 | Euclides - 1863 - 122 sider
...are equal to the same thing, are equal to one nnother. 2. If equals be added to equals, the wholes are equal. 4. If equals be added to unequals, the wholes are unequal. 3. It equals be taken from equals, the remainders are equal. 5. If equals be taken from uuequals, the... | |
 | Euclides - 1865 - 80 sider
...AXIOMS. 1. Things which are equal to the same thing, or to equal things, are equal to one another. 2. If equals be added to equals, the wholes are equal....equals be added to unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Things which are double, triple,... | |
 | Edward Clarke Lowe - 1866 - 172 sider
...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 equal....equals be added to unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the... | |
 | Euclid, Isaac Todhunter - 1867 - 426 sider
...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 equal,...equals be added to unequals the wholes are unequal. 5. If equals be taken from unequals the remainders are unequal. 6. Things which are double of the same... | |
 | Euclid, Isaac Todhunter - 1867 - 424 sider
...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... | |
 | Alexander Bain - 1870 - 474 sider
...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...equals be 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.... | |
 | Alexander Bain - 1870 - 478 sider
...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 - 1873 - 238 sider
...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... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - 1874 - 236 sider
...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....equals be added to unequals the wholes are unequal. 5. If equals be taken from unequals the remainders are unequal. 6. Things which are doubles of the... | |
 | Euclides - 1874 - 342 sider
...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 equal....equals be added to unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the... | |
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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... 
