 | Edward Clarke Lowe - 1866 - 172 pages
...at any distance from that centre. AXIOMS. 1. Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the...are unequal. 6. 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. 8. Magnitudes... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...at any distance from that centre. AXIOMS. 1. Things which are equal to the same thing are equal to one another. 2. If equals be added to equals the wholes...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.... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...at any distance from that centre. AXIOMS. 1. Tiiings which are equal to the same thing are equal to one another. 2. If equals be added to equals the wholes are equal, 3. If equals be taken from equals the remamders are equal. 4. If equals be added to unequals the wholes are unequal. 5. If equals be taken... | |
 | Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...remainders are equal. 4. When equals are added to unequals, the wholes are unequal. 5. 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. 7. Things which are halves of the same thing are equal.... | |
 | Horatio Nelson Robinson - Geometry - 1868 - 276 pages
...remainders art tqual. 4. When equals are added to unequals the wholes are unequal, ' 5. 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. I. Things which are halves of the same thing, or of... | |
 | Euclides - 1870 - 270 pages
...called by Euclid COMMON NOTIONS. are — 1. Things which are equal to the same thing, are equal to one another. 2. If equals be added to equals, the...are unequal. 6. 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. II. The... | |
 | Alexander Bain - Logic - 1870 - 474 pages
...bearing, These axioms, made familiar to us by Euclid, have to be tried by the two tests already laid down. (3) If equals be taken from equals, the remainders...added to unequals, the wholes are unequal. (5) If from unequals, equals be taken, the remainders are unequal. (6) Doubles of the same are equal. (7)... | |
 | Alexander Bain - Logic - 1870 - 478 pages
...unquestionable axioms, conforming to both the criteria. The five succeeding are — AXIOMS OF EDCLID. 209 (3) If equals be taken from equals, the remainders are equal. (4) If equals be added to tmequals, the wholes are unequal. (5) If from unequals, equals be taken, the remainders are unequal.... | |
 | William Alexander Myers - Circle-squaring - 1873 - 238 pages
...equal to the same thing are equal to one another. 2. If equals be added to equals the wholes will be equal. 3. If equals be taken from equals the remainders...equal. 4. If equals be added to unequals the wholes will be unequal. 5. If equals be taken from unequals the remainders will be unequal. 6. Things which... | |
 | Euclides - 1874 - 342 pages
...at any distance from that centre. AXIOMS. 1. THINGS which are equal to the same thing are equal to one another. 2. If equals be added to equals, the...are unequal. 6. 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. 8. Magnitudes... | |
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Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals, the wholes are unequal. 5. If equals... 
