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Axiom
The Axioms of Geometry.
9
Mathematics
10th Grade
10/02/2008

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Term
Axiom 1
Definition
Quantities that are equal to the same quantity or to equal quantities are equal to each other.
Term
Axiom 2
Definition
If equals are added to equals, the sums are equal. (addition axiom)
Term
Axiom 3
Definition
If equals are subtracted from equals, the remainders  are equal. (Subtraction axiom)
Term

Axiom 4

Definition
Doubles of equals are equal. In general, if equals are multiplied by equals, the products are equal. ( multiplication axiom)
Term
Axiom 5
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)

Term
Axiom 6
Definition
The whole is equal to the some of all its parts.
Term
Axiom 7
Definition
The whole is greater then any of its parts.
Term
Axiom 8
Definition
A quantity may be substituted for its equal in any process. (subtraction axiom)
Term

Axiom 9

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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