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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... "
Euclid, books i. & ii., with notes, examples, and explanations, by a late ... - Page 6
by Euclides - 1879
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History of Mathematics, Volume 2

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...
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The Beginnings of Greek Mathematics

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...
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Geometry and the Visual Arts

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...
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Aristotle: The Desire to Understand

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...
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Mathematical Thought from Ancient to Modern Times: Volume 1

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...
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Thinking Things Through: An Introduction to Philosophical Issues and ...

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...
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The Poincaré Half-plane: A Gateway to Modern Geometry

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...
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Encyclopedia of the History of Arabic Science, Volume 2

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...
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Foundations and Fundamental Concepts of Mathematics

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...
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Episodes from the Early History of Mathematics, Volume 13

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...
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