Euclidean Geometry : What Euclid actually said...
by Stu Savory, 2005.
- Euclid's Definitions
- A point is that which has no parts.
- A line is that which has length without breadth.
- The limits of a line are points.
- A straight line is that which lies equally to the points on it.
- A surface is that which has only length and breadth.
- The limits of a surface are lines.
- A plane surface is that which lies equally to the straight lines on it.
- Euclid's Axioms
- Things which are equal to the same thing are also equal to one another.
- If equals be added to equals, the wholes are equal.
- If equals be subtracted from equals, the remainders are equal.
- Things which coincide with one another are equal to one another.
- The whole is greater than the part.
- Euclid's Postulates
- A straight line can be drawn between any two points.
- A finite line can be extended infinitely in both directions.
- A circle can be drawn with any centre and any radius.
- All right angles are equal to each other.
- Given a line and a point not on the line, only one line can be drawn through the point parallel to the line.
And you can deduce all the rest, given the things above :-)
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