Page:First six books of the elements of Euclid 1847 Byrne.djvu/29

Rh the letter which marked the vertex of the angle being always placed in the middle. Thus the black and red lines meeting together at C, form the blue angle, and has been usually denominated the angle FCD or DCF. The lines FC and CD are the legs of the angle; the point C is its vertex. In like manner the black angle would be designated the angle DCB or BCD. The red and blue angles added together, or the angle HCF added to FCD, make the angle HCD; and so of other angles. When the legs of an angle are produced or prolonged beyond its vertex, the angles made by them on both sides of the vertex are said to be vertically opposite to each other: Thus the red and yellow angles are said to be vertically opposite angles. Superposition is the process by which one magnitude may be conceived to be placed upon another, so as exactly to cover it, or so that every part of each shall exactly coincide. A line is said to be produced, when it is extended, prolonged, or has its length increased, and the increase of length which it receives is called its produced part, or its production. The entire length of the line or lines which enclose a figure, is called its perimeter. The first six books of Euclid treat of plain figures only. A line drawn from the centre of a circle to its circumference, is called a radius. The lines which include a figure are called its sides. That side of a right angled triangle, which is opposite to the right angle, is called the hypotenuse. An oblong is defined in the second book, and called a rectangle. All the lines which are considered in the first six books of the Elements are supposed to be in the same plane. The straight-edge and compasses are the only instruments,