Purchase of this book includes free trial access to www.million-books.com where you can read more than a million books for free. This is an OCR edition with typos. Excerpt from book: eurve that cannot be cut in two places by one straight line. 4. There is one thing more that I want you to learn at this lesson. Whenever a straight line joins two points of a curve, there is always some point on the curve between the two points at which the curve goes in the same direction as the straight line. So in my figure you see that the curve at c goes in the same direction as the straight line A B. Draw on your slate figures of curves, and cut them by straight lines, and you will find it always so. This seems like a very limple thing, and yet it is a very useful truth. CHAPTER IV. ABOUT ANGLES. 1. When two straight lines go in different directions, the difference of their directions is called anangle. The size of the angle depends, then, on the difference of the directions of the lines, and not on their length. So that the angle which I have blackboard, cross it by a straight line, and then, moving the chalk along the curve, require the scholars to say "now," whenever the chalk is moving in the same direction as the Straight line. Whal is an angli ? On what does the size of an angle depend ? Let the teacher draw angles on the blackboard, andask which is the larger, which the smaller, etc., being careful to make some of the angles without vertices. What is the ver- ex of an angle ? Let the teacher call the scholar to the board to point out the vertices of the angles he has drawn. When Iwo straight lines cross each other, what is always true aboutthe angles they make ? What is a right angle ? What examples can you give of a right angle ? What is the common name for the vertex of a right angle ? The teacher must be very careful not to let the child confound the measure of an angle with either the length of the sides, or area of the opening between them ; bu...