 | James Smith - 1870 - 634 σελίδες
...63 agreed. If I : 2 : : 2 : 4, the converse of this proportional holds good ; 4 : 2 : : 2 : I, and the product of the means is equal to the product of the extremes : mxn = « xm, whatever values we may put upon m and «, and in either way, works out to the same result... | |
 | Josiah Rhinehart Sypher - 1872 - 340 σελίδες
...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 - 1872 - 330 σελίδες
...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 - 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... | |
 | Charles Davies - 1872 - 464 σελίδες
...the other is diminished. In this case, their product is a fixed quantity, as xy = m. PROPOSITION I THEOREM. If four quantities are in proportion, the product of the means will be equal to the product of the extremes. Assume the proportion, A : B : : C : D; whence, -j =... | |
 | Henry Bartlett Maglathlin - 1873 - 362 σελίδες
...repeated 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
.... . (1) п. С clearing of fractions, we have, bc — ad; (2) hence, the following principles: 1°. If four quantities are in proportion, the product...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
...right 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 Frothingham Bradbury - 1877 - 280 σελίδες
...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... | |
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In any proportion, the product of the means is equal to the product of the extremes. 
