 | Robert Potts - Algebra - 1879 - 672 pages
...li d 7 л and?.* .. f.?. f'f'g'k 18. Prop. If three quantities a, b, с be in continued proportion, the first is to the third as the square of the first is to the square of the second. (Eue. VIII. 11, 26.) Since a, b, с are proportionals ab зЪЬ -,... | |
 | Webster Wells - 1885 - 368 pages
...m ' nm ' n Note. Either m or n may be unity. 307. 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. mu ab Then, - = b с Therefore, ax- = -xi о с... | |
 | Webster Wells - Algebra - 1885 - 370 pages
...m ' n m' n Note. Either m or n may be unity. 307. 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... | |
 | Webster Wells - Algebra - 1885 - 372 pages
...' nm ' n Note. Either m от n may be unity. 307. 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. mu ab Then, - = b с Therefore, «xb = 2x^ b с bb... | |
 | Webster Wells - Algebra - 1889 - 584 pages
...m ' n m' n Note. Either m or n may be unity. 323. 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. _b Then, a& a b с Therefore, = ¿x|a2 b2' Or, a с... | |
 | David Martin Sensenig - Algebra - 1890 - 556 pages
...+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 cube... | |
 | Webster Wells - Algebra - 1890 - 604 pages
...manner we may prove that \/a : \/6 = Vc : Vd. 396. 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, f = ^oc Therefore, ox6 = oxooro* 6 cbbc Ir . Whence,... | |
 | George Irving Hopkins - Geometry, Plane - 1891 - 208 pages
...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. If four quantities form a proportion, the sum of the squares of... | |
 | William Freeland - Algebra - 1895 - 328 pages
...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. .-.... | |
 | George Washington Hull - Algebra - 1895 - 358 pages
...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. If... | |
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If three quantities are proportional, the first is to the third, as the square of the first, to the square of the second ; or as the square of the second, to the square of the third. 
