| Joseph Ray - 1867 - 240 σελίδες
...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,... | |
| William Frothingham Bradbury - 1868 - 264 σελίδες
...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 a : b = c : d ac l = d Clearing of fractions, ad = be A proportion is an equation ; and making... | |
| John Fair Stoddard - 1868 - 428 σελίδες
...denoting the equality of two ratios, either, or both, being compound. As in Simple Proportion, 386, The product of the means is equal to the product of the extremes. Hence, 1. A factor in either extreme equals the product of the means divided by the product of the... | |
| John Fair Stoddard - 1888 - 480 σελίδες
...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... | |
| James Smith - 1869 - 459 σελίδες
...: 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... | |
| James Smith - 1869 - 490 σελίδες
...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... | |
| Henry Bartlett Maglathlin - 1869 - 332 σελίδες
...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 - 1870 - 634 σελίδες
...63 agreed. If I : 2 : : 2 : 4, the converse of this proportional holds good ; 4 : 2 : : 2 : I, and the product of the means is equal to the product of the extremes : mxn = « xm, whatever values we may put upon m and «, and in either way, works out to the same result... | |
| Josiah Rhinehart Sypher - 1872 - 340 σελίδες
...and second terms of a proportion must be the same as the relation between the third and fourth terms. The product of the means is equal to the product of the extremes. A missing extreme may be found by dividing the product of the means by the given extreme. A mean may... | |
| James Smith - 1872 - 330 σελίδες
...the area of a circumscribing square to the latter = 16. Hence: r28 : 1-6384 :: 12-5 : 16 ; therefore, the product of the means is equal to the product of the extremes, and proves that the areas of circles are to each other as the areas of their circumscribing squares.... | |
| |