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AXIOM is a self-evident truth ; such as, — 1. Things which are equal to the same thing, are equal to each other. 2. If equals be added to equals, the sums will be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals be...
Elements of Geometry: Containing the Principal Propositions in the First Six ... - Page 5
by John Bonnycastle - 1803 - 279 pages
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## The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - Geometry - 1890 - 418 pages
...with any centre, at any distance from that centre. AXIOMS. 46. 1. Things which are equal to the same thing are equal to each other. 2. If equals be added to equals the sums will be equal. 3. If equals be taken from equals the remainders will be equal. 4. If equals be...
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## Plane and Solid Geometry: Suggestive Method

Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 522 pages
...can be drawn between two points. 38. AXIOMS. 1. Things which are equal to the same or equal things are equal to each other. 2. If equals be added to equals the sums will be equal, 3. If equals be subtracted from equals the differences will be equal. 4. If equals...
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## Elements of Geometry, Volume 1

Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...truth to another the following general axioms are also employed, viz. : (l.) Things equal to the same thing are equal to each other. (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...
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## Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 570 pages
...truth to another the following general axioms are also employed, viz. : (1.) Things equal to the same thing are equal to each other. (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...
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## Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...conclusion and the hypothesis of the other. AXIOMS 1. Things that are equal to the same or equal things are equal to each other. 2. If equals be added to equals, the sums are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. If equals be added...
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## Plane Geometry

Arthur Schultze - 1901 - 260 pages
...conclusion and the hypothesis of the other. AXIOMS 1. Things that are equal to the same or equal things are equal to each other. 2. If equals be added to equals, the sums are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. If equals be added...
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## Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...conclusion and the hypothesis of the other. AXIOMS 1. Things that are equal to the same or equal things are equal to each other. 2. If equals be added to equals, the sums are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. If equals be added...
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## Plane Geometry

Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...stated as follows: GENERAL AXIOMS 1. Things which are equal to the same thing, or to equal things, are equal to each other. 2. If equals be added to equals, the sums are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. Doubles of equals...
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## A Scrap-book of Elementary Mathematics: Notes, Recreations, Essays

William Frank White - Mathematical recreations - 1908 - 274 pages
...equations with a list of axioms such as the following: 1. Things equal to the same thing or equal things are equal to each other. 2. If equals be added to equals, the sums are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. If equals be multiplied...
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## The Science-history of the Universe, Volume 8

Francis William Rolt-Wheeler - Science - 1909 - 356 pages
...and also assumes its infinitude. The five common notions are : 1. Things which are equal to the same thing are equal to each other. 2. If equals be added to equals, the sums are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. Things which coincide...
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