 | Edward Clarke Lowe - 1866 - 172 pages
...from any centre, 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...be taken from unequals, the remainders are unequal. 6. Things which are double of the same are equal to one another. 7. Things which are halves of the... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...from any centre, 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...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... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...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...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... | |
 | Euclides - 1870 - 270 pages
...magnitude, were 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...be taken from unequals, the remainders are unequal. 6. Things which are double of the same, are equal to one another. 7. Things which are halves of 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)... | |
 | 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
...from any centre, 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...be taken from unequals, the remainders are unequal. 6. Things which are double of the same, are equal to one another. 7. Things which are halves of the... | |
 | Euclides - 1874 - 120 pages
...from any centre, 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...be taken from unequals the remainders are unequal. 6. Things which are double of the same are equal to one another. 7. Things which are halves of the... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...that the line B is equal to the line C; and from this it follows that the three lines are all equal. 2. If equals be added to equals the wholes are equal....be taken from unequals the remainders are unequal. 6. Things which are doubles of the same, or of equals, are equal to one another. 7. Things which are... | |
 | William Alexander Myers - Circle-squaring - 1874 - 207 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... | |
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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. 
