| David E. Smith - Mathematics - 1958 - 756 pages
...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 - History - 1978 - 378 pages
...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 - Mathematics - 1983 - 338 pages
...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 - Philosophy - 1988 - 356 pages
...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 - Mathematics - 1990 - 434 pages
...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 - Philosophy - 1997 - 406 pages
...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 - Geometry, Non-Euclidean - 1993 - 320 pages
...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 - Science - 1996 - 430 pages
...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 - Mathematics - 1997 - 370 pages
...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 - History - 1963 - 154 pages
...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... | |
| |