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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. |