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" Composition, when the sum of the first and second is to the second as the sum of... "
The student's algebra - Page 13
by John Darby (teacher of mathematics.) - 1829
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Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ...

Sir John Leslie - Geometry, Plane - 1809 - 522 pages
...alternately A : C :: B : D. PROP. IX. THEOR. The terms of an analogy are proportional by composition; or the sum of the first and second is to the second, as the sum of the third and fourth to the fourth. Let A : B :: C : D; then by composition A+B : B :: C +D: D. Because A : B :: C: D, the...
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An Easy Introduction to the Mathematics: In which the Theory and ..., Volume 2

Charles Butler - Mathematics - 1814 - 528 pages
...first above the second is to the first, as the excess of the third above the fourth to the fourth. 70. If four quantities be proportionals, the sum of the first and second is to their difference, as the sum of the third and fourth to their difference. Let a : b :: c : d, then...
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Easy Introduction to Mathematics, Volume 2

Charles Butler - 1814 - 582 pages
...ALTEUccd NDO, or PERMUTANDO. Euclid 1G, 5. 65. Jf four quantities be proportionals, the sum of the first d second is to the second, as the sum of the- third and fourth the fourth. Let a : b : : c : d, then will a+b :b:: c+d: d. Because — = b -, kt unity be added to...
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The First Six Books with Notes

Euclid - 1822 - 222 pages
...the third. Prop. 20. 16. By composition, when we infer that if there be four magnitudes proportional, the sum of the first and second is to the second, as the sum of the third and fourth to the fourth. Cor. Prop. 21. 17- By division, when we infer that if there be four magnitudes proportional,...
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An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan - Algebra - 1824 - 550 pages
...and aħt : k ; : eid •. d. a ^ Hence, when four quantities are proportionals, the sum or difference of the first and second is to the second as the sum or difference of the third and fourth, is to the fourth. 479. In like manner, if a : b : : c : d ;...
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The Practical Analyst: Or, A Treatise on Algebra, Containing the Most Useful ...

Enoch Lewis - Algebra - 1826 - 180 pages
...still be a true one. _ а с ас a^-bc^-d For T=-d-'- b^=^1' or —=Т' Or, a*rb : b : : c~rd : d. 64. If four quantities be proportionals, the sum of the first and second is to their difterence,.as the sum of the third and fourth is to their difference. * The terms are similarly...
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The First Six Books of the Elements of Euclid: With Notes

Euclid - Euclid's Elements - 1833 - 216 pages
...the third. Prop. 20. 16. By composition; when we infer that if there be four magnitudes proportional, the sum of the first and second is to the second, as the sum of the third and fourth to the fourth. Cor. prop. 21. 17. By division ; when we infer that if there be four magnitudes proportional,...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 410 pages
...the second, as the excess of the third above the fourth is to the fourth : and, (2.) by composition, the sum of the first and second is to the second, as the sum of the third and fourth to the fourth. If A : B : : C : D ; then, by division, A — B:B::C_D:D; and by composition, A + B...
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The elements of algebra

Andrew Bell (writer on mathematics.) - 1839 - 500 pages
...alternation, when the first is to the third as the second to the fourth ; (329.) By composition, when the sum of the first and second is to the second, as the sum of the third and fourth to the fourth ; (330.) By addition, when the first is to the sum of the first and second, as the third...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclides, James Thomson - Geometry - 1845 - 382 pages
...&c. PROP. X. THEOR. (V. l8 and l7). — If four numbers be proportionals ; then, (l) by composition, the sum of the first and second is to the second, as the sum of the third and fourth to the fourth : and, (2) by division, the excess of the first above the second is to the second, as...
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