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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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Geometry: Plane and Fancy

David A. Singer - Mathematics - 1998 - 176 pages
...I quote from [18], pp. 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
...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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A Course in Modern Geometries

Judith Cederberg - Mathematics - 2004 - 472 pages
...than the two right 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
...Table 2.3.2. Table 2.3.2 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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God and Reason in the Middle Ages

Edward Grant - Education - 2001 - 412 pages
...Sir Thomas L. Heath's translation, Euclid has (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"; and (3) "If equals be subtracted from equals, the remainders are equal." See The Thirteen Books of...
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Mathematics and Its History

John Stillwell - Mathematics - 2004 - 576 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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Geometry: Our Cultural Heritage

Audun Holme - Mathematics - 2002 - 408 pages
...the following: Euclid's 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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A Long Way from Euclid

Constance Reid - Mathematics - 2004 - 306 pages
...47, AXIOMS AND 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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Euclid: The Great Geometer

Chris Hayhurst - Juvenile Nonfiction - 2005 - 118 pages
...notions in book I. All five are about 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. 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. īt 4. Things which coincide with one another are...
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