 | Alexander Bain - 1870 - 478 páginas
...unquestionable axioms, conforming to both the criteria. The five succeeding are — AXIOMS OF EDCLID. 209 (3) If equals be taken from equals, the remainders are equal. (4) If equals be added to tmequals, the wholes are unequal. (5) If from unequals, equals be taken, the remainders are unequal.... | |
 | Euclid - 1872 - 284 páginas
...from any centre, with any radius. COMMON NOTIONS, OR AXIOMS. 1 . Things which are equal to the same are equal to one another. 2. If equals be added to equals, the wholes will be equal. 4. If to unequals, equals be added, the wholes are unequal. 5. If from unequals, equals... | |
 | William Alexander Myers - 1873 - 238 páginas
...polygon with any given number of sides expressed by 2 n -f- 1, provided, 2 n -|- 1 is a prime number. 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 are equal. 4. If equals be added to... | |
 | Euclides - 1874 - 120 páginas
...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 thing...equals be added to unequals the wholes are unequal. 5. If equals be taken from unequals the remainders are unequal. 6. Things which are double of the same... | |
 | Euclides - 1874 - 342 páginas
...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 thing...equals be added to unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - 1874 - 236 páginas
...that the line B is equal to the line C; and from this it follows that the three lines are all equal. 2. If equals be added to equals the wholes are equal....equals be added to unequals the wholes are unequal. 5. If equals be taken from unequals the remainders are unequal. 6. Things which are doubles of the... | |
 | Edward Atkins - 1874 - 428 páginas
...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 thing...If equals be added to equals the wholes are equal. I 3. If equals be taken from equals the remainders are equal. 4. If equals be added to unequals the... | |
 | William Alexander Myers - 1874 - 207 páginas
...a polygon with any given number of sides expressed by 2n + 1, provided, 2n -(- 1 is a prime number. 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 are equal. 4. If equals be added to... | |
 | William Alexander Willock - 1875 - 196 páginas
...equals be added to the same or equals, the wholes are equal. 3. If equals be taken from the same or equals, the remainders are equal. 4. If equals be added to unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Magnitudes which are doubles of... | |
 | Edward Atkins - 1876 - 130 páginas
...the same thing are equal to One another. EXPLANATION OF TERMS AND ABBREVIATIONS. 9 3. If equals bo taken from equals the remainders are equal. 4. If...equals be added to unequals the wholes are unequal. 5. If equals be taken from uncquals the remainders are unequal. G. Things which are double of the same... | |
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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... 
