 | 1906 - 600 páginas
...that a circle may be described from any center, at any distance from that center. His axioms state : 1. Things which are equal to the same thing 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 double 01 the same... | |
 | David E. Smith - 1958 - 756 páginas
...Axioms. Euclid laid down certain axioms, or "common notions," probably five in number, as follows: 1 . Things which are equal to the same thing are equal...added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. Things which coincide with one another are equal... | |
 | A. Szabó - 1978 - 378 páginas
...a rather different kind. They read as follows: 1. Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal. [4. If equals be added to unequals, the wholes are... | |
 | Daniel Pedoe - 1983 - 338 páginas
...Euclid's introduction ends with some Common Notions: 1. Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be substracted from equals, the remainders are equal. 4. Things which coincide with one another are equal... | |
 | Jonathan Lear - 1988 - 356 páginas
...angles. Common notions: 1 Things which are equal to the same thing are also equal to one another, 1 If equals be added to equals, the wholes are equal. 3 If equals be subtracted from equals, the remainders are equal. 4 Things which coincide with one another are equal... | |
 | Morris Kline - 1990 - 434 páginas
...less than the two right angles. COMMON NOTIONS 1 . Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 4. Things which coincide with one another are equal to one another. 5. The whole is greater than the... | |
 | Clark N. Glymour - 1997 - 406 páginas
...one another in either direction. Common notions 1. Things that are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. Things which coincide with one another are equal... | |
 | Saul Stahl - 1993 - 320 páginas
...us now examine Euclid's definition of equality. 1. Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal. The modern reader may be puzzled by the need for... | |
 | Régis Morelon - 1996 - 430 páginas
...with each other. These axioms are as follows: 1. Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals the wholes are equaL 3. If equals be subtracted from equals, the remainders are equaL 4. Things which coincide with one another are equal... | |
 | Howard Whitley Eves - 1997 - 370 páginas
...together less than two right angles. Common notions 1. Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equaL 3. If equals be subtracted from equals, the remainders are equaL 4. Things which coincide with one another are equal... | |
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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... 
