 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.  Advanced Algebra - Page 142by Arthur Schultze - 1905 - 562 pagesFull view - About this book
 | William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 286 pages
...PROPOSITION II. THEOREM. 328. If the product of two quantities is equal to the product of two others, either pair may be made the means and the other pair the extremes of a proportion. Given ad = be. To prove a:b = c:d. Proof. Dividing both members of the given equation by bd, a—c... | |
 | Herbert Edwin Hawkes, William Arthur Luby, Frank Charles Touton - Algebra - 1910 - 374 pages
...Therefore, If the product of any two numbers (ps) equals the product of two other numbers (qr), one pair may be made the means and the other pair the extremes of a proportion. If - = - > then from (1) and (2), - = -• Here - = - is said CL С to be obtained from - = - by alternation.... | |
 | Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 328 pages
...J£xiy = b:c, isdx:y = b :cd a, true proportionf PROPOSITION II. THEOREM (Converse of Prop. I) 393 If the product of two numbers is equal to the product...means and the other pair the extremes of a proportion. Given ad = be. To prove a: 5 = c: d. ARGUMissrr REASONS 1 ad = be. 1. By hyp. 2. bd = bd. 2. By iden.... | |
 | Herbert Edwin Hawkes, William Arthur Luby, Frank Charles Touton - Algebra - 1911 - 288 pages
...Therefore, If the product of any two numbers (ps) equals the pvoduct of two other numbers (qr), one pair may be made the means and the other pair the extremes of a proportion. If T = - > then from (1) and (2), - = -• Here - = - is said bd ^ ' ^ ' с d cd f* f> to be obtained... | |
 | William James Milne - Algebra - 1911 - 332 pages
...fourth proportional to a, b, and c. Find a fourth proportional to ¿, |, and \. 394. PRINCIPLE 3. — If 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... | |
 | 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... | |
 | Clara Avis Hart, Daniel D. Feldman - Geometry - 1912 - 504 pages
...616. 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...means and the other pair the extremes of a proportion. Given ad = be. To prove a:b — c:d. AROUMBVT 1 ad— be. 2. bd = bd. 3. A - = -; ie a:b = c:d. QED... | |
 | Webster Wells, Walter Wilson Hart - Algebra - 1912 - 344 pages
...bc, by 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 — =... | |
 | 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...two other numbers, either pair may be made the means of a proportion in which the other two are taken as the extremes. Given ad = be, to prove that a/b... | |
 | 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...two other numbers, either pair may be made the means of a proportion in which the other two are taken as the extremes. Theorem C. If four quantities are... | |
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