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SHOWING THE PROPOSITIONS OF LEGENDRE WHICH CORRESPOND TO THE PRINCIPAL PROPOSITIONS OF THE FIRST SIX BOOKS OF EUCLID.

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AN INDEX

Euclid.

Cor.2. of 32 Prop.

33

34

9 Prop.

9

6

Book II.

Legendre.

4

12

13

35

36

37 Cor. 2. of 2

38 Cor. 2. of 2

4

2

47

11

Book III.

27 Prop.

30

28

Book IV.

13

12

Book III.

6

3 Prop.
10 Cor. of 7

11 Cor. of

14

12 Cor. of 14)

14

8

15

2

18

9

20

18

21 Cor. of 18||

Euclid.

26 Prop.

28

29

31

35

36

Book VI.

1

2

3

4

Legendre.

8

14

15

19

20

S Cor. 2.

& 3.

15

5

5

}

Book IV.

18

28

30

Cor. 1. of 4

Cor. of 6

15

16

17

18

19

20

22

25

{Cor. of 15

25

26

27

ELEMENTS OF GEOMETRY.

BOOK I.

THE PRINCIPLES.

Definitions.

1. GEOMETRY is the science which has for its object the measurement of extension.

Extension has three dimensions, length, breadth, and height, or thickness.

2. A line is length without breadth, or thickness.

The extremities of a line are called points: a point, therefore, has neither length, breadth, nor thickness, but position only.

3. A straight line is the shortest distance from one point to another.

4. Every line which is not straight, or composed of straight lines, is a curved line.

Thus, AB is a straight line; ACDB is a broken line, or one composed of straight A lines; and AEB is a curved line.

E

B

The word line, when used alone, will designate & straight line; and the word curve, a curved line.

5. A surface is that which has length and breadth, without height or thickness.

6. A plane is a surface, in which, if two points be assumed at pleasure, and connected by a straight line, that line will lie wholly in the surface.

7. Every surface, which is not a plane surface, or composed of plane surfaces, is a curved surface.

8. A solid or body is that which has length, breadth, and thickness; and therefore combines the three dimensions of extension

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