Axioms
Common notions used throughout Euclid’s Elements. Read each axiom slowly and reflect on what it permits.
Showing 7 axioms.
- 1
Things which are equal to the same thing are also equal to one another.
- 2
If equals be added to equals, the wholes are equal.
- 3
If equals be subtracted from equals, the remainders are equal.
- 4
Things which coincide with one another are equal to one another.
For example, if two line segments AB and CD can be made to coincide with each other exactly, then we can say that they are equal, in the sense that they have equal lengths.
- 5
The whole is greater than the part.
- 6
Things which are double of the same things are equal to one another.
- 7
Things which are halves of the same things are equal to one another.