 | John Bonnycastle - Euclid's Elements - 1803 - 470 pages
...•i • f • 1 AXIOMS. 1 . Things which are equal to the fame thing are equal to each other. I 5. If equals be added to equals the wholes will be equal....If equals be taken from equals the remainders will berequal. 4. If equals be added to unequals the wholes will be unequal. 5. If equals be taken from... | |
 | 1854 - 1112 pages
...which are equal to the same thing are equal to one another. 2. If equals be added to equals, the sums will be equal. 3. If equals be taken from equals, the remainders will be equal. This might be deduced from the former, but it is not less simple. 4. The whole is greater than its... | |
 | Charles Davies - Surveying - 1839 - 376 pages
...AF, AE, AD, AC, are diagonals. 19. An axiom is a self-evident proposition. 20. A theorem is a truth, which becomes evident by means of a train of reasoning...other. 2 If equals be added to equals, the wholes will he equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals be added to... | |
 | Charles Davies - Geometrical drawing - 1840 - 264 pages
...preceding propositions. 17. An Axiom is a self evident truth. .. AXIOMS. 1. Things which are equal to the same thing are equal to each other. 2. If equals be...be taken from equals the remainders will be equal. ClOEST.— 11. What is a theorem 1 12. What is a problem 1 13. What is a proposition 1 May it be a... | |
 | Scottish school-book assoc - 1845 - 444 pages
...circle may be described from any centre, and with any radius. AXIOMS. 1. Things that 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 are equals. 4. If equals be added... | |
 | Euclides - 1846 - 272 pages
...radius. COMMON NOTIONS, OR AXIOMS. 1 . Things which are equal to the same are equal to one another. 2. If equals be added to equals, the wholes will be equal. 3. If from equals, equals be taken, the remainders are equal. 4. If to unequals, equals be added, the wholes... | |
 | Charles Davies - Trigonometry - 1849 - 372 pages
...be explained in its proper place. Axioms. 1. Things which are equal to the same thing, are equal t» each other. 2. If equals be added to equals, the wholes...be taken from equals, the remainders will be equal. 5. If equals be taken from unequals, the remainders will be unequal. 4. If equals be added to unequals,... | |
 | Almon Ticknor - Measurement - 1849 - 156 pages
...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 whole will be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals... | |
 | Charles Davies - Geometry - 1850 - 218 pages
...and CD is the altitude of the trapezoid. Of A xio in s . AXIOMS. 1. Things which, are equal to the same thing are equal to each other. 2. If equals be...remainders will be equal. 4. If equals be added to imequals, the wholes will be unequal. 5. If equals be taken from unequals, the remainders will be unequal.... | |
 | Charles Guilford Burnham - 1850 - 350 pages
...Art. 54, or Part I. AXIOMS An axiom is a self-evident proposition. 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. 8. If equals be taken from equals, the remainders will be equal. 4. If equals be added to unequals,... | |
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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 will be equal. 4. If equals be... 
