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" LEMMA 4. — A common divisor of two numbers is a divisor of their sum and also of their difference. "
Elementary Geometry: Including Plane, Solid, and Spherical Geometry, with ... - Page 14
by Edward Olney - 1883 - 333 pages
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The National Arithmetic on the Inductive System: Combining the Analytic and ...

Benjamin Greenleaf - Arithmetic - 1857 - 452 pages
...that will divide them without a remainder ; thus, 2 is a common divisor of 4, 8, and 10. 196i A common divisor of two numbers is a divisor of their sum, and also of their difference. Thus, 6, a common divisor of 12 and 18, is a divisor of their sum, 40, and of their difference, 6....
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The National Arithmetic on the Inductive System: Combining the Analytic and ...

Benjamin Greenleaf - Arithmetic - 1858 - 458 pages
...that will divide them without a remainder ; thus, 2 is a common divisor of 4, 8, and 10. 196, A common divisor of two numbers is a divisor of their sum, and also of their difference. Thus, 6, a common divisor of 12 and 18, is a divisor of their sum, 40, and of their difference, 6....
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The National Arithmetic on the Inductive System: Combining the Analytic and ...

Benjamin Greenleaf - Arithmetic - 1858 - 456 pages
...will divide them without a remainder ; thus, 2 is a common divisor of 4, 8, and 10. 196« A common divisor of two numbers is a divisor of their sum, and also of their difference. Thus, 6, a common divisor of 12 and 18, is a divisor of their sum, 40, and of their difference, C....
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The Normal Written Arithmetic: By Analysis and Synthesis, Designed for ...

Edward Brooks - Arithmetic - 1863 - 350 pages
...will enable the pupil to understand the next method of greatest common divisor. PRIN. I. — A common divisor of two numbers is a divisor of their sum and also of their difference. DEM. — Take any two numbers, 12 and 20, of which 4 ii a common divisor. Now, 12 = 3 times four, and...
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Practical Arithmetic, Embracing the Science of Numbers and the Art of ...

John Fair Stoddard - Arithmetic - 1868 - 356 pages
...2. — A divisor of a number is a divisor of any numbei of times that number. PBIN. 3. — A common divisor of two numbers is a divisor of their sum, and also of their difference. PEIN. 4. — The greatest common divisor of the difference of two numbers and one of them, is the greatest...
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Stoddard's Complete Arithmetic: Being the New Practical Arithmetic of the ...

John Fair Stoddard - Arithmetic - 1888 - 480 pages
...2. — A divisor of a number is a divisor of any number of times that number. PRIN. 3. — A common divisor of two numbers is a divisor of their sum, and also of their difference. PBIN. 4. — The greatest common divisor of the difference of two numbers and one of them, is the greatest...
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A Treatise on Special Or Elementary Geometry, Volumes 1-2

Edward Olney - Geometry - 1872 - 562 pages
...theorem demonstrated for the purpose of using it in the demonstration of another theorem. ILL. — Thus, in order to demonstrate the rule for finding...difference." This theorem, when proved for such a purpose, is culled a Lemma. The term Lemma is not much used, and is not very important, since most theorems, once...
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A University Algebra ...

Edward Olney - Algebra - 1873 - 354 pages
...it is evident that it goes into n times 6, or nb, n times q, or nq times. 128. LEMMA 4. — A common divisor of two numbers is a divisor of their sum and also of their difference. DEM. — Let a be a CD of m and n, going into m, p times, and into n, q times. Then (те ± n) -f-...
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The Science of Arithmetic: For High Schools, Normal Schools, Preparatory ...

Edward Olney - Arithmetic - 1876 - 322 pages
...contained in 26 twice as many tunes, in 36 3 times as many times, etc. 170. PROP. 2.—A divisor of any two numbers is a divisor of their sum and also of their difference. This also is self-evident. Thus if a is contained in m 5 times, and in n 3 times, it is evident that it...
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The Normal Higher Arithmetic: Designed for Common Schools, High Schools ...

Edward Brooks - Arithmetic - 1877 - 528 pages
...of the Number 7. 8. Proof by Excess of 9's and ll's. 9. Scales of Notation. GENERAL PRINCIPLES. 1 . A divisor of two numbers is a divisor of their sum and also of their difference (Prin. 4, Art. 175). 2. A divisor of one of two numbers, and not of the other, will divide neither...
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