Content
- Axiom 1
- Quantities equal to the same or equal quantities are equal.
- If A = B, and B = C, then A = C
- Axiom 2, Addition Axiom
- If equals are added to equals, their sums are equal
- Axiom 3, Subtraction Axiom
- If equals are subtracted from equals, their differences are equal
- Axiom 4, Multiplication Axiom
- Doubles of equals are equal.
- In general, if equals are multiplied by equals, their products are equal
- Axiom 5, Division Axiom
- Halves of equals are equal
- In general, if equals are divided by equals, their quantities are equal
- Axiom 6
- The whole is equal to the sum of its parts
- Axiom 7
- The whole is greater than any of its parts
- Axiom 8
- Any quantity bay be substituted for its equal in any process: A = B, A + 2 = C, then B + 2 = C
- Axiom 9
- If A > B, and B > C, then A > C
- Axiom 10
- If equals are added to, or subtracted from, unequals, the results are unequal in the same order
- Axiom 11
- If unequals are multiplied or divided by equals, the results are unequal in the same order
- Axiom 12
- If unequals are added to unequals of same order, their sums are unequal in the same order
- Axiom 13
- If equals are subtracted from unequals, their remainders are unequal in the reverse order