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Math stuff
| Term | Definition |
|---|---|
| Ax 1 | Quantities that are equal to the same quantity or to equal quantities are equal to each other |
| Ax 2 (addition) | If equals are added to equals, the sums are equal |
| Ax 3 (subtraction) | If equals are subtracted from equals, the remainders are equal |
| Ax 4 (multiplication) | Doubles of equals are equal. In general, if equals are multiplied by equals, the products are equal. The divisor must not be zero |
| Ax 5 (division) | Halves of equals are equal. In general, if equals are divided by equals, the quotients are equal. The divisor must not be zero. |
| Ax 6 | The whole is equal to the sum of all its parts |
| Ax 7 | The whole is greater than any of its parts |
| Ax 8 (substitution) | A quantity may be substituted for its equal in any process |
| Ax 9 | If the first of three quantities is greater than the second quantity, and the second is greater than the third then the first is greater than the third |
| Post 1 | Through two given points one and only one straight line can be drawn |
| Post 2 | A straight line is the shortest line that can be drawn between two points |
| Post 3 | A straight line may be extended indefinitely or it may be limited at any point |
| Post 4 | A circle or part of one may be drawn about any point as the center and with any given radius |
| Post 5 | A geometric figure may be freely moved in space without any change in form or size |
| IS 1 | The sum of the three angles of a triangle is equal to one straight angle |
| IS 2 | Two straight lines can intersect at only one point |
| IS 3 | A line can be divided into two equal parts by only one point |
| IS 4 | A given angle can be divided into two equal part by only one line |
| IS 5 | All straight angles are equal |
| IS 6 | All eight angles are equal |
| IS 7 | Only one perpendicular can be drawn to a line at a point in the line |
| IS 8 | Complements of equal angles or of the same angles are equal |
| IS 9 | Supplements of equal angles or of the same angle are equal |
| IS 10 | The sum of all the angles about a point on one side of a straight line through the point is a straight angle |
| IS 11 | The sum of all the angles bout a point is equal to 360 |
| IS 12 | If the sum of two adjacent angles equal a straight angle, their exterior sides form one straight line |
| IS 13 | When two straight lines intersect, the vertical angles formed are equal |
| IS 14 | The sum of two sides of a triangle is greater than the third side |