 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.  Plane and Solid Geometry - Page 133by Walter Burton Ford, Charles Ammerman - 1913 - 321 pagesFull view - About this book
 | Webster Wells, Walter Wilson Hart - Geometry, Plane - 1915 - 330 pages
...proportion and y from the second. EXAMPLE. — If - = - and - = -, then x should equal y. 3 xoy 252. If the product of two numbers is equal to the product of two other numbers, one pair may be made the means of a proportion having the other pair as the extremes. T. ,, in y If... | |
 | Webster Wells, Walter Wilson Hart - Geometry - 1916 - 490 pages
...proportion and y from the second. EXAMPLE. — If - = - and - = -. then x should equal y. 3 x 3 y 252. If the product of two numbers is equal to the product of two other numbers, one pair may be made the means of a proportion having the other pair as the extremes. If mn =xy, then... | |
 | Jacob William Albert Young, Lambert Lincoln Jackson - Geometry, Plane - 1916 - 328 pages
...2 x and compare their <e~2' ' y — 3~y' values. 12. Show that if the product of two numbers equals the product of two other numbers, either 'pair may be made the means and the other the extremes of a proportion. Write each of the following as proportions in two different... | |
 | 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... | |
 | 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 the extremes... | |
 | 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 mn —pq. To prove... | |
 | 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... | |
 | 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... | |
 | 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...two other numbers, either pair may be made the means and the other pair the extremes of a proportion. EXERCISES 1. Start with the equation ad = be and obtain... | |
 | Walter Burton Ford, Charles Ammerman - Algebra - 1920 - 334 pages
...c : d, show that no number x can be found such that 102. Second Fundamental Theorem. THEOREM B. // the product of two numbers is equal to the product...in which the other two are taken as the extremes. PROOF. Suppose mn = xy. Dividing both members by nx gives m/x = y/n, orm:x = y:n, which is one of the... | |
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