402 



GEOMETRY 



ness. A body or solid, fig. 3, is a figure of three 

 dimensions, namely, length, breadth, ami depth, or 

 thickness. A right line, or straight line, lies all 

 in the same direction, between its extremities ; and is 

 the shortest distance between two points. When a 

 line is mentioned simply, it means a right line. 

 4 5 6 



pairs of opposite sides parallel. A rectangle, fig. 14 

 w a parallelogram, having a right angle. 

 14 I5 16 17 



A curve, fig. 4, continually changes its direction 

 between its extreme points. Parallel lines, fig. 5, 

 are always at the same perpendicular distance ; and 

 they never meet, though ever so far produced. Ob- 

 Mque lines, fig. 6, change their distance, and would 

 meet, if produced on the side of the least distance. 

 And an angle is the inclination or opening of two 

 lines, AB and AC, having different directions and 

 meeting in a point A. In designating an angle, the 

 'etter at the point of meeting, is placed in the mid- 

 dle : thus we say, angle BAG or C A B, but not 

 A B C or A C B, fig. 7. 



789 



A square fig. 14, is an equilateral parallelogram 

 rectangle ; having its length and breadth equal? A 

 rhomboid, fi g . la, i* an oblique-angled parallelogram. 

 A rhombus, fig 16, is an equilateral rbomuoid 

 having all its sides equal, but its angles oblique \ 

 trapezium, fig 17, i s a quadrilateral which hath not 

 its sides parallel. 

 18 



A right angle, B A C or B A D, fig. 7, is that 

 which is made by one line A B perpendicular to an- 

 ther C D. Or when the angles on each side are 

 equal to one another, they are right angles. An 

 oblique angle is that which is made by two oblique 

 lines ; and is either less or greater than a right 

 angle. An acute angle, ABC, fig. 8, is less than 

 a right angle. An obtuse angle, ABC, fig. 9, is 

 greater than a right angle. Superficies or surfaces are 

 either plane or curved. A plane superficies, or a 

 plane, is that with which a right line may, every 

 way, coincide. Or, if the line touch the plane in 

 two points, it will touch it in every point. But, if 

 not, it is curved. Plane figures are bounded either 

 by right lines or curves. Plane figures that are 

 bounded by right lines have names according to the 

 number of their sides, or of their angles ; for they 

 have as many sides as angles ; the least number 

 being three. 



10 11 12 13 



A trapezoid, fig. 18, has only one pair of opposite 

 sides parallel. A diagonal is a line joining any two 

 opposite angles of a quadrilateral. Plane figures that 

 have more than four sides are, in general, called 

 polygons. A pentagon is a polygon of five sides ; 

 a hexagon, of six sides ; a heptagon, seven ; an 

 octagon, eighL ; a nonagon, nine ; a decagon, ten ; 

 an undecagon, eleven; and a dodecagon, twelve 

 sides. A regular polygon has all its sides and all its 

 angles equal. If they are not both equal, the poly- 

 gon is irregular. Any figure is equilateral, when all 

 its sides are equal : and it is equiangular when all iti 

 angles are equal. A circle, BDAE, fig. 19, is a 

 plane figure bounded by a curve line, called the cir- 

 cumference, which is everywhere equidistant from a 

 certain point C within, called its centre. The cir- 

 cumference itself is often called a circle, and also the 

 periphery. The radius of a circle CB, fig. 19, is a 

 line drawn from the centre to the circumference. 

 The diameter of a circle is a line AB, fig. 20, drawn 

 through the centre, and terminating at the circum- 

 ference on both sides. An arc, fig. 4, of a circle is 

 any part of the circumference. A chord AB, fig. 

 21, is a right line joining the extremities of an arc 

 ACB. A segment ACB, fig. 21, is any part of a 

 circle bounded by an arc and its chord. A semicir- 

 cle is half the circle, or a segment cut off by a dia- 

 meter. The half circumference is sometimes called 

 the semicircle. 



22 23 24 



\ 



A figure ABC, fig.10, of three sides and angles is cal- 

 led a triangle. An equilateral triangle is that whose 

 three sides are all equal. An isosceles triangle, 

 fig. 10, is that which has two sides equal. A sca- 

 lene triangle is that whose three sides are all un- 

 equal. A right-angled triangle, fig. 11, is that 

 which has one right angle, ABC. In a right- 

 angled triangle, the side A C opposite to the right 

 angle, is called the hypotenuse, and the other two 

 sides are called the legs, or sometimes the base C B, 

 and perpendicular B A. Other triangles are ob- 

 lique-angled, and are either obtuse or acute. An 

 obtuse-angled triangle, fig, 12, has one obtuse angle. 

 An acute-angled triangle, fig. 13, has all its three 

 angles acute. A figure of four sides and angles is 

 called a quadrangle, or quadrilateral. A parallel- 

 ogram, fig. 14, is a quadrilateral which has both its 



A sector ACB, fig. 22, is any part of a circle 

 which is bounded by an arc, and two radii drawn to 

 its extremities. A quadrant, fig. 23, or quarter of 

 a circle, is a sector having a quarter of the circum- 

 ference for its arc, and its two radii are perpendicu- 

 lar to each other. A quarter of the circumference 

 is sometimes called a quadrant. The height or 

 altitude of a figure ABCD, fig. 24, is a perpendicu- 

 lar AB let fall from an angle A, or its vertex, to the 

 opposite side. CD, called the base. The circumfer- 

 ence of every circle is supposed to be divided into 

 360 equal parts, called degrees ; and each degree 

 into 60 minutes, each minute into 60 seconds, and 

 so on. Hence a semicircle contains 180 degrees, 

 and a quadrant 90 degrees. The French have a 

 different method of division. (See Degree.) The 

 measure of an angle, is an arc AB, fig. 22, of any 

 circle contained between the two lines ("A, CB. 



