 If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.  Elements of Algebra - Page 1851839 - 355 pagesFull view - About this book
 | James Morford Taylor - Algebra - 1889 - 340 pages
...a : b = b : c, then b2 = ac, or b = Va c. 192. Conversely, if the product of two quantities equals the product of two other quantities, two of them may...extremes and the other two the means of a proportion. If ad = cb, then by dividing both members by bd we obtain a : b = c : d . (i.) Inversion : If a : b... | |
 | 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. It follows,... | |
 | Edward Albert Bowser - Geometry - 1890 - 414 pages
...Proposition 2. 283. Conversely, if the product of two quantities be equal to the product of two others, two of them may be made the extremes, and the other two the means, of a proportion. Hyp. Let ad = be. To prove a : b = c : d. Proof. Dividing the given equation by bd, a _c b=~d' that... | |
 | 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 of two others, one pair may be made the extremes, and the other pair the means, of a proportion. Let ad =... | |
 | 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 two quantities,... | |
 | 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 two quantities,... | |
 | James Morford Taylor - Algebra - 1893 - 358 pages
...х2. 216. Conversely, if the product of t>vo numbers is equal to the product of two other numbers, two of them may be made the extremes and the other two the means of a proportion. For, let ad = bc. Divide by dc, a:c=b:d, or b : d = a : c. Or divide by а6, d : b = с : a, or с... | |
 | William Chauvenet - 1893 - 340 pages
...product. 6. Conversely, if the product of two numbers is equal to the product of two others, either two may be made the extremes, and the other two the means, of a proportion. For, if we have given ab' = a'b, then, dividing by bb', we obtain l = *,ora:b = a':b'. Corollary. The... | |
 | 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 of two others, one pair may be made the extremes, and the other pair the means, of a proportion. Let ad =... | |
 | Emerson Elbridge White - Algebra - 1896 - 418 pages
...numbers is equal to the product of two other numbers, the four numbers are proportionals; and any tim of them may be made the extremes, and the other two the means, of a proportion. Let ad. = be. Dividing by bd, — = — ; whence - = - ; ie, a:b — c:d. The equation ad = be, if... | |
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