 | Horatio Nelson Robinson - Algebra - 1850 - 358 pages
...: c : c—tt. or a : b—a : : c : d—c. (Theorem 4.) If four magnitudes be proportional, the sum of the first and second is to their difference, as...sum of the third and fourth is to their difference. Admitting that a : b : : c : d, we are to prove that a-\-b : a—b ; : c-\-d : c—d From the same... | |
 | Joseph Ray - Algebra - 1852 - 408 pages
...275. PROPOSITION IX. — If four quantities are in proportion, the sum of the first and second will be to their difference, as the sum of the third and fourth is to their difference. Let a : b : : c : d (1), then will a+6 : a — b : : c-\-d : c — d. From the 1st, by Composition,... | |
 | Horatio Nelson Robinson - Conic sections - 1854 - 350 pages
...C—D Or . . A:B— A: : C:D— C. THEOREM 9. If four magnitudes be proportional, the sum of thefirsl and second is to their difference, as the sum of the third and fourth is to their difference. Admitting that . A : B : : C : D, we are to prove that A+B : A—B : : C+D : C—D From the same hypothesis,... | |
 | James William M'Gauley - 1854 - 284 pages
...means, ac — ad=ac — be ad=be 24. We may mix : and, then, " the sum of the first and second terms is to their difference, as the sum of the third and fourth is to their difference." a:b: :C:d Mixing, a-\-b:a — b: :c-\-d:C—d Multiplying extremes, and means, ac-\-bc— ad— bd=ac—... | |
 | Joseph Ray - Algebra - 1857 - 408 pages
...275. PROPOSITION IX. — If four quantities are in proportion, the sum of the first and second will be to their difference, as the sum of the third and fourth is to their difference. Let a:b::c:d (1), then will a-\-b : a — b : : c-\-d : c — d. From the 1st, by Composition, (Art.... | |
 | Isaac Todhunter - Algebra - 1858 - 530 pages
...convertendo. 396. When four quantities are proportionals, the sum of thf first and second is to tlieir difference as the sum of the third and fourth is to their difference. If a : b :: с : d, then a + b : ab :: с + d : с - d. By Art. 393, ^=^, O (í and by Art. 394, ^-... | |
 | Horatio Nelson Robinson - Algebra - 1859 - 368 pages
...: c — ds or a : b — a : : c : d — c. (Theorem 4.) If four magnitudes be proportional, the sum of the first and second is to their difference, as the sum of the third and fourth is to (heir difference. Admitting that a : b : : c : d, we are to prove that a-\-b : a — 6 : : c+rf : c... | |
 | John Fair Stoddard, William Downs Henkle - Algebra - 1859 - 538 pages
...student prove this. PROPOSITION (393.) 12. When four quantities are in proportion, the sum of the ßrst and second is to their difference as the sum of the third and fourth is to their difference. DEMONSTRATION. Let a : b : : с : d. We are to prove that a + b : a—b : : c+d : c—d By Prop. 8,... | |
 | James B. Dodd - Algebra - 1859 - 368 pages
...v :: w : x : y : z. THEOREM XIII. (163.) The sum of the first, and second terms in any Proportion, is to their difference, as the sum of the third and fourth is to their difference. Let a : b : : x : y, then is a-\-b : a — b : : x-\-y : x — y. By Composition and Division, in the... | |
 | Joseph Allen Galbraith - Optics - 1860 - 94 pages
...the mirror, this relation becomes r:: alternmdo (Euc. V. 16) — A + |r : A- |r :: and since the sum of the first and second is to their difference as...sum of the third and fourth is to their difference, we have, componendo et dividendo (Euc. V. 1 7, 18), ^& : r : : r : ^8, or, finally, making /=-, *«=/';... | |
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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. 
