 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. Let ad = ос.  Plane and Solid Geometry - Page 79by James Howard Gore - 1898 - 210 pagesFull view - About this book
 | David Martin Sensenig - Algebra - 1889 - 388 pages
...other mean. II. If the product of two quantities equals the product of two other quantities, either pair may be made the extremes, and the other pair the means, of a proportion. Given mX n = pX Ч (A) Prove, 1. m :p: :q: n 5 • p : m : : n •9 2. m :q: :p: n в • p : n: :... | |
 | Charles Davies - Algebra - 1889 - 330 pages
...Conversely, if we divide both members of ( 2 ) by ca, we shall have, - . = - ; or, a : b : : c : d. Hence, ac If the product of two quantities is equal to the product, of two other quantities, the first two may be made the means, and the second two the extremes, of a proportion.... | |
 | Webster Wells - Algebra - 1890 - 560 pages
...mean is equal to the product of the extremes divided by the other mean. 384. (Converse of Art. 381.) If the product of two quantities is equal to the product...the means, of a proportion. Let ad = be. Dividing bjMi M=S'c"HWhence, a : b = c : d. In like manner we may prove that a : c = 6 : d, c:d = a:b, etc.... | |
 | Webster Wells - Algebra - 1890 - 604 pages
...mean is equal to the product of the extremes divided by the other mean. 384. (Converse of Art. 381.) If the product of two quantities is equal to the product...the other pair the means, of a proportion. Let ad = 6e. Dividing by H ad=b± orа e. bd bd' bd Whence, a : b = с : d. In like manner we may prove that... | |
 | Seth Thayer Stewart - Geometry, Modern - 1891 - 422 pages
...are in proportion, they are in proportion by division. SECTION II.— EQUAL PRODUCTS. 297. PROP. VI. If the product of two quantities is equal to the product of two other quantities, the two quantities that form either product may be made the extremes, and the other... | |
 | Seth Thayer Stewart - Geometry - 1891 - 428 pages
...the antecedent or the consequent. SECTION II.— EQUAL PRODUCTS. PROPOSITION VI. 31§. Theorem : // the product of two quantities is equal to the product of two other quantities, the two quantities that form either product may be made the extremes, and the other... | |
 | Webster Wells - Geometry - 1894 - 256 pages
...from (1), b 2 = ac. (§ 231.) Whence, b — Vac. PROPOSITION II. THEOREM. 233. (Converse of Prop. I.) If the product of two quantities is equal to the product...other pair the means, of a proportion. Let ad = be. To prove a: b = c: d. Dividing both members of the given equation by bd, ad be bd~bd' 1-1That is, a:b... | |
 | Webster Wells - Geometry - 1894 - 398 pages
...from (1), b 2 = ac. (§ 231.) Whence, b = Vac. PROPOSITION II. THEOREM. 233. (Converse of Prop. I.) If the product of two quantities is equal to the product...the other pair the means, of a proportion. Let ad = bc. To prove a : b = c:d. Dividing both members of the given equation by bd, ad be bd~bd' 1-3That... | |
 | Webster Wells - Geometry - 1894 - 400 pages
...from (1), &2 = ac. (§231.) Whence, b = -Vac. PROPOSITION II. THEOREM. 233. (Converse of Prop. I.) Jf the product of two quantities is equal to the product...other pair the means, of a proportion. Let ad = be. To prove a:b = c:d. Dividing both members of the given equation by bd, ad be bd~bd' 1-3That is, a:b... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...' 251. THEOREM. Conversely, if the product of two numbers equals the product of two others, either pair may be made the extremes and the other pair the means of a proportion. GIVEN ad=tc. (2) To PROVE - = -. (1) bd Divide both sides of (2) by bd, the product of the denominators... | |
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