 | Thomas Kimber - 1874 - 352 pages
...+ 6* a* — b*' 7. Show that when> four numbers are proportionals, 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 : : с : d, show that (a* + c*) (b" + d") = (ab + с d)2. 8. Find the sum of a given number... | |
 | Joseph Ficklin - Algebra - 1874 - 446 pages
...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 to the sum of the corresponding... | |
 | William Alexander Willock - Circle - 1875 - 196 pages
...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 being contained... | |
 | Horatio Nelson Robinson - Algebra - 1875 - 430 pages
...— 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 Prop. VI, a:a + b—c:c... | |
 | Benjamin Greenleaf - Algebra - 1875 - 338 pages
...four quantities be in proportion, the sum of the first and second is to their difference at the turn of the third and fourth is to their difference. Let a : b : : c : d; Then, a-\-b : a — b : : c -\-d : c — d By Theo. VI., and by Theo. VII., ^~- = c, — - c —... | |
 | Lewis Hensley - Algebra - 1875 - 274 pages
...sum of their fourth powers. (2) If four numbers are proportionals, the sum of the first and second is to their difference as 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... | |
 | Robert Potts - Arithmetic - 1876 - 392 pages
...sum or difference of the third and fourth has to the fourth. 5. The sum of the first and second terms is to their difference, as the sum of the third and fourth terms is to their difference. 6. If the corresponding terms of two proportions be multiplied together,... | |
 | Robert Potts - Arithmetic - 1876 - 418 pages
...sum or difference of the third and fourth has to the fourth. 5. The sum of the first and second terms is to their difference, as the sum of the third and fourth terms is to their difference. 6. If the corresponding terms of two proportions be multiplied together,... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...D:C. PROPOSITION VIII. THEOREM. If four quantities 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. Let A:B::C:D; then will A+B: A— B::C+D: C— D. ByPr.6, A+B : A::C+D:C; and by Pr. 7, A— B: A::C—... | |
 | 1877 - 188 pages
...+ 6* a« — 6»' 7. Show that when four numbers are proportionals, 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 : L : : с : d, show that 8. Find the sum of a given number of terms of a geometrical progression,... | |
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If four magnitudes 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. 
