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6. A plane superficies is that which is everywhere perfectly flat and even.

7. A plane rectilineal angle is the inclination or opening of two right lines which meet in a point.

8. One right line is said to be perpendicular to another, when it makes the angles on both sides of it equal to each other.

9. A right angle is that which is made by two right lines that are perpendicular to each other.

10. An obtuse angle is that which is greater than a right angle.

II. An acute angle is that which is less than a right angle.

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12. A figure is that which is inclosed by one or more boundaries.

13. A circle is a plane figure, contained by one line, called the circumference, which is every where equally distant from a point within the figure, called the centre.

14. Rectilineal figures are those which are contained by right lines.

15. All plane figures, bounded by three right lines, are called triangles.

16. An equilateral triangle, is that which has all its fides equal to each other.

17. An isosceles triangle, is that which has only two of its fides equal to each other.

18. A right-angled triangle, is that which has one right angle; the side which is opposite to the right angle being called the hypotenuse.

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19. An obtuse-angled triangle, is that which has one obtufe angle,

20. Parallel right lines are such as are in the same plane, and which, being produced ever so far both ways, will

never meet.

21. Every plane figure, bounded by four right lines, is called a quadrangle, or quadrilateral.

22. A parallelogram, is a quadrangle whose opposite fides are parallel.

23. The diagonal of a quadrangle, is a right line joining any two of its opposite angles.

24. The base of any figure is that fide upon which it is supposed to stand ; and the vertical angle is that which is opposite to the base.

Note, When an angle is expressed by means of three letters, the one which stands at the angular point, must always be placed in the middle,

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POSTULAT E S.

1. Let it be granted that a right line may be drawn from any one given point to another.

2. That a terminated right line, may be produced to any length in a right line.

3. That a circle may be described from any point as a centre, at any

distance from that centre.

4. And that a right line, which meets one of two parallel right lines, may be produced till it meets the other.

AXIOM S.

1. Things which are equal to the fame thing are equal to each other,

2. If equals be added to equals the wholes will be equal

3. If equals be taken from equals the remainders will

be equal.

4. If equals be added to unequals the wholes will be unequal.

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5. If equals be taken from unequals the remainders will be unequal.

6. Things which are double of the same thing are equal to each other.

7. Things which are halves of the same thing are equal to each other.

8. The whole is equal to all its parts taken together.

9. Magnitudes which coincide, or fill the same space, are equal to each other.

R E M ARK S.

A PROPOSITION, is something which is either proposed to be done, or to be demonstrated.

A PROBLEM, is something which is proposed to be done.

A THEOREM, is something which is proposed to be demonstrated.

A LEMMA, is something which is previously demonstrated, in order to render what follows more easy.

A COROLLARY, is a consequent truth, gained from some preceding truth, or demonstration.

A SCHOLIUM, is a remark or observation made upon fomething going before it.

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