| Horatio Nelson Robinson - 1869 - 276 pages
...between the third and fourth. THEOREM IX. If four magnitudes are proportional, the sum ojthe^first **and second is to their difference as the sum of the third and fourth** is to their difference. Let A, B, C, and D be the four magnitudes which give the proportion A : B ::... | |
| Isaac Todhunter - Algebra - 1870 - 626 pages
...This operation is called convertendo. 396. When four quantities are proportionals, the sum of tlie **first and second is to their difference as the sum of the third and fourth** is to their difference. If a : b :: с : d, then a + b : ab :: c + d : c — d. By Art. 393, "v-^,... | |
| Isaac Todhunter - 1870 - 818 pages
...This operation is called convertendo. 396. When four quantities are proportionals, the sum of tJte **first and second is to their difference as the sum of the third and fourth** is to their difference. If a : b :: с : d, then a + b : ab :: c + d : cd. a + bc + d By Art. 393,... | |
| Isaac Todhunter - Algebra - 1872 - 356 pages
...b а а с а с or а-Ъ : a :: cd : c; therefore a : а-Ъ :: с : cd. 367. JVhenfbur numbers are **proportionals, the sum of the first and second is to their difference as the** »um of the third and fourth is to their difference; that is, if a : Ъ :: с : d, then a+b : а-Ъ... | |
| Elias Loomis - Algebra - 1873 - 396 pages
...and we have a , c , ,, . a—b c—d that is, -£- = -^-, 306. If four quantities are proportional, **the sum of the first and second is to their difference, as the sum of the third and fourth** it to their difference. Let a : b : : c : d. By composition, Art. 304, a+b: b::c+d: d. By alternation,... | |
| Thomas Kimber - 1874 - 354 pages
...when a = 2 b : a , ab «* a*62 "r _ в _ 6* a* + 6* a* — b*' 7. Show that when> four numbers are **proportionals, the sum of the first and second is...their difference as the sum of the third and fourth** is to their difference. If a : b : : с : d, show that (a* + c*) (b" + d") = (ab + с d)2. 8. Find... | |
| Joseph Ficklin - Algebra - 1874 - 446 pages
...+ b : a = с + d : c, and a — b : a~ с — d : c; that is, If four quantities 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. 436. TJie sum of any number of the antecedents of a continued proportion is... | |
| Lewis Hensley - Algebra - 1875 - 274 pages
...numbers into the sum of their squares into the sum of their fourth powers. (2) If four numbers are **proportionals, the sum of the first and second is...the sum of the third and fourth to their difference.** (3) A quantity consisting of the sum of the squares of three numbers and of twice the product of every... | |
| William Alexander Willock - Circle - 1875 - 196 pages
...sums. BY COMPOSITION AND DIVISION. — When the first is to the second as the third to the fourth, **the sum of the first and second is to their difference as the sum of the third and fourth** is to their difference. This is a consequence of the preceding changes in the proportions, the submultiples... | |
| Horatio Nelson Robinson - Algebra - 1875 - 430 pages
...+ b:a= c + d: c, a — b:a = c — d: c. PROPOSITION VII. — If four quantities 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. If a : b = c : d, we are to prove that a + b : a — b = c + d : c — d. By... | |
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