38
ON THE CIRCLE.
THIRD LESSON.
A circle is a plane surface, of which the boundary calledthe circumference is, in all its points, equally distant froma single point called the centre.
All the right lines drawn from the centre to the circum-ference, measuring equal distances, are equal to each other.These lines are called radii; and thus all the radii of acircle are equal to one another.
When two radii are directly opposite to each other, theone to the right, the other to the left of the centre, thesingle right line which they form is called the diameterof the circle.
Thus, in the circle ABDE, fig. 1, plate 3, C being the centre,CA, CB, CD, CE, are radii, all being equal to one another. Ifthe two radii CA, CD, form a right line ACD, this line is a dia-meter of the circle.
Every diameter DA, fig. 1, pi. 3, divides the circleinto two equal parts.
To be convinced of this it is only necessary to double the partDAB over the part DAE, turning it on the diameter DA, as on ahinge. If any point of the circumference DAB fell within any pointof the circumference DAE, it would be nearer the centre than thispoint; if any point in DAB fell outside of any point in DAE it wouldbe further from the centre. But this cannot be the case, for all thepoints of the circumference ABDEA are equally distant from thecentre. The part DBA will therefore fall in every point on thepart DAE, and the two portions of the circle separated by the diame-ter DA are equal to each other.