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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... "
Euclid's plane geometry, practically applied; book i, with explanatory notes ... - Page 17
by Euclides - 1863
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Episodes from the Early History of Mathematics, Volume 13

Asger Aaboe - History - 1963 - 154 pages
...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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Foundations and Fundamental Concepts of Mathematics

Howard Whitley Eves - Mathematics - 1997 - 370 pages
...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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Geometry: Plane and Fancy

David A. Singer - Mathematics - 1998 - 176 pages
...154-155: 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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Space from Zeno to Einstein: Classic Readings with a Contemporary Commentary

Nick Huggett - Philosophy - 1999 - 292 pages
...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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A Course in Modern Geometries

Judith Cederberg - Mathematics - 2004 - 472 pages
...angles. The 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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Geometry Civilized: History, Culture, and Technique

J. L. Heilbron - History - 2000 - 344 pages
...Euclid's common notions l. 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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Geometry: Our Cultural Heritage

Audun Holme - Mathematics - 2002 - 408 pages
...Common Notions or Axioms 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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Mathematics and Its History

John Stillwell - Mathematics - 2004 - 576 pages
...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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A Long Way from Euclid

Constance Reid - Mathematics - 2004 - 306 pages
...POSTULATES OF EUCLID ° AXIOMS 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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此零非彼O

洪萬生 - Mathematics - 2006 - 378 pages
...Й9 ) l . Things which are equal to the same thing are also equal to one another. ( $*MS) t#4ifc*Mi*) 2. If equals be added to equals, the wholes are equal. ( 3 . If equals be subtracted from equals, the remainders are equal. ît 4. Things which coincide with one another are...
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