| 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 - 179 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 - 372 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 - 236 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 - 158 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 - 186 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 - 129 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 - 183 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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