 | Euclides - 1852 - 48 pages
...centre, with any distance from that centre as radius. AXIOMS. 1. Things which are equal to the same, are equal to one another. 2. If equals be added to...equals be added to unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. ф 6. Things which are double of the... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...extracted ; thus V2 means the square-root of 2 ; VAxB means the square-root of the product of A and B. AXIOMS. 1. Things which are equal to the same thing,...another. 2. If equals be added to equals, the wholes will be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals be added... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...described from any centre, at any distance from that centre. AXIOMS. 1. Things which are equal to the same are equal to one another. 2. If equals be added to...equals be added to unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 7. Thitigs which are halves of the... | |
 | 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,...equals be added to unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Magnitudes which are double of... | |
 | Euclid, John Playfair - Geometry - 1853 - 336 pages
...line. 3. And that a circle may be described from any centre, at any distance from that centre. v • ,V AXIOMS. 1 . 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, the remainders are equal. 4. If equals... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...extracted ; thus V2 means the square•root of 2 ; </AXB means the square•root of the product of A and B. AXIOMS. 1. Things which are equal to the same thing,...another. 2. If equals be added to equals, the wholes will be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals be added... | |
 | Daniel O'Gorman - Ready-reckoners - 1856 - 186 pages
...infallible proof of the truth or falsity of propositions. AXIOMS. 1. — Those things which are equal to the same thing are equal to one another. 2. — If equals be added to equals, the whole shall be equal. 3. — If equals be taken from equals, the remainder will be equal. 4. — If... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...extracted ; thus V2 means the square-root of 2 ; VAxB means the square-root of the product of A and B. AXIOMS. 1. Things which are equal to the same thing,...another. 2. If equals be added to equals, the wholes will be 3. If equals be taken from equals, the remainders will be equal. 4. If equals be added to unequals,... | |
 | Euclides - 1858 - 248 pages
...to number and quantity as well as to magnitude, were called by Euclid COMMON NOTIONS. They are — 1. Things which are equal to the same thing, are equal...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... | |
 | Daniel O'Gorman - 1858 - 248 pages
...infallible proof of the truth or falsity of propositions. AXIOMS. 1. — Those things which are equal to the same thing are equal to one another. 2. — If equals be added to equals, the whole will be equal. 3. — If equals be taken from equals, the remainder will be equal. 4. — If... | |
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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... 
