...multiplied by the third term : ji 1 fi for as 7 : 8 : : 14 : 16, therefore - = — = 8x14=16x7, or the product of the means is equal to the product of the extremes. Hence if any three numbers be given, a fourth proportional to them may be found, such as, this 4th...

...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. (п). Suppose we have the equation ad=bc. If we divide both members by b and d, we have — = —,...

...to the quotient obtained by dividing the product of the extremes by the other mean. (5.) 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 problem is called...

...to the quotient obtained by dividing the product of the extremes by the other mean. (b.) 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...

...obtained, by dividing the fourth term by the third, we can readily deduce the following PROPOSITIONS. 1. The product of the means is equal to the product of the extremes. Therefore, 2. If the product of the means be divided by one extreme, the quotient will be the other...

...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,...

...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,...

...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...

...or, - = - • . . (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....

...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...