 | Euclides - 1860 - 288 pages
...length in a straight line ; 3. And that a circle may be described from any centre, and with any radius. 1. Things which are equal to the same thing are equal...another. 2. If equals be added to equals, the wholes arc equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals,... | |
 | Euclides - 1862 - 140 pages
...any other point. 2. That a terminated straight line may be produced to any length in a straight line. AXIOMS. 1. Things which are equal to the same thing...equal. 4. If 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... | |
 | Euclides - 1863 - 74 pages
...Euclid COMMON NOTIONS. They are — 1. Things which are equal to the same thing, are equal to one anothf 2. If equals be added to equals, the wholes are equal....4. If equals be added to unequals, the wholes are unequal. •I. If equals be taken from unequals, the remainders are unequal. 6. Things which are double... | |
 | Euclides - 1863 - 122 pages
...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,... | |
 | Euclides - 1865 - 80 pages
...to any given straight line. 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...4. If 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,... | |
 | Edward Clarke Lowe - 1866 - 172 pages
...straight line. 3. And that a circle may be described from any centre, at any distance from that centre. AXIOMS. 1. Things which are equal to the same thing...4. If 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... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...straight line : 3. And that a circle may be described from any centre, at any distance from that centre. AXIOMS. 1. Things which are equal to the same thing...equal. 4. If 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... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...described from any centre, at any distance from that centre. AXIOMS. 1. Tiiings which are equal to the same thing are equal to one another. 2. If equals...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 - 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...(4) If 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... | |
 | 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.... | |
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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... 
