| Joseph Ray - Algebra - 1866 - 250 pages
...in proportion? Example. What is the second term called? The third ? 244. Proposition I. — In every proportion, the product of the means is equal to the product of the extremes. Let a : 6 : : c : d. Then, since this is a true proportion, we must have bd Clearing of fractions,... | |
| Robert Robinson (inspector of national sch, Ireland.) - 1867 - 384 pages
...leads to the least misconception of what is really stated, and forms the best test of its accuracy. The product of the means is equal to the product of the extremes. Those who know that the expressions 3 : 4 : : 6 : 8 and are equivalent, and who understand some little... | |
| Joseph Ray - Algebra - 1867 - 240 pages
...100—3z= B's gain, and 40z — 200= A's stock. Therefore, 4te— 200 : 20a; : : 3x : 100—3z. Since the product of the means is equal to the product of the extremes, 60z2=(40z— 200)(100— 3«). Reducing, z2— J{°x=— i°o°. Whence, z=20; hence, &c=60= A's gain,... | |
| John Fair Stoddard - Arithmetic - 1888 - 480 pages
...3 4 6 becomes 5=5. multiplying each member by 2 and 3, we jy *_) have 4x3=6x2. Hence, 382. In every proportion, the product of the means is equal to the product of the extremes. 1. Either extreme is equal to the product of the means divided by the other extreme. 2. Either mean... | |
| John Fair Stoddard - Arithmetic - 1868 - 428 pages
...: 3 4 6 becomes s=o> multiplying each member by 2 and 3, we 2i o have 4x3=6x2. Hence, 382. In every proportion, the product of the means is equal to the product of the extremes. 1. Either extreme is equal to the product of the means divided by the other extreme. 2. Either mean... | |
| William Frothingham Bradbury - Algebra - 1868 - 270 pages
...fourth terms of a proportion are called the extremes, and the second and third the means. 106. In a proportion the product of the means is equal to the product of the extremes. Let ie a : b = c : d Clearing of fractions, ad = be A proportion is an equation ; and making the product... | |
| Joseph Ray - Arithmetic - 1857 - 358 pages
...the proportion 2 : 3 : : 4 : 6, 2 and 6 are the extremes, and 3 and 4 the means. ART. 200. In every proportion, the product of the means is equal to the product of tJie extremes. ILLUSTRATIONS. — If we have 3 : 4 : : 6 : 8, the ratios of each couplet being equal... | |
| Henry Bartlett Maglathlin - Arithmetic - 1869 - 332 pages
...between the other two. Thus, In 12 : 6 :: 6 : 3, 6 is a mean proportional. TOIIVCIIVLES. 328. 1. In every proportion the product of the means is equal to the product of the extremes. For, in the proportion 6 : 3 : : 4 : 2, since the ratios are equal (Art. 326), WB have $ = £. Now,... | |
| James Smith - Mathematics - 1869 - 492 pages
...or proportion, A : B : : B : C, when A denotes * ^* and B denotes I ; then, -8 : I : : I : -125, and the product of the means is equal to the product of the extremes. Now, if the radius of a circle = -125, then, (6 x -125) = 75 = the perimeter of a regular inscribed... | |
| James Smith - Circle-squaring - 1869 - 459 pages
...: B : C. When A denotes ^-^ and B denotes i, then, C = 1-28 : that is, 78125 : i : : I : 1-28, and the product of the means is equal to the product of the extremes. Hence : -~I*±*A and —-^ are equivalent ratios, and it follows, that the product of any number multiplied... | |
| |