 | Euclid - 1872 - 284 σελίδες
...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 - 1872 - 336 σελίδες
...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... | |
 | Henry Bartlett Maglathlin - 1873 - 362 σελίδες
...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 - 1875 - 348 σελίδες
...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 σελίδες
...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 - 1876 - 412 σελίδες
...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 - 1877 - 416 σελίδες
...mean proportional between the segments of the diameter). = MNX NO = aX b, §259 (the product oftlie means is equal to the product of the extremes). QEF...taking for its side a mean proportional between the hase and one-half the altitude of the triangle. 356. COR. 2. A square may bo constructed equivalent... | |
 | George Albert Wentworth - 1877 - 416 σελίδες
...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...QEF 355. COROLLARY 1. A square may be constructed eqxiivalent to a triangle, by taking for its side a mean proportional between the base and one-half... | |
 | George Albert Wentworth - 1877 - 426 σελίδες
...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 - 1877 - 416 σελίδες
...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... | |
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In any proportion, the product of the means is equal to the product of the extremes. 
