 | George Albert Wentworth - Geometry, Modern - 1879 - 262 pages
...demonstration. 46. AXIOMS. •,-I. Tilings which are equal to the same thing are equal to each - 4 other. 2. When equals are added to equals the wholes...remainders are equal. 4. When equals are added to uijequals the wholes are unequal. 5. When equals are taken from unequals the remainders are unequal.... | |
 | Franklin Ibach - Geometry - 1882 - 208 pages
...in a proposition or in a demonstration. 38. A Scholium is a comment on one or more propositions. 39. AXIOMS. 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... | |
 | Alfred Hix Welsh - Geometry - 1883 - 326 pages
...Scholium is a remark upon some feature of a proposition. AXIOMS. An Axiom is a self-evident truth: 1. Things which are equal to the same thing are equal to each other. 2. If the same operation be performed upon equals, the results will be equal. Thus, if the same quantity... | |
 | George Albert Wentworth - Geometry - 1885 - 424 pages
...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 to uneqnals the sums are unequal. 5. When equals are taken from unequals the remainders are unequal. 6.... | |
 | 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 to each other. 2. If equals are added to equals, the sums are equal. 3. If equals are subtracted from equals, the remainders... | |
 | Charles Davies - Geometry - 1886 - 352 pages
...stand ; and the altitude is a line drawn from the opposite side or angle, perpendicular to 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 wholes will be equal. 3. If equals be taken from equals, the remainders... | |
 | George Albert Wentworth - Algebra - 1886 - 284 pages
...reciprocals of each other when their product is equal to unity. Thus, a and - are reciprocals. 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... | |
 | George Albert Wentworth - Algebra - 1888 - 514 pages
...value of an expression evidently depends upon the values given to the several symbols involved. 18. Axioms. 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 numbers. 3. If equal numbers be... | |
 | George Albert Wentworth - Geometry - 1888 - 264 pages
...point. 2. That a straight line can be produced to any distance, or can be terminated at any point. 82. AXIOMS. 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 taken from equals the remainders... | |
 | David Martin Sensenig - Algebra - 1889 - 388 pages
...Axioms. 45. An Axiom is a self-evident truth. 46. The following are the principal axioms of algebra : 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... | |
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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. 
