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# Geometry

### Axioms

Geometry | Axioms |
---|---|

Axiom 1 | Quantities that are equal to the same quantity or to equal quantities are equal to each other. |

Axiom 2 | If equals are added to equals, the sums are equal. (addition axiom) |

Axiom 3 | If equals are subtracted from equals, the remainders are equal. (subtraction axiom) |

Axiom 4 | Doubles of equals are equal. In general, if equals are multiplied by equals, the products are equal. (multiplication axiom) |

Axiom 5 | Halves of equals are equal. In general, if equals are divided by equals, the quotients are equal. The divisor must not be zero. (division axiom) |

Axiom 6 | The whole is equal to the sum of all its parts. |

Axiom 7 | The whole is greater than any of its parts. |

Axiom 8 | A quantity may be substituted for its equal in any process. (substitution axiom) |

Axiom 9 | If the first of three quantities is greater than the second quantity, and the second is greater than the third, then the first is greater than the third. |

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bekaboo121390