 | Henry Bartlett Maglathlin - 1869 - 332 σελίδες
...repeated between the other two. Thus, In 12 : 6 :: 6 : 3, 6 is a mean proportional. TOIIVCIIVLES. 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), WB have $ = £. Now,... | |
 | James Smith - 1869 - 492 σελίδες
...or proportion, A : B : : B : C, when A denotes * ^* and B denotes I ; then, -8 : I : : I : -125, and the product of the means is equal to the product of the extremes. Now, if the radius of a circle = -125, then, (6 x -125) = 75 = the perimeter of a regular inscribed... | |
 | James Smith - 1869 - 459 σελίδες
...: B : C. When A denotes ^-^ and B denotes i, then, C = 1-28 : that is, 78125 : i : : I : 1-28, and the product of the means is equal to the product of the extremes. Hence : -~I*±*A and —-^ are equivalent ratios, and it follows, that the product of any number multiplied... | |
 | 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... | |
 | Joseph Ray - 1866 - 420 σελίδες
...other as 6 to 7? Let 3a:= the first, and 5x= the second number. Then, 3z-|-9 : 5.r+9 : : 6 : 7. But in every proportion, the product of the means is equal to the product of the extremes. (RAT'S ARTTH., 3d Book, Art. 200.) Hence, 6(5a;+9)=7(3a;+9). From which the answer is readily found.... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | Henry Bartlett Maglathlin - 1873 - 362 σελίδες
...a term 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,... | |
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In any proportion, the product of the means is equal to the product of the extremes. 
