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12 23 and 24 are 14 and 15-831 are in the 17.

19 Cor. 1.. 12 useless.

20

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8. 10 Prob. 36.' 9.11 Prob. 31. 10.12 Prob. 32.

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27

to the 15.

28

16.

11.13 Prob. 30.

29, 30 and

16

9.32 Cor. 1. 17.

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22 Prob. 14. 23 Prob. 4.

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27 and 28-4.133 Prob. 44. 29 Cor. 1&2, 4.134 Prob. 43. 535

30

31 Prob. 5. 36

20:1

21 Axiom.

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24 17.BOOK VIII. 25 Prob. 38. 12 of Euclid. 26-Cor. to 17. 14. 6. 16.2718. 2 Cor. 1.14.6. 28 and 29 are

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137

24.

14.

32

10.37 Converse.

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33-Cor. to 15.

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BOOK V.

lix Problems.

ted, as useless.

35, 36,

37 & 38. J

and 40. Cor. to

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lefs.

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Prob. 20.

43

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Ax.

4.

11 of Euclid.

12 Cor. 1 & 2.7.

44 Prob. 23.

45 Prob. 22.

9 Ax. 5. to Ax. 6.

1 Ax. 1.

2 Ax. 4.

47

24, 20 & 21.

46 Prob. 17% 12

20. 14 Ax. 12.

48-Cor. to 20. 15 Ax. 7 & 8. 16

BOOK III. 17

11 Ax. 13.

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and the fame

as 15 of B. 7. 2.14-Cor. 3. 6.

5-Cor. to 2.15-Cor. to 8.

3.16 & 17 are uselefs, and pro8-Cor. to 3. lix Problems. 4.18-Cor, to 9.

is an Axiom,

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9.11 Prob. 1.

2.123

10.12 Prob. z.

Article

1. How the Area of a Square is obtained.

2. Of any Rectangle whatever. 3. Of the Triangle.
4. All Figures, having equal circuit, are not equal in Area.
5. A Square contains a greater Area than any other
Rectangle, the fums of whofe Sides are equal.

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4

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

8. Of the Circle.

9. The Affinity between Circles, and Poligons.

10. That a Circle has a greater Area than a Square, or
any other Figure, having equal circuit.

-

7

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II

12

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 and 15. The Conftruction and ufe of Scales, for mea-
furing or delineating; in Decimals and Duodecimals.

16. Of irregular Figures; as a Field, &c.

17. How to divide any right-lined Figure into two equal
parts, by a Right Line, from any Point in any Side.
18. How to obtain the Area of a Triangle, from the 1
measure of its Sides only, without a Perpendicular.

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14

15

16

17

18

19

2T

22

22

Of Solids.

1. How the Area of a Cube is obtained.

23

4. Of Pyramids and Cones.

2. Of other right-angled Parallelopipeds..

3. Of any Parallelopiped, Prifm or Cylinder whatever.

5. How the Area of a Sphere is ascertained.

24

24

25

26

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A mechanichal demonstration of Theo. 20. 1.-47 Euclid.
Line of Chords, conftructed and explained.

29

30

Practical Geometry.

Page. Line.

240.

Fage. Line.
23.-9. Art. 4. for, Circles, reaa, 244.-
Circumferences.

38. 8. for, CDAB, read, CDbB.
41.-10. read, interfecting at F.
42.. B. far, A, read, H.

7. B. for equality of Ratios, read, Ratio of Equality. and 4. B. for, Ratio, read,

2 Increase. [244.10. B. for, A & C, r. A & B. 5. B. read, if A be 3. 257.11. for, Def. 6. read Ax. 6. -19. for, A: B, read, if A:B. 7. B. far, B. read, C, and for C, read, B.

5. B. f. Axiom, r. Poftulate. B. for, as A to B, read, as B to A.

47.- 7. for, CDG, read, CDG.
31. Line laft, for 10, read, 20.
57. 8. B for, 20..1. read, 18.1.
58.-6. for, AHCD, r. GHCD. 258.
62.- 9. B. for, 12. 2. read, 12.3.261.10.
67.
4. read, to the fourth.
70-15. for, AH, read, AF.
75.-12. for, AC, read, a C.
96.-11. for, MN, read, KM.
98.-11. for, Def. 15. and 18. 7th.
read, 1 and 6. 8th.

104.7. Prob. 7 for, H, read, K;
and, for, K, read, H.

107.-16. for, and, read, i.e. that is.

In the Elements.

267.-12. B. for, D to G, r. C to G.
268.- 2. DEM. for, A and B,
read, A and C.
4. read, Triangles.

300.

329.-10. for, 8. 4. read, 9. 4. 6. for, AC, read, BC.

338.

339.

4. B. for, ABC, read, AB. 10. B. for, EG, read, EF. 347.-10. DEM. read, Draw other Right Lines.

349.

355

3. DEM. for, on, read, or. 6. B. for, F&G, r. D & E. 8 & 10. B. for, G, read, D. 8. for, AG, read, CG. 3. DEM. for, BK, read, BL. 6. for, Ax. 4. 5. read, 5.5. 388.- 5. for, Def. 7. read. 8. 391. 3. for, Ax. 11. 7.read, Def. 401.- laft. for BF. read, Bf. 408.-13. DEM. add, and having equal Altitudes.

116.3 & 4. for, E, read, A.
$20.-Bottom, for, ECB, r. DCB. 356.-
358.-
125. 5. for, Ax. 3. read, 7.
135.5. Theo. 2.f.BAG,r.EAG. 365.
146. 7. for, CD, read, BC.
147-13. for, Hyp. AB, read, AC.
156. 9. Th. 2. for, AE,read, AD
-1 ∙14. for, Ax. 3. read, 2.
158. 2. B. for EA, read, EH.
171.6 for, EB, read, EC.

372

5. Bottom,for, 13th,read, 14 182.—13. for, Def. 44, read, 43. 183 7. Cor.2. for, in A, r. in H. 190.7. Bottom, read, DG in D. 195.-11. read, srofs each other. 223. 5. B. for AF□FB,read, AFD=AE 0+EFO 225.- 8. Cor. read, Duodecagon.

In the Appendix...

13 5. for, BE. read, DE. 14.- 8. B. for, 425, read 375. 1919 & 20, for, K, read, F. 25-13, 15, & 16, for, G, read, E. 32. 6. for, Chord of 90, read, 60,

THE mathematical World will, I doubt not, be furprized at

a fresh 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 fufpend their opinion, and not pass a too hafty cenfure, on account of the obfcurity of the Author, till after they have given it a fair and candid perufal, and then proceed to judgment with candour and impartiality.

I do not pretend to much knowledge in the Mathematics, ha ving been brought up in a way of life, very different from my inclination; yet, what time I could fpare from bufinefs and the demands of my family, I chofe to employ in fuch studies; and have, by dint of ftudy, only, and without any other instruction, made fome progrefs in mathematical Sciences; of which, Geometry is the firft, and a fure key to the reft.

Since I have made myfelf, by felf-application, a Proficient in Geometry, and have made fome branches of the Mathematics my Study and Profeffion, I have often been furprized at the negligence and deficiency of our common Schools, for the cultivation of Youth who are intended to fill the middle fphere of Life, in mechanic Trades, &c. They, almoft in general, pursue one common Plan or track of Learning. After the fift and necessary branches, Reading, Writing, and Arithmetic; which, indeed, might be acquired in half the time it ufually is; the next step (if the Pupil has made a progrefs thro' Arithmetic in any reasonable time) is the Grammar of the Latin Tongue through which, he fweats and labours to little purpofe. If the Pupil has three or four years to spare, before he goes out to bufinefs, he perhaps gets into the Cordery or Erafmus; 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

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16 and 17
8

1. 20

2.21

9.11 Prob. 31.

27

to the 15.

10. 12 Prob. 32.

28

16.

10 22

11.13 Prob. 30.

12 23 and 24 are 14 and 15.-831 are in the 17.

29, 30 and

19-Cor. 1.

12

ufelefs.

16

9.32 Cor. 1. 17.

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Prob. 40.

21

22 Prob. 14.

14 26 and 27-10.

17Cor. to
18 Prob. 16.

9.33

18.

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23 Prob. 4.

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201

24

and

21 Axiom.

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12.22

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25 are 30 Prob. 8.

in Cor. to 8. 3T

.11.32 - 13.23

27 and 28-4.33 Prob. 44. 29 Cor. 1&2, 4.134 Prob. 43.

24

13.3623.

15.38-Cor. 2. 9.

11.

17.BOOK VIII. 12 of Euclid.

25 Prob. 38.
14. 26-Cor. to 17.
16.27 18.
28 and 29 are
ufelefs,and pro-
lix Problems.

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14. 6.

2 Cor. 1.14.6.

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35, 36,

18

37 & 38. f

Thofe which are 30 Prob. 35. 5
not numbered 31
16.

ted, as useless.

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39 and 40.

Cor. to

18.

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are wholly 0-32 is useless: 8
mitted, as ufe-33

1.BOOK VII. Cor. i& 2.6.

7.

19-9

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8.

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Ax.

4.

11 of Euclid.

12 Cor. & 2.7.

24, 20 & 21. 46 Prob. 17.

47

44 Prob. 23. 45 Prob. 22.

9 Ax. 5. 10 Ax. 6.

11 Ax. 13.

12

20. 14 Ax. 12.

48-Cor. to 20.15 Ax. 7 & 8.

-16

BOOK III. 17

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is

13 an Axiom,

and the fame

as 15 of B. 7. 2.14-Cor. 3. 6.

5-Cor. to 2.15-Cor. to 8.

3.16 & 17 are uselefs, and pro8-Cor. to 3. lix Problems. 4.18-Cor, to 9.

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9.11 Prob. 1.

2.123

10.12 Prob. z.

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