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" 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 added to unequals, the sums will be unequal. "
Ticknor's Mensuration, Or, Square and Triangle: Being a Practical and ... - Page 22
by Almon Ticknor - 1849 - 144 pages
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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1886 - 352 pages
...stand ; and the altitude is a line drawn from the opposite side or angle, perpendicular to the base. AXIOMS. 1. Things which are equal to the same thing...to each other. 2. If equals be added to equals, the wholes will be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals...
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Shorter Course in Algebra

George Albert Wentworth - Algebra - 1886 - 284 pages
...reciprocals of each other when their product is equal to unity. Thus, a and - are reciprocals. AXIOMS. 43. 1. Things which are equal to the same thing are equal to each other. 2. If equal numbers be added to equal numbers, the sums will be equal. 3. If equal numbers be subtracted...
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Bizarre; Notes and Queries; a Monthly Magazine of History, Folk ..., Volumes 3-4

1886 - 580 pages
.../OTKS, rto». M., 395. J. y. ^., 300. Jostf, 284. -^ Geometrical Axioms. 1. Things that 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 subtracted from equals, the remainders will be equal. 4. If equals...
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A Text-book of Geometry

George Albert Wentworth - Geometry - 1888 - 264 pages
...point. 2. That a straight line can be produced to any distance, or can be terminated at any point. 82. AXIOMS. 1. Things which are equal to the same thing are equal to each other. 2. If equals are added to equals the sums are equal. 3. If equals are taken from equals the remainders are equal....
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A College Algebra

George Albert Wentworth - Algebra - 1888 - 514 pages
...value of an expression evidently depends upon the values given to the several symbols involved. 18. Axioms. 1. Things which are equal to the same thing are equal to each other. 2. If equal numbers be added to equal numbers, the sums will be equal numbers. 3. If equal numbers be subtracted...
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Numbers Symbolized: An Elementary Algebra

David Martin Sensenig - Algebra - 1889 - 388 pages
...Axioms. 45. An Axiom is a self-evident truth. 46. The following are the principal axioms of algebra : 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 subtracted from equals the remainders will be equal. а. If equals...
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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - Geometry - 1890 - 418 pages
...line. 3. That a circle may be described 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 - 524 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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Syllabus of Geometry

George Albert Wentworth - Mathematics - 1896 - 68 pages
...That a circumference may be described about any point as a centre with a radius of given length. 82. AXIOMS. 1. Things which are equal to the same thing are equal to each other. 2. If equals are added to equals the sums are equal. 3. If equals are taken from equals the remainders are equal....
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Elements of Geometry, Volume 1

Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...geometric 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...
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