| Henry Bartlett Maglathlin - Arithmetic - 1869 - 332 pages
...repeated 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 - 1869 - 490 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... | |
| James Smith - 1870 - 634 pages
...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... | |
| Joseph Ray - Algebra - 1866 - 420 pages
...other as 6 to 7? Let 3a:= the first, and 5x= the second number. Then, 3z-|-9 : 5.r+9 : : 6 : 7. But **in every proportion, the product of the means is equal to the product of the extremes.** (RAT'S ARTTH., 3d Book, Art. 200.) Hence, 6(5a;+9)=7(3a;+9). From which the answer is readily found.... | |
| Josiah Rhinehart Sypher - Teaching - 1872 - 340 pages
...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... | |
| Josiah Rhinehart Sypher - History - 1872 - 336 pages
...second terms of a proportion must be the same as the relation between the third a^id 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 - Circle-squaring - 1872 - 330 pages
...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.... | |
| Euclid - Geometry - 1872 - 284 pages
...dividing the antecedent by the consequent is called the ratio. If four quantities are proportional, **the product of the means is equal to the product of the extremes;** in the proportion a : b : : c : d, a and d are the extremes, b and c the means. Wherefore, in order... | |
| Henry Bartlett Maglathlin - Arithmetic - 1873 - 362 pages
...a term repeated between the other two. Thus, In 12 : 6 :: 6 : 3, 6 is a mean proportional. 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), we have f = -J- Now,... | |
| |