 | David E. Smith - 1958 - 756 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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... | |
 | Asger Aaboe - 1963 - 154 σελίδες
...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. 3. If equals be subtracted from equals, the remainders are equal. 4. Things which coincide with one another are equal... | |
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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... 
