 | Sir John Leslie - Geometry, Plane - 1809 - 522 pages
...mean terms. A+B:B::C+D:D. PROP. X. THEOR. The terms of an analogy are proportional by division; or the difference of the first and second is to the second, as the difference of the third and fourth to the fourth. Let A : B : : C: D; suppose A to be greater than... | |
 | Charles Butler - Mathematics - 1814 - 528 pages
...named ALTBRac Co NANDO, Or FERMUTANDO. Euclid 16, 5. 65. If four quantitks be proportionals, the sum of the first and second is to the second, as the sum of the third and fourth «o the fourth. a Let a: b:: c: d, then will a+ b : b : : c+ d : d. Because... | |
 | Sir John Leslie - Geometry - 1817 - 456 pages
...A+B : B : : C + D : D. PROP. X. THEOB. The terms of an analogy are proportional by division ; or the difference of the first and second is to the second, as the difference of the third and fourth to the fourth. Let A : B : : C : D ; suppose A to be greater than... | |
 | Bewick Bridge - Algebra - 1818 - 254 pages
..." If four quantities be proportional, then the sum " or difference of the first and second will be to the second " as the sum or difference of the third and fourth is to the " fourth." For let a : L : : с : d, then - = - : add or subtract о а 1 from each side of the equation ; then... | |
 | Bewick Bridge - Algebra - 1821 - 284 pages
..." If four quantities be proportional, then the sum " or difference of the first and second will be to the second " as the sum or difference of the third and fourth is to the " fourth." For let a : b : : с : d, then r= -, ; add or subtract о а 1 from each side of the equation ; then... | |
 | Euclid - 1822 - 222 pages
...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... | |
 | James Ryan, Robert Adrain - Algebra - 1824 - 542 pages
...first as the fourth to the third. XV. Componendo, by composition, when it is inferred that the sum of the first and second is to the second as the sum of the third and fourth is to the fourth. XVI. Dividendo, by division, when it is inferred that the... | |
 | James Ryan - Algebra - 1824 - 550 pages
...first as^the fourth to the third. XV. Componendo, by composition, when it is inferred that the sum of the first and second is to the second as the sum of the third and fourth is to the fourth. XVI. Dividendo, by division, when it is inferred that the... | |
 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...quantities be proportional, then the SUM or DIFFERENCE of thcfast and second will be to the second a» the SUM or DIFFERENCE of the third and fourth is to the fourth. For let a : I : : с : d, then ^ =c, ; add or subtract 1 from each bd side of the equation; then г±1=т±1,... | |
 | James Ryan - Algebra - 1826 - 430 pages
...: 6: : o or bd — c ±jl : d. Hence, when four quantities are proportionals, the sum or differerce of the first and second is to the second as the sum...difference of the third and fourth, is to the fourth. 470. In like manner, if a : b : : c : d • then, ma : mb : : £c : i<*. For £=^ ; /. (Art. 1 18).^=T^;... | |
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Division, when the difference of the first and second is to the second as the difference of the third and fourth is to the fourth... 
