 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.  A College Algebra - Page 107by James Morford Taylor - 1889 - 317 pagesFull view - About this book
 | Edward Brooks - Geometry - 1868 - 284 pages
...^; multiplying by B X D, we have, A X D = B X C. Therefore, if four quantities are, etc. THEOREM II. If the product of two quantities equals the product...two other quantities, two of them may be made the means, and two the extremes of a proportion. Suppose we have AXD — SXC; dividing by B X .A we have,... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...to the product of the extremes. PROPOSITION n. THEOREM. If the product of two quantities is equal to the product of two other quantities, two of them may be made the means, and the other two the extremes of a proportion. If we have, AD = BC, by changing the members... | |
 | Shelton Palmer Sanford - Algebra - 1879 - 348 pages
...From which we learn the important truth — viz. : If the product of any two quantities is equal to the product of two other quantities, two of them may...extremes, and the other two the means, of a proportion. Ex. 1. Convert ax = by into a proportion. Ans. a : b ::y : x. 2. Change bm = en into a proportion.... | |
 | Alfred Hix Welsh - Geometry - 1883 - 326 pages
...For (1) T — T by definition; and clearing of fractions, fl £ (2) ad=bc. Therefore, etc. THEOREM H. If the product of two quantities equals the. product...two other quantities, two of them may be made the means, and the other two the extremes of a proportion. Let (1) a x d = b x c; then will a : b :: c... | |
 | James Wallace MacDonald - Geometry - 1894 - 76 pages
...consequents are the same in both, the other terms are in proportion. Proposition III. A Theorem. 119. If the product of two quantities equals the product of two other quantities, either two may be made the means and the other two the extremes of a proportion. Proposition IV. A... | |
 | David Martin Sensenig - Algebra - 1889 - 388 pages
...extreme. Cor. 2. — Either mean equals the product of the extremes divided by the 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... | |
 | James Wallace MacDonald - Geometry - 1889 - 80 pages
...consequents are the same in both, the other terms are in proportion. Proposition III. A Theorem. 119. If the product of two quantities equals the product of two other quantities, either two may be made the means and . the other two the extremes of a proportion. Proposition IV.... | |
 | George Washington Hull - Algebra - 1895 - 358 pages
...means is equal to the product of the extremes. If a : b = с : d, By ART. 240, « = 2 . bd THEOREM II. If the product of two quantities equals the product of two other qiiantities, two may be made the means and two the extremes. Let ad = be. j ad _ be d _ с ' bd bd'... | |
 | George Washington Hull - Geometry - 1897 - 408 pages
...extremes. If a:b = c:d, ba Clearing of fractions, ad — be. QED !-!• sm PROPOSITION II. THEOREM. 120. // the product of two quantities equals the product of two other quantities, two may be made the means and two the extremes. Let ad = be. Dividing by bd, gg. Whence a: b = c: d. <j.... | |
 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...bd Multiplying both sides by 6 xd, We have axd = bx c. Therefore, etc. PROPOSITION II. — THEOREM. If the product of two quantities equals the product of two other quantities, either two quantities may be made the extremes, and the other two the means of a proportion. Suppose... | |
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