 | Horatio Nelson Robinson - Algebra - 1875 - 430 pages
...like manner it may be shown that a + b:a= c + d: c, a — b:a = c — d: c. PROPOSITION VII. — If four quantities are in proportion, the sum of 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... | |
 | Isaac Todhunter - Algebra - 1875 - 640 pages
...:: c : c — d. This operation is called convertendo. 396. When four quantities are proportionals, the sum of the first and second is to their difference...sum of the third and fourth is to their difference. If a : b :: c : d, then a + b : a — b :: c + d :o — d. By Art. 393, = bd 11 . or, * a — bc —... | |
 | 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...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... | |
 | Lewis Hensley - Algebra - 1875 - 274 pages
...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 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... | |
 | Benjamin Greenleaf - Algebra - 1875 - 338 pages
..._ c — d Of' ~b~ ~d~ ' whence, a — b : b :: c — did. THEOREM VIII. 322i If 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 —... | |
 | Benjamin Greenleaf - 1876 - 332 pages
...DIVISION. Let a : b : : c : d ; then, a — b : b : : c — d THEOREM VIII. 322, If four quantities be in proportion, the sum of the first and second is to their difference as the sum of tht third and fourth is to their difference. Let a : b : : c : d; Then, a-\-b : a — 6: : c-\-d :... | |
 | 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
...Therefore, by Pr.l, A— B: A::C— D:C. PROPOSITION VIII. THEOREM. If four quantities are proportional, the sum of the first and second is to their difference...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
...a* — a* b* ¡Hfl a2 — 6* a* + 6* a« — 6»' 7. Show that when four numbers are proportionals, the sum of the first and second is to their difference...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. 
