CD is to be taken away from the line AB. X is the sign of Multiplication. is the sign of Division. <stands for less than; e. g., the line AB CD means that the line AB is shorter than the line CD. stands for greater than; e. g., the line ABCD means that the line AB is longer than the line CD. stands for parallel; e. g., the line ABCD means that the line AB is parallel to the line CD. #stands for equal and parallel; e.g., the line ABCD means that the line AB is equal, and, at the same time, parallel to the line CD. A point is denoted by a single letter of the alphabet chosen at pleasure; e. g., .B the point B. A line is represented by two letters placed at the beginning and end of it; e. g., letters, the one that stands at the vertex always placed in the middle; e. g., the angle ABC or CBA. It is sometimes also represented by a single letter placed within the angle; e. g., a the angle a. A triangle is denoted by three letters, placed at the three verteces; e. g., the triangle ABC. Any polygon is denoted by as many letters as there are verteces; e. g., the pentagon ABCDE. A quadrilateral is something also denot ed only by two letters, placed at the oppo site verteces; e. g. Α the quadrilateral AB. B QUESTIONS ON NOTATION AND SIGNIFICATIONS. What signs do mathematicians use to abreviate writing? What is the sign of equality? What sign stands for plus, or more? What for minus, or less? What for multiplication? What for division? What for less than? What for more than? What for equal and parallel? How is a point denoted? How a line? How an angle? How a triangle? How a quadrilateral? Axioms. There are certain invariable truths, which are at once plain and evident to every mind, and which are frequently made use of, in the course of geometrical reasoning. As you will frequently be obliged to refer to them, it will be well to recollect the following ones particularly: TRUTH I. Things, which are equal to the same thing, are equal to one another. TRUTH II. Things, which are similar to the same thing, are similar to one another. TRUTH III. If equals be added to equals, the wholes are equal. TRUTH IV. If equals be taken from equals, the remainders are equal. TRUTH V. The whole is greater than any one of its parts. TRUTH VI. The sum of all the parts is equal to the whole. TRUTH VII. Magnitudes, which coincide with one another, that is, which exactly fill the same space, are equal to one another. TRUTH VIII. Between two points only one straight line can be drawn. TRUTH IX. The straight line is the shortest way from one point to another. TRUTH X. Through one point, without a straight line, only one line can be drawn parallel to that same straight line. |