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Common notions

Fixed rules (or theorems) that cannot be proved are called common notions. In the book Elements of Euclid five common notions are described.


Modern text

The five common notions are:

   1.  Things which are equal to the same thing are equal to one another.
   2. If equals be added to equals, the wholes are equal.
   3. If equals are subtracted from equals, the remainders are equal.
   4. Things which coincide with one another are equal to one another.
   5. The whole is greater than the part.



The most influential book in the history of mathematics, called Elements, was compiled by the Greek Euclid in 300 BC.

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