Plane Geometry
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Principles in Geometry
- (1) A straight line is the shortest line between two points.
- (2) Only one straight line can be drawn between two points.
- (3) Two straight lines intersect at only one point.
- (4) Quantities (Lines) equal to the same quantity (line) are equal to each other.
- (5) The whole is equal to the sum of all its parts.
- (6) The whole is greater than any of its parts.
- (7) If equals are added to equals, then the sums are equal.
- (8) If equals are subtracted from equals then the remainders are equal.
- (9) Doubles of equals are equal.
- (10) Halves of equals are equal.
- (11) If the first of three quantities is greater than the second, and the second is greater than the third, then the first is greater than the third.
- (12) All straight lines are equal.