| Charles Butler - 1814 - 528 páginas
...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 will a+b : a—b : : c+d : c—d; for u + li c 4 </ a... | |
| James Wood - 1815 - 338 páginas
...inversely, a : a—b :: c : c — d., (182.) When four quantities are proportionals, the sum of the Jirst and second is to their difference, as the sum of the third and fourth, to their difference. Let a : b :: c : d ; then, ' + b : ab :: c + d: «— d. G Ey ac , If possible,... | |
| Bewick Bridge - 1818 - 254 páginas
...inversely a : a±e : : с : c±.d. Til. 8. " If four quantities be proportional, then the sum " of (.he first and second is to their difference, as the sum...and fourth is to their difference." For by THEOR. 6, £L+Ô=ÎI±^ and ^=£^; invert the two last udud .. . , bd , a + bbc + dd fractions, then - r= - 7;... | |
| James Wood - 1825 - 322 páginas
...: c; and inversely, a : ab :: с : c — d. (182.) When four quantities are 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 :: с : d; then, a + b : a — b :: c + d : c—d. By Art. 179, °—... | |
| George Lees - 1826 - 276 páginas
...by again alternating, a: a — b::c:c — rf. 116. When four quantities are proportionals, the sum of the first and second is to their difference, as the sum of the third and fourth to their difference. This readily appears from Nos. 114 and 115. For, (No. 114.) a+b:b::c+d : d, therefore,... | |
| John Playfair - 1829 - 210 páginas
...A : B j- A : .- C : D ± C. Cor. B^fA^::D^C:C (35). 40. If four quantities be proportional, the sum of the first and second is to their difference, as...sum of the third and fourth is to their difference. Let A : B : : C : D, then (by mixing) A+B:AB::CJ+D:C — D. ForA + B:B::C +D;D(37), .-. A + B : C •+... | |
| John Darby (teacher of mathematics.) - 1829 - 212 páginas
...Thus,ifa:6::e;rf; then will a— b ; b : ; c — did. 5. If four quantities be proportionals, the sum of the first and second is to their difference, as the sum of the third and fourth is to thejr difference. Thus, if a;b:;c:d, then will a+b;a— b: ;c+d;c — d. 6. If four quantities be proportionals,... | |
| George Peacock - 1830 - 732 páginas
...a — bc — d' or a : a — b :: c : c — d. 411. " If four magnitudes be proportionals, the sum of the first and second is to their difference as...sum of the third and fourth is to their difference." Let a : b :: c : d, then also a + b : a — b :: c + d : c — d. T. .ac Forif 6-3' x, , a + bc + da... | |
| 1836 - 366 páginas
...whose terms are not equimultiples of a and b. 232. When four quantities are proportionals, the sum of the first and second is to their difference as the sum of the third and fourth to their difference. 234. Express a + b . Jl]. and log, (a + 6 v'~) in the c + « v __ l form A -|-... | |
| Andrew Bell - 1837 - 290 páginas
...excess above the second, as the third is to its excess above the fourth. 27- By mixing, when the sum of the first and second, is to their difference, as the sum of the third and fourth to their difference. 28. By equality, when there is any number of magnitudes more than two, and as... | |
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