 | Sir John Leslie - Geometry, Plane - 1809 - 522 pages
...THEOR. The terms of an analogy are proportional by mixing ; or the sum of the first and second to the difference, as the sum of the third and fourth to their difference. For, by conversion, A: A+B:: C : C+1), and alternately A : C ::A+B: C+D. Again, by conversion A : A—B... | |
 | Sir John Leslie - Geometry - 1817 - 456 pages
...THEOR. The terms of an analogy are proportional by mixing ; or the sum of the first and second is to the difference, as the sum of the third and fourth to their difference. Let A : B : : C : D, and suppose A-^-B ; then A+B : A— B : : C+D : C— D. For, by conversion, A : A + B : : C : C + D,... | |
 | Bewick Bridge - Algebra - 1818 - 254 pages
...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 of " the third and fourth is to their difference." For by THEOR. 6, £L+Ô=ÎI±^ and ^=£^; invert the two last udud .. . ,... | |
 | Bewick Bridge - Algebra - 1821 - 284 pages
...± d : c, ,'. inversely a : a+_b : : с : c+_d. Tн. 8. " If four quantities be proportional, then the sum " of the first and second is to their difference, as the sum of " the third and fourth is to their difference." For by _ ., a + bc + d , a— t c—d . , ,, , THEOR. 6, — : — =• ,... | |
 | Bewick Bridge - Algebra - 1821 - 644 pages
....'. inversely a : a+_b : : 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... | |
 | James Wood - Algebra - 1825 - 322 pages
..., that is, ab : a :: cd : c; and inversely, a : ab :: с : c — d. (182.) When four quantities are proportionals, the sum of the first and second is...the third and fourth, to their difference. Let a : b :: с : d; then, a + b : a — b :: c + d : c—d. By Art. 179, °— = C±d-; and by Art. 180, ^ cd... | |
 | George Lees - 1826 - 276 pages
...— d, and, therefore, by again alternating, a: a — b::c:c — rf. 116. When four quantities are proportionals, the sum of the first and second is...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, (No. 112.) 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 designated... | |
 | John Playfair - Geometry - 1829 - 210 pages
...•'• 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 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 pages
...proportion by making the terms of one product the extremes, and the terms of the other product the means. 3. If four quantities be proportionals, the sum of the first and second is to the second, as the sum of the third and fourth is to the fourth. Thus, if a;b; ;c'd, then will a+b:by.c+d;d.... | |
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If four magnitudes are proportional, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference. 
