 If the product of two quantities is equal to the product of two others, one pair may be made the extremes, and the other pair the means, of a proportion.  Elementary Algebra - Page 318by Frederick Howland Somerville - 1908 - 407 pagesFull view - About this book
 | Robert Louis Short, William Harris Elson - Mathematics - 1910 - 202 pages
...easily proved by clearing the equation (proportion) , a- c b~d' of fractions. Whence, ad = be. 2. If the product of two numbers is equal to the product of two other numbers, a proportion may be formed., making one product the means and the other product the extremes. Thus,... | |
 | William James Milne - Algebra - 1911 - 378 pages
...proportional to a, b, and c. Find a fourth proportional to ^, ^, and -£. 394. PRINCIPLE 3. — Tjf the product of two numbers is equal to the product of two other numbers, one pair of them may be made the extremes and the other pair the means of a proportion. For, given ad — be.... | |
 | Webster Wells, Walter Wilson Hart - Algebra - 1912 - 344 pages
...clearing of fractions. bd EXAMPLE. Since f = f, 2 • 9 should equal 3 • 6. Does it ? 218. If the product of two numbers is equal to the product of two other numbers, one pair may be made the means and the othcr the. extremes of a proportion. If mn = xy, then — = - • xn Prove this by dividing... | |
 | Clara Avis Hart, Daniel D. Feldman - Geometry - 1912 - 504 pages
...Ifx:y = b:c,iadx:y = b:cda true proportion t PBOPOSITION II. THEOREM (Converse of Prop. I) 393 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. Given ad = be. To... | |
 | Frederick Howland Somerville - Algebra - 1913 - 458 pages
...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...proportion. In like manner we may obtain a proportion, a : c = b : d, etc. 375. Given a:b = c:d. Then b: a = d:e. Proof: ? = °. Then, 1 .,- ? = 1 -s-5. bd... | |
 | Webster Wells, Walter Wilson Hart - Algebra - 1913 - 360 pages
...clearing of fractions. bd EXAMPLB. Since f = f , 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 = xn, then — = ". xn Prove this by dividing... | |
 | Walter Burton Ford, Earle Raymond Hedrick - Geometry, Modern - 1913 - 272 pages
...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 - 1913 - 490 pages
...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... | |
 | Walter Burton Ford, Charles Ammerman - Geometry, Solid - 1913 - 176 pages
...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.... | |
 | Walter Burton Ford, Charles Ammerman - Geometry, Plane - 1913 - 378 pages
...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.... | |
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