**
Addition Axiom
** -
If equals are added to equals, their sums are equal. If unequals are added to
equals, their sums are unequal.

**
Division Axiom
** -
If equals are divided by equals, their quotients is equal. If unequals are
divided by equals, their quotients is unequal.

**
Multiplication Axiom
** -
If equals are multiplied by equals, their products are equal. If unequals are
multiplied by equals, their products are unequal.

**
Partition Axiom
** -
A quantity is equal to the sum of its parts. A quantity is greater than any one
of its parts.

**
Reflexive Property
** -
A quantity is equal to itself.

**
Substitution Axiom
** -
Equals can be substituted for each other in any equality or inequality.

**
Subtraction Axiom
** -
If equals are subtracted from equals, their differences are equal. If unequals
are subtracted from equals, their differences are unequal.

**
Transitive Property
** -
If two quantities are equal to a third quantity, they are equal to each other.
If a quantity is greater than another quantity, which is greater than a third
quantity, then the first quantity is greater than the third quantity.