CHAMBERS'S INFORMATION FOR THE PEOPLE. 



these angles is called a right angle, and the line 

 AC is in that position said to be perpendicular, or 

 at right angles to AB. 



When AC, in revolving round A, arrives at the 

 position indicated in fig. 5, and such that it forms 



B 6'" 



one continuous line with AB, the angle thus 

 formed is said to be an angle of two right angles. 



An angle which is less than a right angle is said 

 to be acute, as in figs. I and 2. 



An angle which is greater than a right angle is 

 said to be obtuse, as in fig. 4. 



An angle greater than two right angles is said 

 to be reflex, as in figs. 6 and 7. 



A figitre is a portion of space inclosed by one 

 or more boundaries. 



A plane figure is inclosed by one or more 

 lines. A 



A triangle is a plane figure 

 inclosed by three lines; thus 

 ABC is a triangle, the lines 

 AB, AC, BC are called its 

 sides ; and any one of these 

 sides, with reference to the other two, is termed 

 the base. 



If the sides of the triangle are all 

 equal, it is said to be equilateral. 



If two sides are equal, the tri- 

 angle is said to be isosceles. 



If one angle, as C, of a triangle, ABC, be a 

 right angle, the triangle is said to 

 be right-angled, and the side AB, 

 which is opposite the right angle, 

 is called the hypotenuse; and if 

 one angle be obtuse, it is an obtuse- 

 angled triangle. 



A quadrilateral is a figure of four sides, and a 

 polygon of several ; when the sides and angles of 

 a polygon are equal, it is said to be a regular 

 polygon. 



Parallel lines are lines in 



the same plane, which, being 



produced ever so far both ways, never meet 



A parallelogram is a four- / -r 



sided figure, whose opposite / / 



aides are parallel. L. / 



610 



A rectangle is a parallelogram, 

 having one of its angles a right 

 angle. 



A square is a rectangle, having its adjacent 

 sides equal, or a four-sided figure 

 having its sides equal, and each 

 of its angles a right angle. 



A circle is a plane figure con- 

 tained by one line called the 

 circumference, and is such that all 

 straight lines drawn from a certain 

 point within it to the circumference are equal 

 to one another. This point is called the centre. 



The circumference of a circle may be defined 

 as the line traced out by a point which moves 

 in such a manner that its dis- 

 tance from a fixed point is 

 always the same. 



An arc of a circle is any por- 

 tion of the circumference. 



A chord is the line joining any 

 two points on the circumference. 



A diameter is a chord which passes through 

 the centre, as AB. 



A radius is a line drawn from the centre to the 

 circumference, as OC. 



A segment of a circle is the figure contained by 

 an arc and its chord. 



A semicircle is a segment whose chord is a 

 diameter. 



POSTULATES. 



Let it be granted, 



1. That a straight line may be drawn from one 

 point to another. 



2. That a terminated straight line may be pro- 

 duced or continued any length. 



3. That a circle may be described with any 

 radius, and hence that a length equal to a given 

 length may be cut from a given line. 



AXIOMS. 



1. Things which are equal to the same thing 

 are equal to one another. 



2. If equals be added to equals, the wholes are 

 equal. 



3. If equals be taken from equals, the remain- 

 ders are equal. 



4. If equals be added to unequals, the wholes 

 are unequal. 



5. If equals be taken from unequals, the re- 

 mainders are unequal. 



6. Things which are double of the same are 

 equal 



7. Things which are halves of the same are 

 equal 



8. Magnitudes which exactly coincide that is, 

 which exactly fill the same space are equal. 



9. The whole is greater than any part of it 



10. All right angles are equal. 



n. Lines which intersect cannot be parallel to 

 the same line. 



ANGLES. 



PROPOSITION I. The angles which one straight 

 line makes with another upon the same side of it 

 are together equal to two right angles. 



