 | Horatio Nelson Robinson - 1869 - 276 σελίδες
...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 - 626 σελίδες
...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 σελίδες
...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 - 1872 - 350 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...+ 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 σελίδες
...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 - 1875 - 196 σελίδες
...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 - 1875 - 430 σελίδες
...+ 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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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. 
