 | Elias Loomis - Geometry - 1871 - 302 pages
...a supposition made either in the enunciation of a proposition, or in the course of a demonstration. Axioms. 1. Things which are equal to the same thing are equal to each other. 2. If equals are added to equals, the wholes are equal. 3. If equals are taken from equals, the remainders... | |
 | Benjamin Greenleaf - Geometry - 1873 - 202 pages
...not equal to either of the other sides. AXIOMS. 26. An Axiom is a self-evident truth ; such as, — 1. Things which are equal to the same thing, are equal to each other. 2. If equals be added to equals, the sums wili be equal. 3. If equals be taken from equals, the remainders... | |
 | Benjamin Greenleaf - Geometry - 1874 - 206 pages
...not equal to either of the other sides. AXIOMS. 26. An Axiom is a self-evident truth ; such as, — 1. Things which are equal to the same thing, are equal to each other. 2. If equals be added to equals, the sums will be equal. 3. If equals be taken from equals, the remainders... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...is a supposition made in the enunciation of a proposition, or in the course of a demonstration. 46. AXIOMS. 1. Things which are equal to the same thing...each other. 2. When equals are added to equals the sums are equal. 3. When equals are taken from equals the remainders are equal. 4. When equals are added... | |
 | George Albert Wentworth - Geometry - 1877 - 436 pages
...of a proposition, or in the course of a demonstration. 46. AXIOMS. 1. Tilings which are equal to the same thing are equal to each other. 2. When equals are added to equals the sums are equal. 3. When equals are taken from equals the remainders are equal. 4. When equals are added... | |
 | Thomas Hunter - Geometry, Plane - 1878 - 142 pages
...plane figure is that side upon which it is supposed to stand. Any side may be considered the base. Axioms. 1. Things which are equal to the same thing are equal to each other. 2. If equals be added to equals the sums are equals. 3. If equals be taken from equals the remainders... | |
 | William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...is a supposition made either in the statement of a proposition or in the course of a demonstration. AXIOMS. 1. Things which are equal to the same thing are equal to each other. 2. If equals be added to equals, the sums will be equal. 3. If equals be subtracted from equals, the remainders... | |
 | 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 to each other. 2. If equals are added to equals, the sums are equal. 3. If equals are subtracted from equals, the remainders... | |
 | George Albert Wentworth - 1881 - 266 pages
...is a supposition made in the enunciation of a proposition, or in the course of a demonstration. 46. AXIOMS. 1. Things which are equal to the same thing...each other. 2. When equals are added to equals the sums are equal. 3. When equals are taken from equals the remainders are equal. 4. When equals are added... | |
 | George Albert Wentworth - Algebra - 1881 - 400 pages
...reciprocals of each other whep their product is equal to unity. Thus, a and - are reciprocals. a AXIOMS. 43. 1. Things which are equal to the same thing are equal to each other. 2. If equal numbers be added to equal numbers, the sums will be equal. 3. If equal numbers be subtracted... | |
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When equals are taken from unequals, the remainders are unequal. 6. Things which are double of the same thing, or equal things, are equal to each other. 
