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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 Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 532 pages
...are called homologous sides or angles. AXIOMS. 34. 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 Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 518 pages
...are called homologous sides or angles. AXIOMS. 34. An AXIOM is a self-evident trath ; 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: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 504 pages
...are called homologous sides or angles. AXIOMS. 34. 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 Trigonometry

Adrien Marie Legendre - Geometry - 1863 - 464 pages
...RHOMBOID is a parallelogram whose angles are all oblique. AXIOMS. 1. Tilings 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. 4. If equals...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1868 - 340 pages
...are called homologous sides or angles. AXIOMS. 34. 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 Trigonometry: With Practical Applications

Benjamin Greenleaf - 1869 - 516 pages
...angles. AXIOMS. 34. An AXIOM is a self-evident truth ; such as, — 1. Things which arc 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, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1871 - 302 pages
...resulting from one or more propositions. 27. A scholium is a remark appended to a proposition. 28. An hypothesis is a supposition made either in the enunciation...the same thing are equal to each other. 2. If equals are added to equals, the wholes are equal. 3. If equals are taken from equals, the remainders are equal....
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Psychology: Or, The Science of Mind

Oliver Spencer Munsell - History - 1871 - 360 pages
...and contradiction. For example, take the first, second, and third axioms; I quote from Robinson: " 1. Things which are equal to the s'ame thing are equal to each other; " " 2. When equals are added to equals, the wholes are equal; " " 3. When equals are taken from equals, the...
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Psychology: Or, The Science of Mind

Oliver Spencer Munsell - History - 1871 - 368 pages
...and contradiction. For example, take the first, second, and third axioms ; I quote from Robinson : " 1. Things which are equal to the same thing are equal to each other ; " " 2. When equals are added to equals, the wholes are equal ; " " 3. When equals are taken from equals, the...
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New Elementary Geometry: With Practical Applications ; a Shorter Course Upon ...

Benjamin Greenleaf - Geometry - 1873 - 202 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 wili be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals be...
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