 | Joseph Ray - Algebra - 1857 - 408 pages
...numo ber, and 5x for the second, which fulfills the first condition. Then, 3a:+9 : 5x+9 : : 6 : 7. But in every proportion, the product of the means is equal to the product of the extremes. (Arith. Part 3rd, Art. 209.) Hence, 6(5a:+ff)=7(3z+9). 30a+54=21 x+63, 30a:—21a;=63—54, 9*=9, x=l,... | |
 | Dana Pond Colburn - 1858 - 288 pages
...to the quotient obtained by dividing the product of the extremes by the other mean. (k.) Hence, in a proportion, the product of the means is equal to the product of the extremes. 105. Problems in Proportion. NOTE.— These problems may be solved by analysis instead of proportion,... | |
 | Education - 1863 - 746 pages
...solution of problems. Some might prefer to show how any missing term may be found, by first showing that the product of the means is equal to the product of the extremes. In that case, such a method as the following might be adopted.] T. Let us now compare the product of... | |
 | Robert Johnston (F.R.G.S.) - 1860 - 188 pages
...are called means (t) and 10) ; the first and fourth, extremes (15 and 6). When four numbers form a proportion, The product of the means is equal to the product of the extremes. Thus, 6 : 3 : : 8 : 4 ; here, 6X4, the extremes, =8X3, the means, = 24. 156. If the product of any... | |
 | Dana Pond Colburn - Arithmetic - 1860 - 388 pages
...to the quotient obtained by dividing the product of the extremes by the oiher mean. (6.) Hence, in a proportion — The product of the means is equal to the product of the extremes. 161. Practical Problems. (a.) The forming of a proportion from the conditions of a probiem is called... | |
 | Charles Davies - Algebra - 1860 - 332 pages
...- • . . (1.) ac Clearing of fractions, we have, bc = ad (2.) Hence, 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 ca, we shall have, - — - ; or, a : b : : c : d.... | |
 | James Bates Thomson - Arithmetic - 1860 - 440 pages
...the work is right. (Art. 500.) Demtrmtral'ian. -If four numbers are proportional, we have seen that the product of the means is equal to the product of the extremes ; (Art. 498 ;) therefore the priduct of the second and thin/ terms must be equal to that of the first... | |
 | Thomas Sherwin - 1862 - 252 pages
...6 d b and d, we have ad=bc. But a and d are the extremes, and 6 and c are the means. Hence, In any proportion, the product of the means is equal to the product of the extremes. (n). Suppose we have the equation ad—be. If we divide both members by 6 and d, we have — = —,... | |
 | James Bates Thomson - Arithmetic - 1862 - 436 pages
...work is right. (Art. 500.) Demmatratian. -If four numbers are proportional, we have seen that th« product of the means is equal to the product of the extremes ; (Art. 498 ;} therefore the prxiict of the second and third terms must be equal to that of the first... | |
 | Robert Johnston (F.R.G.S.) - 1863 - 254 pages
...proportion are called means (9 and 10); the first and fourth extremes (15 and 6). When four numbers form a proportion, the product of the means is equal to the product of the extremes. Thus, 6 : 3 : : 8 : 4 ; here, 6x4, the extremes, = 8x3, the means, = 24. If the product of any two... | |
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In any proportion, the product of the means is equal to the product of the extremes. 
