 | Euclides - 1879 - 146 pages
...equals be taken from unequals the remainders are unequal. 6. Things which are double of the same thing are equal to one another. 7. Things which are halves of the same thing are equal to one another. 8. Magnitudes which coincide with one another, that is, which exactly... | |
 | Rolla Rouse - 1879 - 400 pages
...5. If equals be taken from unequals, the remainders are unequal (B — A unequal to D — C). Axiom 6. Things which are double of the same are equal to one another (A — 2B . C = 2B .-. A = C). Axiom 7. Things which are halves of the same are equal to one another... | |
 | Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...equals be taken from unequals the remainders are unequal. 6. Things which are double of the same thing are equal to one another. 7. Things which are halves of the same thing are equal to one another. 8. Magnitudes which coincide with one another, that is, which exactly... | |
 | T S. Taylor - 1880 - 152 pages
...one another. 6a. (Not given by Euclid, but assumed by him). Things which are doubles of equal things are equal to one another. 7. Things which are halves of the same thing are equal to one another. 8. Magnitudes which coincide with one another are equal to one another.... | |
 | Elias Loomis - Conic sections - 1880 - 452 pages
...from unequals, the remain ders are unequal. G. Things which are doubles of the same, or of equals, arc equal to one another. 7. Things which are halves of the same, or of equals, are equal to one another. 8. Magnitudes which coincide Avith one another, that is, which... | |
 | Euclides, Frederick Burn Harvey - Geometry - 1880 - 178 pages
...unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. Things which are double of the same are equal to one another. Things which are halves of the same are equal to one another. 8. Magnitudes which coincide with one... | |
 | Marianne Nops - 1882 - 278 pages
...another.' From this naturally follow axioms 6 and 7. 6. 'Things which are double of the same thing are equal to one another.' 7. ' Things which are halves of the same thing are equal to one another.' These axioms may of course be extended to any multiple or fraction.... | |
 | Euclides - 1883 - 176 pages
...equals be taken from unequals the remainders are unequal. 6. Things which are doubles of the same thing are equal to one another. 7. Things which are halves of the same thing are equal to one another. 8. The whole is greater than its part. 9. Magnitudes which coincide... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...equals be taken from unequals the remainders are unequal. 6. Things which are double of the same thing are equal to one another. 7. Things which are halves of the same tiling are equal to one another. 8. Magnitudes which coincide with one another, that is, which exactly... | |
 | Euclides - 1884 - 182 pages
...them " common notions," that is, notions which people in general have in their minds. AXIOMS 1 — 7, 1. Things which are equal to the same thing are equal...Things which are halves of the same, are equal to cue another. Although these are all so easy to understand, it will be to our future advantage to work... | |
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Things which are double of the same, are equal to one another. 7. Things which are halves of the same, are equal to one another. 
