mention all Euclid's axioms
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- Things which are equal to the same thing are equal to one another.
- If equals are added to equals,the wholes are equals.
- If equals are 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.
- Things which are doubles of the same things are equal to one another.
- Things which are halves of the same things are equal to one another.
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What are axioms?
Axioms are the sentences that are accepted in real life and are self evidently true.
Here are few axioms stated by Euclid :
- Euclid's first axiom states that things which are equal to the same thing are equal to one another.
- Euclid's second axiom states that If equals are added to equals, the wholes are equals.
- Third axiom states that If equals are subtracted from equals, the remainders are equals.
- Fourth axiom of Euclid states that Things which coincide with one another are equal to one another.
- The fifth axiom tells us that The whole is greater than the part.
- Sixth axiom of Euclid states that Things which are double of the same things are equal to one another.
- Euclid's seventh and the last axiom states that things which are halves of the same things are equal to one another.
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