| 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.... | |
| 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
...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
...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
...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 - 412 pages
...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) ac Multiplying both members of (1) by... | |
| George Albert Wentworth - Geometry - 1877 - 426 pages
...the diameter is a mean proportional between the segments of the diameter). Then SС> = MС X СN, § 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 given... | |
| George Albert Wentworth - Geometry - 1877 - 416 pages
...circumference to the diameter is a mean proportional between the segments of the diameter). N0 = a Xb, §259 (the product of the means is equal to the product of the extremes). a. EF 355. COROLLARY 1. A square may be constructed equivalent to a triangle, by taking for its side... | |
| William Frothingham Bradbury - Algebra - 1877 - 280 pages
...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
...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 a mean... | |
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