 If the product of two numbers is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means. For, if ad = be, then, dividing by bd, ad_ be bd~bd' ac or j- — -  A College Algebra - Page 155by George Albert Wentworth - 1888 - 494 pagesFull view - About this book
 | Walter Burton Ford, Charles Ammerman - Geometry, Plane - 1913 - 376 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... | |
 | 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... | |
 | 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... | |
 | Elmer Adelbert Lyman, Albertus Darnell - Algebra - 1917 - 520 pages
...86 84 3 Can a proportion be made from the numbers involved in the equation 4 • 10 = 5 • 8 ? III. If the product of two numbers is equal to the product of two other numbers, the factors of either product may be made the means and the factors of the other product... | |
 | 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... | |
 | 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.... | |
 | 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.... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 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... | |
 | Raleigh Schorling, William David Reeve - Mathematics - 1919 - 520 pages
...(c). o « 370. Theorem. The preceding discussion illustrates the use of the theorem which says that if the product of two numbers is equal to the product of two other numbers, either pair may be made the means and the other pair the extremes of a proportion. EXERCISES... | |
 | Matilda Auerbach, Charles Burton Walsh - Geometry, Plane - 1920 - 408 pages
...theorem which will express the mean proportional as a function of the other terms of the proportion. 401. If the product of two numbers is equal to the product of two other numbers, the factors of either product may be made the means of a proportion of which the factors... | |
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