Fig. 98.
Before proceeding with the examples, a few elementary statements belonging to the science of geometry are presented; these will be useful to the student, not only while “doing” the problems, but in many cases of every-day—future—experience.
Geometry is one of the oldest and simplest of sciences; it may be defined as the science of measurement; geometry is the root from which all regular mathematical calculations issue. It has claimed the best thought of practical men from the times of the Greeks and Romans two thousand years ago; they derived their knowledge of the science from the Egyptians, who in turn were indebted to the Chaldeans and Hindoos in times beyond any authentic history; hence it was under the operations of the laws explained in geometry, that the pyramids of Egypt and the temples of Greece were constructed, as well as the engines of war and appliances of peace of ancient times.
A point is mere position, and has no magnitude.
A line is that which has extension in length only. The extremities of lines are points.
A surface is that which has extension in length and breadth only.
A solid is that which has extension in length, breadth and thickness.
An angle is the difference in the direction of two lines proceeding from the same point.
Lines, Surfaces, Angles and Solids constitute the different kinds of quantity called geometrical magnitudes.