| 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... | |
| 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... | |
| Henry Bartlett Maglathlin - Arithmetic - 1873 - 362 pages
...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,... | |
| William Guy Peck - Algebra - 1875 - 348 pages
.... (1) clearing of fractions, we have, ffc thence, the following principles: 1°. If four quantities **are in proportion, the product of the means is equal to the product of the extremes.** Conversely, if we divide both members of (2) by ca, we have, - = -; or, a : b :: c : d; hence, ac If... | |
| Education Department,London - 1876 - 1010 pages
...the angle at A is a right angle : find the area. SECTION X. 1. Define ratio and proportion. Shew that **when four numbers are in proportion, the product of...the means is equal to the product of the extremes.** 3. State as precisely as possible your view« as to the value of Mental Arithmetic simply asan Educational... | |
| William Guy Peck - Conic sections - 1876 - 376 pages
...consequent, the proportion is said to be transformed by division. PROPOSITION II. THEOREM. If four quantities **are in proportion, the product of the means is equal to the product of the extremes.** Assume the proportion, a : b :: c : d, whence - = - ; . . . (1) Multiplying both members of (1) by... | |
| William Frothingham Bradbury - Algebra - 1877 - 280 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 a : b = с : d a с 6 = 5 Clearing of fractions, ad^bc A proportion is an equation ; and making... | |
| Samuel Mecutchen, George Mornton Sayre - Arithmetic - 1877 - 200 pages
...last terms of a proportion are called the Extremes, and the second and third terms the Means. In any **proportion the product of the means is equal to the product of the extremes.** Thus, in the proportion 4 : 8 :: 12 : 24, 8x 12 = 4 x 24. ORAL EXERCISES. 1. If 2 pounds of butter... | |
| George Albert Wentworth - Geometry - 1877 - 416 pages
...the diameter is a mem proportional between the segments of the diameter). Then tiCl = MCXCN, §259 **(the product of the means is equal to the product of the extremes).** QEF GEOMETRY. BOOK IV. PROPOSITION XXVI. PROBLEM. 359. To construct a parallelogram equivalent to a... | |
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