| William Guy Peck - Algebra - 1875 - 348 pages
...fractions, we have, bc — ad; (2) hence, 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 cq, we have, - = - ; or, a : b : : c : d ; hence, ac... | |
| Education Department,London - 1876 - 1010 pages
...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
...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... | |
| 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... | |
| 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... | |
| 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... | |
| William Guy Peck - Arithmetic - 1877 - 428 pages
...have equal denominators ; hence, their numerators are equal, that is, 5 x 8 = 2 x 20 ; in this case **the product of the means is equal to the product of the extremes.** But we can reason in like manner on any proportion ; hence, we have the following principle : 1°.... | |
| Stoddard A. Felter, Samuel Ashbel Farrand - Arithmetic - 1877 - 496 pages
...numerator by the other denominator, the products are equal. Hence, iu every proportion, PRINCIPLE I. — **The product of the means is equal to the product of the extremes.** If multiplying either the means or extremes together produces the same product, dividing this product... | |
| George Albert Wentworth - Geometry - 1877 - 416 pages
...circumference to the diameter is a mean proportional between the segments of the diameter). aXb, §259 (flu **product of the means is equal to the product of the extremes).** QEF 355. COROLLARY 1. A square may be constructed eqxiivalent to a triangle, by taking for its side... | |
| Edwin Pliny Seaver - Arithmetic - 1878 - 380 pages
...preceding illustration may be derived the following principles : 1. When four general numbers form a **proportion, the product of the means is equal to the product of the extremes.** 2. A missing extreme may be found by dividing the product of the means by the given extreme. 3. A missing... | |
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