1.
Two lines are said to be commensurable when each contains a line taken as the standard of measurement (or, as it is commonly called, the unit of length) an exact number of times.. 4.
Since the standard contains itself once, its measure is unity, and it will be represented by 1.
To measure a line AB we fix upon some line as a standard of linear measurement: then if AB contains the standard line p times, p is called the measure of AB, and the magnitude of AB is represented algebraically by the symbol p. 3.
By way of introduction to the subject we have to treat in this chapter, first, of the representation of lines by Algebraic Symbols, and, secondly, of the relation existing between the circumference of a circle and its diameter. 2.
Trigonometry was originally, as the name imports, the science which furnished methods for determining the magnitude of the sides and angles of triangles, but it has been extended to the treatment of all theorems involving the consideration of angular magnitudes. 1
