| Sir John Leslie - Geometry, Plane - 1809 - 493 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 - 454 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 - 227 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 - 288 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 - 227 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 - 266 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 - 166 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 - 186 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 - 214 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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