 | Charles Butler - 1814 - 528 σελίδες
...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 σελίδες
...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 σελίδες
...: 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 .. . ,... | |
 | Bewick Bridge - 1821 - 648 σελίδες
...: 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... | |
 | George Lees - 1826 - 276 σελίδες
...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 σελίδες
...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),... | |
 | John Darby (teacher of mathematics.) - 1829 - 212 σελίδες
...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... | |
 | George Peacock - 1830 - 732 σελίδες
...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... | |
 | 1836 - 366 σελίδες
...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 - 1837 - 410 σελίδες
...: C— D, and alternately A + B:A — 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 + A: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. 
