Here I present: Euclid, The Elements’, 300 BC, CONTINUED.
INTRODUCTION.
Geometry is only superseded by arithmetic and algebra as basic mathematical subjects. Here is some of my most basic geometry remembered from student days.
| EUCLIDEAN AXIOMS AND POSTULATES. |
| The Elements’ includes the following five (5) common notions. |
| 1. Things that are equal to the same thing are equal to one another (Transitive Property of Equality). |
| 2. If equals are added to equals, then the wholes are equal (Additive Property of Equality). |
| 3. If equals are subtracted from equals, then the remainders are equal (Subtraction Property of Equality). |
| 4. Things that coincide with one another are equal to one another (Reflexive Property). |
| 5. A whole is greater than its parts (Whole Property). |
| EUCLIDEAN AXIOMS. |
| 1. Through a point, an infinite number of lines pass; a point has no dimensions. |
| 2. The shortest distance between two points is a line segment; a line has one dimension. |
| 3. The intersection of a line and a plane is a point. |
| 4. The intersection of two planes is a line. |
| 5. Three planes are to be defined to established a solid 3D figure. |
| EUCLIDEAN POSTULATES. |
| Euclid determined some first postulates to determine the following. |
| 1. Draw a straight line from any point to any point. |
| 2. To produce extension: a finite straight line is continuously in a straight line. |
| 3. That all right angles are equal to one another. |
| 4. The Parallel Postulate: That if a straight line falling on two straight lines makes the interior angle on the same side less than two right angles. |
| The two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles. |
