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.
9
Prob.

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.
IT Cor. to. 9. 33

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.
7

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
less.

5. 42

BOOK VII. Cor. 1 & 2.0. 43

Ax.
4.

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:
E-Cor. 10 3

lix Problems, 1 Prob. 39.

18

6.
9

4.18-Cor. to 9. 2 Ax. si 19

Article

Page

Į. How the Area of a Square is obtained.

3
2. Of any Rectangle whatever. 3. Of the Triangle.

4
4. All Figures, having equal circuit, are not equal in Area. 4
5. A Square contains a grea er Area than any other
Rectangle, the sums of whose Sides are equal.

} s
6. The Difference between a Rectangle and other Parallelogram 6
7. How the Areas of regular Polizons are obtained.

7
8. Of the Circle.

7
9. The Affinity between Circles, and Poligons.

8
16. That a Circle has a greater Area than a Square, or

any other Figure, having equal circuit.
11. The Area of a Rectangle ascertained, and accounted for.
12. By Duodecimals, or Feet and Inches.
13. By decimal Parts; the difference explained.

14
14 and 15. The Construction and use of Scales, for mea- 15

suring or delineating ; in Decimals and Duodecimals. 16
16. Of irregular Figures; as a Field, &c.

17
17. How to divide any right-lined Figure into two equal

18
parts, by a Right Line, from any Point in any Side.
18. How to obtain the Area of a Triangle, from the
measure of its Sides only, without a Perpendicular.

19
S

10

}

IZ

23
2+
24
25
26

1, How the Area of a Cube is obtained.
2. Of other right-angled Parallelopipeds.
3. Of any Parallelopiped, Prism or Cylinder whatever.
4. Of Pyramids and Cones.
5. How the Area of a Sphere is ascertained.
6. Of the Segment of a Sphere. า
7. Of Guaging Vefsels, Barrels, &c. s
8. Of irregular Solids.
A mechanichal demonstration of Theo. 20. 1.-

-47 Euclid.
Line of Chords, constructed and explained.

27
28
29
30

?

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.
In the Elements, 349.- 3. Dem. for, on, read, or.

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.

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.
Theo. Prop: Theo.Prop.

Theae
Prop.
Theo.|

5 & 6 Ax. 3. 24-Cor. to 3.13 Coco Prob. z. Prob. 11. 7

5.25
tim I'4

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.
9

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.
7

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.
5.

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.