| Euclid - Geometry - 1872 - 261 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... | |
| J.R. Sypher - 1872
...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... | |
| Josiah Rhinehart Sypher - Teaching - 1872 - 327 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 - 336 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 - 331 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
...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 - 366 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... | |
| Stoddard A. Felter, Samuel Ashbel Farrand - Arithmetic - 1877 - 471 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... | |
| William Guy Peck - Arithmetic - 1877 - 341 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°.... | |
| George Albert Wentworth - Geometry - 1877 - 398 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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