 | Charles Butler - Mathematics - 1814 - 528 pages
...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 - Algebra - 1815 - 338 pages
...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 - Algebra - 1818 - 254 pages
...: 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 of " the third and fourth is to their difference." For by THEOR. 6, £L+Ô=ÎI±^ and ^=£^; invert the two last udud .. . , bd , a + bbc + dd fractions,... | |
 | Bewick Bridge - Algebra - 1821 - 648 pages
...: c : c£d. TH. S. " If four quantities be proportional, then the .•mm " of the first and second is to their difference, as the sum of " the third and fourth is to their difference." For by THEOR. 6, ^~=^—, and ^- =^^-; invert the two last bdba , , bd , a+bb c+dd fractions, then... | |
 | George Lees - 1826 - 276 pages
...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 - Geometry - 1829 - 210 pages
...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 the 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 •+ D : : B : D... | |
 | John Darby (teacher of mathematics.) - 1829 - 212 pages
...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 - Algebra - 1830 - 732 pages
...a — b :: c : c — d. 411. " If four magnitudes be proportionals, the sum of the first and second is to their difference as the 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 — bc — d... | |
 | Mathematics - 1836 - 366 pages
...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 -|-... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...B:: C + D:C — D: that is, if four numbers be proportional, the sum of the first and second terms is to their difference, as the sum of the third and fourth terms \a to their difference. It is evident that if B be greater than A, the analogy will become B... | |
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If four magnitudes are in proportion, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference. 
