A Postulate is a problem, the solution of which is self-evident.
Let it be granted—
III. That a straight line can be drawn from any one point to any other point;
III. That a straight line can be produced to any distance, or terminated at any point;
III. That the circumference of a circle can be described about any center, at any distance from that center.
The common algebraic signs are used in Geometry, and it is necessary that the student in geometry should understand some of the more simple operations of algebra. As the terms circle, angle, triangle, hypothesis, axiom, theorem, corollary and definition are constantly occurring in a course of geometry, they are abbreviated as shown in the following list:
| Addition is expressed by | + |
| Subtraction is expressed by | - |
| Multiplication is expressed by | × |
| Equality and Equivalency are expressed by | = |
| Greater than, is expressed by | > |
| Less than, is expressed by | < |
| Thus B is greater than A, is written | B > A |
| Thus B is less than A, is written | B < A |
| A circle is expressed by | O |
| An angle is expressed by | L |
| A right angle is expressed by | R. L |
| Degrees, minutes and seconds are expressed by | ° ′ ″ |
| A triangle is expressed by | △ |
| The term Hypothesis is expressed by | (Hy.) |
| The term Axiom is expressed by | (Ax.) |
| The term Theorem is expressed by | (Th.) |
| The term Corollary is expressed by | (Cor.) |
| The term Definition is expressed by | (Def.) |
| The term Perpendicular is expressed by | ⊥ |
| The difference of two quantities, when it is not known which is the greater, is expressed by the symbol | ~ |
| Thus, the difference between A and B is written | A ~ B |
GEOMETRICAL AXIOMS.
1. Things which are equal to the same thing are equal to each other.
2. When equals are added to equals the wholes are equal.