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| Quantities that are equal to the same quantity or to equal quantities are equal to each other. |
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| If equals are added to equals, the sums are equal. (addition axiom) |
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| If equals are subtracted from equals, the remainders are equal. (Subtraction axiom) |
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| Doubles of equals are equal. In general, if equals are multiplied by equals, the products are equal. ( multiplication axiom) |
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Definition
Halves of equals are equals. In general, if equals are divided by equals, the quotinents are equal. the divisor must not be zero. (division axiom) |
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Definition
| The whole is equal to the some of all its parts. |
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Definition
| The whole is greater then any of its parts. |
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| A quantity may be substituted for its equal in any process. (subtraction axiom) |
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Definition
| If the first of three quantites is greater than the second quantity, and the second is greater then the third, then the first is greater than the third. |
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