 | Horatio Nelson Robinson - 1869 - 276 pagina’s
...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 - 1870 - 818 pagina’s
...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 - 1870 - 626 pagina’s
...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 - 1872 - 350 pagina’s
...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 - 1873 - 396 pagina’s
...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 - 352 pagina’s
...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 - 1874 - 446 pagina’s
...+ 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 - 1875 - 274 pagina’s
...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... | |
 | Horatio Nelson Robinson - 1875 - 430 pagina’s
...+ 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... | |
 | William Alexander Willock - 1875 - 196 pagina’s
...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... | |
| |
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. 
