 | 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, the wholes are equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals,... | |
 | 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, the wholes are equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals,... | |
 | Daniel O'Gorman - Ready-reckoners - 1856 - 186 pages
...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
...means the square-root of the product of A and B. AXIOMS. 1. Things which are equal to the same thing, are equal to one 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
...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 equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals,... | |
 | Daniel O'Gorman - 1858 - 248 pages
...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... | |
 | James B. Dodd - Algebra - 1859 - 368 pages
...which are equal to the same thing, are equal to each other. 2. If equals be added to equals, the sums will be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals be multiplied by equals, the products will be equal. 5. If equals be divided by equals, the quotients... | |
 | Euclides - 1860 - 288 pages
...may be described from any centre, and with any radius. 1. Things which 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 are equal. 4. If equals be added to unequals,... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...which are equal to the same thing, are equal to each other. 2. If equals be added to equals, the sums will be equal. 3. If equals be taken from equals,...will be equal. 4. If equals be added to unequals, the sums will be unequal. -• 5. If equals be taken from unequals, the remainders will be unequal. 6.... | |
 | Benjamin Greenleaf - Geometry - 1861 - 638 pages
...which are equal to the same thing, are equal to each other. 2. If equals be added to equals, the sums will be equal. 3. If equals be taken from equals,...will be equal. 4. If equals be added to unequals, the sums will be unequal. 5. If equals be taken from unequals, the remainders will be unequal. 6. Things... | |
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AXIOMS. 1. 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. 
