 If the product of two numbers is equal to the product of two other numbers, either two may be made the means, and the other two the extremes of a proportion.  Elementary Algebra - Page 225by Elmer Adelbert Lyman, Albertus Darnell - 1917 - 503 pagesFull view - About this book
 | Frederick Howland Somerville - Algebra - 1913 - 458 pages
...their product. 374. Given ad - bc. Then a:bTO-c:d. Proof : ad = be. Dividing by bd, 5 = 5. bd That is : If the product of two numbers is equal- to the product of two other numbers, one pair may be made the extremes, and the other pair the means, of a proportion. In like manner we... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 490 pages
...Find the third proportional to (a) 9 and 12, (6) 14 and 21, (c) 1 and a. PROPOSITION II. THEOREM 279. If the product of two numbers is equal to the product of two other numbers, either two may be made the means, and the other two the extremes, of a proportion. Given mn =pq. To... | |
 | Webster Wells, Walter Wilson Hart - Algebra - 1913 - 362 pages
...bc, by clearing of fractions. bd EXAMPLE. Since | = £ , 2 . 9 should equal 3 • 6. Does it ? 190. If the product of two numbers is equal to the product of two other numbers, one pair may be made the means and the other the extremes of a proportion. If mn — xy, then — =... | |
 | Walter Burton Ford, Charles Ammerman - Geometry, Solid - 1913 - 184 pages
...Corollary 1. If the two antecedents of a proportion are equal, the consequents are also equal. Theorem B. If the product of two numbers is equal to the product of two other numbers, either pair may be made the means of a proportion in which the other two are taken as the extremes.... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 328 pages
...Find the third proportional to (a) 9 and 12, (6) 14 and 21, (c) 1 and a. PROPOSITION II. THEOREM 279. If the product of two numbers is equal to the product of two oiIier numbers, etther two may be made the means, and the other two the extremes, of a proportion.... | |
 | Webster Wells, Walter Wilson Hart - Algebra - 1913 - 300 pages
...by clearing of fractions. о а EXAMPLE. Since § = J, 2 • 9 should equal 3 • 6. Does it ? 190. If the product of two numbers is equal to the product of tгvo other numbers, one pair may be made the means and the other the extremes of a proportion. If... | |
 | George William Myers, George Edward Atwood - Algebra - 1916 - 362 pages
...the expressions obtained are not proportions. 286. Principle. // the product of two numbers equals the product of two other numbers, the factors of either product may be made the means and those of the other product the extremes of a proportion. Suppose a • d = b • c „ ac . ab 1 o... | |
 | George Hervey Hallett, Robert Franklin Anderson - Algebra - 1917 - 432 pages
...proportionals, prove that either extreme is equal to the product of the means divided by the other extreme. 20. If the product of two numbers is equal to the product of two other numbers, prove that a proportion may be formed by taking one pair of numbers for the extremes and the other... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1918 - 360 pages
...a proportion are raised to the same power, the results form a proportion. ij. ED 313. COROLLARY 1. If the product of two numbers is equal to the product of two other numbers, then the first two are the extremes of a proportion of which the other two are the means. Proof : If... | |
 | Herbert Ellsworth Slaught - 1918 - 344 pages
...a proportion are raised to the same power, the results form a proportion. QED • 313. COROLLARY 1. If the product of two numbers is equal to the product of two other numbers, then the first two are the extremes of a proportion of which the other two are the means. Proof : If... | |
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