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Geometry

Axioms

GeometryAxioms
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.
Created by: bekaboo121390
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