 | David Martin Sensenig - Algebra - 1890 - 556 pages
...r = -r- ; therefore, b +d+f+hi a + c + e + g:b + d+f+h::a:b. 450. -Z/' any number of quantities are in continued proportion, the first is to the third as the square of the first is to the square of the second ; the first is to the fourth as the cube of the first is to the... | |
 | George Irving Hopkins - Geometry, Plane - 1891 - 204 pages
...proportion, their like powers and like roots will also form a proportion. 310. If three quantities form a proportion, the first is to the third as the square of the first is to the square of the second. 311 (a). Substitute "difference" for "sum" in 311. 312. If two... | |
 | George Washington Hull - Algebra - 1895 - 358 pages
...a+c + e = (b + d + f)r. 0 q + c + e _ = a. 6 + d+/ 6 Whence, a THEOREM XVII. /f iAree quantities are in continued proportion, the first is to the third as the square of the first is to the square of the second. Let a:b — b: c. -• Whence, a : с = a2 : 6*. THEOREM XVIII.... | |
 | William Freeland - Algebra - 1895 - 328 pages
...bf= eg: dh. Dividing (3) by (4), ad be or, \e J\hJ ab cd " ~e'f^g'h 299. XV. If three quantities are in continued proportion, the first is to the third as the square of the first is to the square of the second. Let а : b = b : c. Then, b2 = ac. Multiplying by a, a&2 = a2c.... | |
 | Webster Wells - Algebra - 1897 - 422 pages
...c" : d". In like manner, we may prove that л/a : л/& = л/с : Vd. 320. 7У í/wee quantities are in continued proportion, the first is to the third as the square of the first is to the square of the second. Let a : b = b : c. Then, а = *. 6 с Therefore, 321. If four... | |
 | Webster Wells - Algebra - 1897 - 426 pages
...?"=^. bn dn Whence, a* : bn = c": d". In like manner, we may prove that 320. If three quantities are in continued proportion, the first is to the third as the square of the first is to the square of the second. Let a:b = b: c. Then, 5 = *. Therefore, а x = ? x 2, or ^ =... | |
 | New York (State). Legislature. Senate - Government publications - 1897 - 1306 pages
...equal, the real parts are equal and the imaginary parts are equal. 6 Prove that if three quantities are in continued proportion, the first is to the third as the square of the first is to the square of the second. 7-8 There are two numbers whose product is 96 and the difference... | |
 | Webster Wells - Algebra - 1897 - 386 pages
...like manner, we may prove that ni n ГГ n/ n/~î V a : -у о = ve : V«320. If three quantities are in continued proportion, the first is to the third as the square of the first is to the square of the second. Let a : b = b : c. Then, H = *. b с Therefore, оХ5 = £х£ог2... | |
 | George Albert Wentworth - Geometry - 1899 - 500 pages
...equations give aek c</m bf I ~ dhn Or aek : bfl = cgm : dhn. QE D_ 337. COR. If three quantities are in continued proportion, the first is to the third as the square 'of the second is to the square of the third. PROPOSITION XI. THEOREM. 338. Like powers of the terms of a proportion... | |
 | George Albert Wentworth - Geometry, Plane - 1899 - 278 pages
...equations give aek — cym ~bfl~~dhn Or aek : bf I = cym : dhn. QED 337. COR. If three quantities are in continued proportion, the first is to the third as the square of the first is to the square of the second. PROPOSITION XI. THEOREM. 338. Like powers of the terms of a proportion... | |
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If three quantities are in continued proportion, the first is to the third as the square of the first is to the square of the second. Let a : b = b : c. Then, 2=*. b с Therefore, ^xb. = ^x± b с bb Or °r 
