 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 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 are...be taken from unequals, the remainders are unequal. 7. Thitigs which are halves of the same are equal to one another. S. Magnitudes which coincide with... | |
 | Euclid - Geometry - 1853 - 176 pages
...frequently employed in the Elements under the form, " Magnitudes which are equal to equals are cqxial to one another." 2. If equals be added to equals,...be taken from unequals, the remainders are unequal. 6. Magnitudes which are double of the same are equal to one another. 7. Magnitudes which are halves... | |
 | Euclid, John Playfair - Geometry - 1853 - 336 pages
...THINGS which are equal to the same thing are equal to one another. 2. If equals be added to squals, the wholes are equal. 3. If equals be taken from equals,...equals be taken from unequals, the remainders are unequaI. S. Things which are doubles of the same thing, are equal to one another. 7. 'r' 'ngo which... | |
 | Euclides - 1858 - 248 pages
...magnitude, were called by Euclid COMMON NOTIONS. They are — 1. Things which are equal to the same thing, are equal to one another. 2. If equals be added to...unequals, the wholes are unequal. 5. If equals be takea from unequals, the remainders are unequal. 6. Things which are double of the same, are equal... | |
 | Euclides - 1860 - 288 pages
...are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes arc equal. 3. If equals be taken from equals, the remainders...be taken from unequals, the remainders are unequal. 6. Things which are double of the same, are equal. . -,3 7. Things which are halves of the same, are... | |
 | Eucleides - 1860 - 396 pages
...in the El'tments under the form, " Magnitudes which are equal to equal's are equal to one another.'1 2. If equals be added to equals, the wholes are equal....equal. 4. If equals be added to unequals, the wholes arc unequal. 5. If equals be taken from unequals, the remainders arc unequal. 6. Magnitudes which are... | |
 | Euclides - 1862 - 140 pages
...may be produced to any length in a straight line. 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 - 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....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 of the... | |
 | 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, the... | |
 | 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...be taken from unequals, the remainders are unequal. 6. Things which are double, triple, etc., of the same thing, or of equal things, are equal to one another.... | |
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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. 
