 | 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... | |
 | 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
...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... | |
 | 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... | |
 | 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... | |
 | 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
...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 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... | |
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In any proportion, the product of the means is equal to the product of the extremes. 
