 | William Guy Peck - Conic sections - 1876 - 412 pages
...then have the square of the mean equal to the product of the extremes. PROPOSITION III. THEOREM. 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 other two the extremes of a proportion. Assume the equation,... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...proposition, A x C=B x B, which is equal to B'. PROPOSITION ii. THEOREM. (Converse of Prop. I.) If the product of two quantities is equal to the product of two others, the one pair may be made the extremes, and the other t/ie means of a proportion. Thus, suppose... | |
 | William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...we have, £ = £, or, A:B = C:DL, £ = 5, or, A:C=B:DIL, ~ = ~, or, B : A = D : C III. CA Hence, if the product of two quantities is equal to the product of two other quantities, one pair of factors may be made the extremes, and the other pair the means, of a proportion. EXERCISE... | |
 | James Bates Thomson - Algebra - 1878 - 322 pages
...By Art. 363, | = * Clearing of fractions, at = 6s. Again, 9:6:: 6-4, and 4 xg = 62. THEOREM III. If the product of two quantities is equal to the product of two others, the four quantities are proportional j the factors of either product being taken for the extremes,... | |
 | Shelton Palmer Sanford - Algebra - 1879 - 348 pages
...I'd' or, a : b : : c : d. 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 be made the extremes, and the other two the means, of a proportion. Ex. 1. Convert ax = by into a proportion. Ans.... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...equal to the product of the meaiis ia merely clearing the equation of fractions. THEOREM II. 14i If the product of two quantities is equal to the product of two others, the factors of either product may be made the extremes, and the factors of the other the means... | |
 | William James Milne - Algebra - 1881 - 360 pages
...What does ad, the first member of the equation, form in the proportion? What be? PRINCIPLE 3. — If the product of two quantities is equal to the product of two otlier quantities, two of them may be made the extremes, and the other two the means, of a proportion.... | |
 | Alfred Hix Welsh - Geometry - 1883 - 326 pages
...clearing of fractions, fl £ (2) ad=bc. Therefore, etc. THEOREM H. If the product of two quantities equals the. product of two other quantities, two of them...means, and the other two the extremes of a proportion. Let (1) a x d = b x c; then will a : b :: c : d. For, (1) + bd = (2)-=°-; .: by definition, a : b... | |
 | National cyclopaedia - 1884 - 670 pages
...term) can be obtained as easily ; for be . ad , ad a=— ,6 = — , and c = — . dcb Conversely, if the product of two quantities is equal to the product of two others, these four are proportionals ; example, 4 times 6 = 3 times 8 ; whence we see that 3 is to... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...a : b = b : c. Then by §242, 62=ac. Whence, b = Vac. PROPOSITION II. THEOREM. 244. CONVERSELY, 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 =... | |
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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. 
