Things which are equal to the same thing, are equal to each other. 2. If equals are added to equals, the sums are equal. 3. If equals are subtracted from equals, the remainders are equal. 4. If equals are added to unequals, the sums are unequal. Elements of Plane Geometry - Page 14by Franklin Ibach - 1882 - 196 pagesFull view - About this book
| Elias Loomis - Conic sections - 1857 - 242 pages
...equal to each other. 2. If equals are added to equals, the wholes are equal. 3. If equals are taken **from equals, the remainders are equal. 4. If equals are added to unequals, the** wholes are unequal. 5. If equals are taken from unequals, the remainders are unequal. 6. Things which... | |
| Elias Loomis - Conic sections - 1858 - 256 pages
...equal to each other. 2. If equals are added to equals, the wholes arje equal. 3. If equals are taken **from equals, the remainders are equal. 4. If equals are added to unequals, the** wholes are unequal. 5. If equals are taken from unequals, the remainders are unequal. 6. Things which... | |
| Elias Loomis - Geometry - 1871 - 302 pages
...equal to each other. 2. If equals are added to equals, the wholes are equal. 3. If equals are taken **from equals, the remainders are equal. 4. If equals are added to unequals, the** wholes are unequal. 5. If equals are taken from unequals, the remainders are unequal. 6. Things which... | |
| William Guy Peck - Conic sections - 1876 - 376 pages
...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...equals, the remainders are equal. 4°. If equals are** multiplied by equals, the products are equal. 5°. If equals are divided by equals, the quotients are... | |
| James Bates Thomson - Algebra - 1878 - 322 pages
...2 = what ? 15. 26 -r- (x — b) + axbxy + zz = what ? AXIOMS. 59. An Axiom is a self-evident truth. **1. Things which are equal to the same thing, are equal...equals, the remainders are equal. 4. If equals are** multiplied by equals, the products are equal. 5. If equals are divided by equals, the quotients are... | |
| Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...VOLUME is a limited portion of space, combining the three dimensions of length, breadth, and thickness. **AXIOMS. 1. Things which are equal to the same thing,...are equal. 8. The whole is greater than any of its** parts. 9. The whole is equal to the sum of all its parts. 10. All right angles are equal. 11. Only... | |
| George Albert Wentworth - Geometry - 1888 - 264 pages
...are equal to each other. 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 added to unequals the sums are unequal,** arid the greater sura is obtained from the greater magnitude. 5. If equals are taken from unequals... | |
| David Martin Sensenig - Algebra - 1890 - 556 pages
...truth. 60. The following are the principal axioms relating to numbers : 1. Things that are equal to the **same thing are equal to each other. 2. If equals are...equals the remainders are equal. 4. If equals are** multiplied by equals the products are equal. 5. If equals are divided by equals the quotients are equal.... | |
| William James Milne - Algebra - 1894 - 212 pages
...truth that does not need demonstration is called an Axiom. AXIOMS. 1. Things that are equal to the **same thing are equal to each other. 2. If equals are...equals, the remainders are equal. 4. If equals are** multiplied by equals, the products are equal. 5. If equals are divided by equals, the quotients are... | |
| William James Milne - Algebra - 1894 - 214 pages
...truth that does not need demonstration is called an Axiom. AXIOMS. 1. Things that are equal to the **same thing are equal to each other. 2. If equals are...equals, the remainders are equal. 4. If equals are** multiplied by equals, the products are equal. 5. If equals are divided by equals, the quotients are... | |
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