| 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... | |
| 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... | |
| 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... | |
| 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,... | |
| 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 ;... | |
| 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... | |
| 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,... | |
| 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... | |
| 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... | |
| 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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