...The following are some of the most important axioms and postulates. Axioms. 1°. Things equal to the same thing are equal to each other. 2°. If equals...are divided by equals, the quotients are equal. 6°. The whole is greater than any of its parts. 7°. The whole is equal to the sum of all its parts. 8°....

...axbxy + zz = what ? AXIOMS. 59. An Axiom is a self-evident truth. 1. Things which are equal to the same thing, are equal to each other. 2. If equals...are divided by equals, the quotients are equal. 6. If a quantity is multiplied and divided by the same quantity, its value is not altered. 7. If the same...

...equal may be substituted. 2. If equals are added to equals, the sums are equal. 3. If equals are taken from equals, the remainders are equal. 4. If equals...are divided by equals, the quotients are equal. 6. A whole is greater than any of its parts. 1. Through a given point in a given direction, only one straight...

...equal may be substituted. 2. If equals are added to equals, the sums are equal. 3. If equals are taken from equals, the remainders are equal. 4. If equals...are divided by equals, the quotients are equal. 6. A whole is greater than any of its parts. 7. Through a given point in a given direction, only one straight...

...multiplied by equals the products will be equal. 5. If equals be divided by equals the quotients will be equal. 6. Equal powers of equal quantities are equal. 7. Equal roots of equal quantities are equal ; positive equal to positive, and negative equal to negative. 8. A quantity equally increased and diminished...

...another is called Transposition. 48. A truth that does not need demonstration is called an Axiom. AXIOMS. 1. Things that are equal to the same thing are equal...equal. 6. Equal powers of equal quantities are equal. 49. PRINCIPLE. Ajmmttity may be transposed from one member of an equation to another by changing its...

...another is called Transposition. 48. A truth that does not need demonstration is called an Axiom. AXIOMS. 1. Things that are equal to the same thing are equal...divided by equals, the quotients are equal. 6. Equal pmvers of equal quantities are equal. 49. PRINCIPLE. A quantity may be transposed from one member of...

...Axiom. AXIOMS. 1. Things that are equal to the same thing are equal to each other. 2. If equals arc added to equals, the sums are equal. 3. If equals...equal. 6. Equal powers of equal quantities are equal. 49. PRINCIPLE. A term may be transposed from one member of an equation to the other if its sign is...

...another is called Transposition. 48. A truth that does not need demonstration is called an Axiom. AXIOMS. 1. Things that are equal to the same thing are equal...equal. 6. Equal powers of equal quantities are equal. 49. PRINCIPLE. A term may be transposed from one member of an equation to the other if its sign is...

...equal. 5. If equal quantities be divided by the same quantity or equal quantities, the quotients will be equal. 6. Equal powers of equal quantities are equal. 7. Equal roots of equal quantities are equal. 205. Transformation of equations is the process of changing their form without destroying the equality...