 | John Greig - 1816 - 224 pages
...is frequently called a maxim. 2. If equals be added to equals, the whole are equal. 3. If equals are taken from equals, the remainders are equal. 4. If equals be added to unequals, the whole are unequal. 5. If equals be taken from unequals, the remainder are unequal. 6. Things which... | |
 | Euclid - 1822 - 222 pages
...line. 3. That a circle may be described from any centre, /&, ff, at any distance from that centre. M o Axioms. 1. Things which are equal to the same are...be taken from unequals, the remainders are unequal. 6. Things which are double of the same or of equals, are equal to one another. 7. Things which are... | |
 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...ate equal to the same are equal to one another. 2. If equals be added to equals the wholes are equals 3. If equals be taken from equals, the remainders...the wholes are unequal. 5. If equals be taken from unequal s, the remainders are unequal. 6. Things which are double of the same, are equal to one another.... | |
 | Euclid - 1826 - 234 pages
...infinitely distant. t For a demonstration of this, see Legendre*s Geometry, proposition 1, book i. AXIOMS. 1. Things which are equal to the same are...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 - 1826 - 226 pages
...being continually produced shall meet on that side where the angles are less than two right angles. AXIOMS. 1. Things which are equal to the same are...the wholes are unequal. 5. If equals be taken from uncquals, the remainders are unequal. 6. Things which are double of the same, are equal to one another.... | |
 | Timothy Walker - Geometry - 1829 - 156 pages
...are to a building. Euclid's axioms are the following : 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... | |
 | John Playfair - Geometry - 1829 - 210 pages
...which are equal to the same thing are equal to one another. Also things which are equal to equal things are equal to one another. 2. If equals be added to...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... | |
 | Timothy Walker - Geometry - 1829 - 138 pages
...Euclid's axioms are the following : I. Things which are equal to the same are equal to one another. 2k If equals be added to equals the wholes are equal....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... | |
 | Timothy Walker - Geometry - 1831 - 166 pages
...the following : 1. Things which are equal to the same thing are equal to one another. 2. If equal sbe added to equals, the wholes are equal. 3. If equals...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 - Euclid's Elements - 1833 - 216 pages
...See N. at any distance from that centre. AXIOMS. 1. Things, which are equal to the same, are equal io one another. 2. If equals be added to equals, the...be taken from unequals, the remainders are unequal. 6. Things, which are double of the same or of equals, are equal to one another. 7. Things, which are... | |
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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. 
