 | Elias Loomis - Conic sections - 1877 - 458 pages
...B: A::C— 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* 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,... | |
 | London univ, exam. papers - 1878 - 164 pages
...value when a=2b: — a ab a2 aW 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 : : a : d show that 8. Find the sum of a given number of terms of a geometrical progression,... | |
 | Public schools - 1878 - 710 pages
...56^/3— v/97 — 56^3. (•) (/>) Prove that " 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." (') 6. (a) From two towns 102 miles apart, A and B set out to meet each other: A went 3 miles the first... | |
 | Benjamin Greenleaf - Algebra - 1879 - 350 pages
...How far did each travel ? 10. Prove that "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." 1. Add 3. Find a number of three digits, such thnt the sum of the digits shall be 15 ; the sum of the... | |
 | Isaac Sharpless - Geometry - 1879 - 282 pages
...A :: CD : C. Proposition 11. Theorem. — If four quantities be 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, then A+B : AB : : C+D : CD. From (IV. 9) From (IV. 10) A+B C+D BD AB CD BD Dividing... | |
 | Robert Potts - 1879 - 668 pages
...to the second, an the difference of the third and fourth is to the fourth. (3) The sum of the first and second is to their difference, as the sum of the third and fourth is to their difference. (Eue. V. 17, 18.) (1) Since a : b : : с : d, •'• т = -3 . а<Ы ! to these equals ; oa then +1=... | |
 | Robert Potts - Algebra - 1879 - 672 pages
...to the second, as the difference of tJie third and fourth is to the fourth. (3) The sum of the first and second is to their difference, as the sum of the third and fourth is to their difference. (Eue. V. 17, 18.) (1) Since a : b : : с : d, .'. - - - , add 1 to these equals ; od , abd and a+b... | |
 | Universities and colleges - 1879 - 88 pages
...parallel, and the figure is a parallelogram. 2. 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 tlieir difference. 3. The diameter which is perpendicular to a chord bisects the chord and also the... | |
 | Isaac Todhunter - Algebra - 1879 - 856 pages
...operation is called convertendo. 396. WJien four quantities are proportionals, the sum of the first and second is to their difference as the sum of the third fourth is to their difference. If a : b :: с : d, then a + b : a — b :: c + d : c — d. By Art.... | |
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In place of adding unity, subtract it, and we shall find that a : a — b :: c : c — d. or a : b — a :: c : d — c. (Theorem 4.) If four magnitudes be proportional, the sum of the first and second is to their difference, as the sum of the third and... 
