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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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New Elementary Geometry: With Practical Applications : a Shorter Course Upon ...

Benjamin Greenleaf - Geometry - 1874 - 206 pages
...not equal to either of the other sides. AXIOMS. 26. An 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...
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Elements of Geometry: And the First Principles of Modern Geometry

William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...connection, use, extension, or limitation. 9. An hypothesis is a supposition made either in the statement of a proposition or in the course of a demonstration....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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Elements of Plane Geometry, Part 1

Thomas Hunter - Geometry, Plane - 1878 - 142 pages
...plane figure is that side upon which it is supposed to stand. Any side may be considered the base. Axioms. 1. Things which are equal to the same thing...to each other. 2. If equals be added to equals the sums are equals. 3. If equals be taken from equals the remainders are equals. 4. If equals be added...
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New Practical Algebra: Adapted to the Improved Methods of Instruction in ...

James Bates Thomson - Algebra - 1878 - 322 pages
...2 = what ? 15. 26 -r- (x — b) + axbxy + zz = what ? AXIOMS. 59. An Axiom is a self-evident truth. 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 subtracted from equals, the remainders are...
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Elements of Algebra

George Albert Wentworth - Algebra - 1881 - 400 pages
...reciprocals of each other whep their product is equal to unity. Thus, a and - are reciprocals. a 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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Elements of Plane Geometry

Franklin Ibach - Geometry - 1882 - 208 pages
...in a proposition or in a demonstration. 38. A Scholium is a comment on one or more propositions. 39. 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 subtracted from equals, the remainders are...
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Intellectual and Practical Lightning Calculator: The Unity and Decimal System

John Alexander Henderson - Ready-reckoners - 1882 - 232 pages
...problem is a question proposed, which requires a solution. AXIOMS. 1. Thmgirwhich are equal to the same thing, are equal 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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Essentials of Geometry

Alfred Hix Welsh - Geometry - 1883 - 326 pages
...Scholium is a remark upon some feature of a proposition. AXIOMS. An Axiom is a self-evident truth: 1. Things which are equal to the same thing are equal to each other. 2. If the same operation be performed upon equals, the results will be equal. Thus, if the same quantity...
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The Eclectic School Geometry

Evan Wilhelm Evans - Geometry - 1884 - 242 pages
...specially to magnitudes in space, and are therefore peculiar to Geometry. AXIOMS. 1. Things 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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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...VOLUME is a limited portion of space, combining the three dimensions of length, breadth, and thickness. 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 subtracted from equals, the remainders are...
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