 | Middlesex Alfred Bailey - Algebra - 1902 - 336 pages
...operations are valid, 3 a : 2 b : : 3 с : 2 d, CJ.ED PROPORTION — PRINCIPLES 15. 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 ; that is, if а : b : : b : c, then a : с : : a2 : b~. Trove... | |
 | Webster Wells - Algebra - 1904 - 642 pages
...ge" + re" + • • • = p (6ft)" + q (ett)" + r r/" Therefore, ' 1 " Or ' 507. If three numbers are in continued proportion, the first is to the third as the square of the first is to the square of the second. Let the proportion be a : b = b : c. HWhence, a : с = a4 : b1.... | |
 | George Albert Wentworth - Geometry - 1904 - 496 pages
...these equations give aek cgm ~ = ' Or aek : bfl = cgm : dhn. Q ED 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... | |
 | Webster Wells - Algebra - 1906 - 484 pages
...In like manner, the theorem may be proved for any number of equal ratios. 345. If three numbers are in continued proportion, the first is to the third as the square of the first is to the square of the second. Let the proportion be a:6 = 6:c;or- = -- b с Then ax6-axa or... | |
 | Webster Wells - Algebra - 1906 - 550 pages
...In like manner, the theorem may be proved for any number of equal ratios. 345. If three numbers are in continued proportion, the first is to the third as the square of the first is to the square of the second. Let the proportion be a:6 = 6:c;or- = -« b с Then, *—*' or«=... | |
 | Webster Wells - Algebra - 1908 - 456 pages
...In like manner, the theorem may be proved for any number of equal ratios. 153. If three numbers are in continued proportion, the first is to the third as the square of the first is to the square of the second. Let the proportion be a : 6 = 6 : с ; or - = -• b с Then,... | |
 | Frederick Howland Somerville - Algebra - 1908 - 428 pages
...Since ^ = -, Ь с it follows that, ?x6=?x2b с b Ь a aWhence, с ог That is : If three numbers are in continued proportion, the first is to the third as the square of the first is to the square of the second. 383. Given a:b = b:c = c:d. Then a:d = cP:W. Proof : Since о... | |
 | George Albert Wentworth, David Eugene Smith - Geometry, Plane - 1910 - 287 pages
...a n : b n = c" : <f. Proof. -=-• §257 od PROPOSITION VIII. THEOREM 271. 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. Iden. § 261 aaa . Q o .'. — or - = TJ- Ax. 4 ac c V .-.a:c... | |
 | Alexander H. McDougall - Geometry - 1910 - 316 pages
...the st. line G be such that BC : EF = EF : G, then A ABC : A DEF = BC : G ; that is :— If three st. lines be in continued proportion, the first is to the third as any A on the first is to the similar A similarly described on the second. NOTE. — Similar As are... | |
 | Frederick Howland Somerville - Algebra - 1913 - 458 pages
...Since - = -, 6 c 4t follows that, °x^ = ?x2. 6 c 6 o Whence, 2 = g. CQ* That is : If three numbers are in continued proportion, the first is to the third as the square of the first is to the square of the second. 383. Given a:b = b:c = c:d. Then a : d = a3 : bs. Proof : Since... | |
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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 
