 31.- Line last, for 10, read, 20. B. far, B. real, C, ånd 57.- 8. B. for, 20..1. read, 18.1. for C, read, B. 58.-16. for, AHCD, r. GHCD. 258.- 5. B. f. Axiom, r. Postulate. 62. 9. B. før, 12. 2. read, 12.30|261.-10. B. for, as A to B, read, 4. read, to the fourth. as B to A. .70 –15. for, AH, read, AF. 267.-12. B. for, D to G, r. Cto G. 75.-12. for, AC, read, a C. 268.- 2. Dem. for, A and B, 96.-11. for, MN, read, KM. read, A and C. 98.-11. for, Def. 15. and 18.7th. 300.- 4. read, Triangles. read, i and 6. 8th. 329.-10. for, 8. 4. read, 9.4. 104.- 7. Prob. 7. for, H, read, K; 338. 6. for, AC, read, BC. and, for, K, read, H. 339. 4. B. for, ABC, read, AB. 107.16. for, and, read, i.e. chatis. 10. B. for, EG, read, EF. 347.-10. Dem. read, Draw otheç Right Lines. 355. .- 6. B. for, F&G, r. D& E. 116.–3 & 4. for, E, read, A. 8 & 10. B. for, G, read, D. $20.- Bottom, for, ECB, 'r. DCB. 356.- 8. for, AG, read, CG. 358.- 3. Dám. for, BK, read,BL, 12.5.- 5. for, Ax. 3. read, 7. 135.5. Theo. 2.f. BAG,"EAG. 365:- 6. for, Ax. 4. 5. read, 5.5. 5. for, Def. 7. read. 8. 146.- 7. for, CD, read, BC. 391. 3. for, Ax. 11.7.read, Def. »47.-13. for, Hyp. AB, read, AC. 156. 9. Th. 2. for, AE, read, AD 401.- laft. for BF. read, Bf. -14. for, Ax. 3. read, 2. 408.- 13. Dem, add, and having cqual Altitudes. 158.- 2. B. for EA, read, EH. 171.- 6 for, EB, read, EC. 172 5. Bottom, for, 13th, read, 14 In the Appendix. . . 182.-13. for, Def. 44, riad, 43. 183 7. Cor. 2. for, ind, r. in H. 190.- .- 7. Bottom, read, DG in D. 13.7 5. for, BE. read, DE. 395.-11. read, sroís each other. 14.- 8. B. for, 425, read 375. 223.- S. B.for AFO=FB 0,read, 19.19 & 20, for, K, read, F. AFO= AE 0+EFO 25-13, 15, & 16, for, G, read, E. 225.- 8. Cor, read, Duodecagon.) 32.- 6. for, Chord of go, read, 6o. 388. , , HE mathematical World will, I doubt not, be surprizei at a frech publication of the Elements of Geometry, by one entirely unknown ; and, on a plan very different from that of others who have wrote on the Subject. I hope they will suspend their opinion, and not pass a too hafty censure, on account of the obscurity of the Author, till after they have given it a fair and candid perusal, and then proceed to judgment with candour and impartiality. I do not pretend to much knowledge in the Mathematics, having been brought up in a way of life, very different from my inclination ; yet, what time I could spare from business and the demands of my family, I chose to employ in such studies; and have, by dint of study, only, and without any other instruction, made some progress in mathematical Sciences; of which, Geometry is the first, and a sure key to the rest. Since I have made myself, by self-application, a Proficient in Geometry, and have in.ade some branches of the Alathematics my Study and Profession, I have often been surprized at the negligence and deficiency of our common Schools, for the cultivation of Youth who are intended to fill the middle sphere of Life, in mechanic Trades, &c. They, almost in general, pursue one common Plan or track of Learning. After the first and necessary branches, Reading, Writing, and Arithmetic; which, indeed, might be acquired in half the time it usually is; the next step (if the Pupil has made a progress thro’ Arithmetic in any reafonable sime) is the Grammar of the Latin Tongue through which, he sweats and labours to little purpose. If the Pupil bas three or four years to spare, before he goes out to business, he perhaps gets into the Cordery or Erasmus ; or, if he reaches Cornelius Nepos, he is looked on as a prodigy. Now, it may reasonably be asked, for what purpose all this Time has been spent ? which might have been employed to much A better 1 1.17 2 4.21 I 2. 18-Cor. 3. Prob. 3. 14-Cor. 1. 1.20 15 2.21 10 22 29, 30 and 20 12.35 22. 24. 1 2. 2 2 BOOK I. ,Prop. Theae 5 & 6 Ax. 3. 24-Cor. to 3.13 Coco Prob. z. Prob. 11. 7 5.25 6. 2 Prob. 2. 8 6. 15 7. 3 Prob. g. 9-Cor. to 5. BOOK VI. 16 8. 4 8. 10 Ax. 4: IO. 5 9.1 and 12 -7. 2.118 9 6-Cor. 3. 9. 13 Ax. 6. 3.19-Cor. 1. g: 8 7:14 3. | 4 4.120 and 22. 13. 9 Prob. 9. 15 Cor. 1. 10 Prob. 8. 16 8. L 5:23 fee NB. 2d. 1. Prob. 6. 17 Prob. 42. 8 7.24 14. 12 Prob. 7. 8. 25 -15 13 1.19-Cor. 2. 10 Prob. 36. : 26 fee N B. 9. u Prob. 31. 27 ) to the 15. 10.12 Prob. 32. 28 16. 16 and 17 11.13 Prob. 30. 18 12 23 and 24 are 14 and 15.-831 are in the 173 19-Cor. 1a, 12 useless. 16 9. 32. Cor. 1. 173 1325 Prob. 40. 17-Cor. to. 9. 33 18. 21 14 26 and 27-10.18. Prob. 16. 34 19. 22 Prob. 14. 128 38 Cor. 2. of 3.13 23 Prob. 4. 20:13:36 23. 24 and 25 are 30 Prob. 8. 21 Axiom. 137 in Cor. io 8. 31 15.38-Cor. 2. 9. 26 11. 32. 13.123 27 and 284.33 Proh. 44. 24 a 17. BOOK VIII. 29. Cor. 1&2. 4. 34 Prob. 43. 25 Prob. 38. 12 of Euclid. 30 5:35 14. 26-Cor. to 17. 16.27. 18. 2 Cor. 1.14.6. 32 Converse. 28 and 29 are 3. and 33-Cor. to 15. useless, and pro- wholly omit34 en 15. BOOK V. lix Problems. ted, as useless. Those which are 30 Prob. 35. and 6 -6. -18 37 & 38. noi numbered 31 16. 4. 39 and 40. are wholly o- 32 - is uselefs: 8 7: Cor. to 18. nitted, as use- 33 19:19 8. 41 less. 5. 42 Prob. 20. 1.BOOK VII.lu Cor. 1 & 2.6. 19.17 Ax. 43 + 11.of Euclid. 12 Cor. 1 & 2.7. 44 Prob. 23. 9 Ax. i Ax. I. 13 is an Axiom; 45 Prob. 22. 2 Ax. 4. and the same u Ax. 13: 3 as 15 of B.7. 26 Prob. 17 4 2. (14-Cor. 3. 6. 47 II. 20. 14 Ax. 12. 5-Cor. to 2.15-Cor. to 8. 48–Cor. to 20.15 Ax. 7 & 8. 6 3.16 & 17 are use. 16 4.1 7. Ax. 3. less, and proBOOK III. 17 7.1 E-Cor. 10 3. lix Problems, 1 Prob. 39. 18 4.18-Cor. to g. 2 Ax. 50 19 5. 3 9.11 Prob. 1. 10.'12 Prob. 2. 3:10 1. 122 2. 123 |