...and mean ratio." For the segment BH is to the segment AH as AH is to the whole line AB; and in such a proportion the product of the extremes equals the product of the means, or in this instance the rectangle under AB and BH is equal to the square on AH, which is proposition...

...properties, the following are '' the most frequent application. i 41. Theorems respecting Proportion. Theorem 1. If four numbers are in proportion, the product of the extremes is equal to the product of the means, and, conversely, if the product of one pair of numbers be equal...

...extremities, are called the extremes ; the two others, placed in the middle, are called the means. In every proportion, the product of the extremes equals the product of the means. Be they the two equal ratios or the proportion — a _ c_ 1 ~ d' If we multiply by d the two terms...

...8 : 12 : : 2 : 3, where 8 and 3 are called the extreme, and 12 2 the mean terms. • 102. In every proportion, the product of the extremes equals the product of the means ; thus, if 8 : 12 : : 2 : 3, then 8X3 8 2 = 12 x 2 ; for if — - = - and both fractions be brought...

...compound and a simple ratio, or of two compound ratios ; as, 5:9) „ , 5:9) (5:2 537. Since in a simple proportion the product of the extremes equals the product of the means (see 532, 1.) ; and since a compound ratio is reduced to a simple one, by multiplying all the antecedents...

...if a : Ъ : : b : с : : с : d : : d : e, we have a continued proportion. 61. Prop. 1. — In any proportion the product of the extremes equals the product of the means. DEM. — If я : Ъ : : e : d then ad = be. For a : b : : с : d is the same as - = -, which l> d cleared...

...; which may be written 4 : 8 : : 5 : 10. These are called proportionals. SIMPLE PROPORTION. In any proportion the product of the extremes equals the product of the means, or the first and fourth terms multiplied equals the second and third multiplied together. 147 In the...

...2O da. JI for ( ) da. We have now to find the number of days in the Sec. cause. And since this is a proportion, the product of the extremes equals the product of the means, and we therefore can readily fill the blank ( ) by Rule I, or II. (281). PR OBLJSHTS. 1. If 6 men build...

...ratio. Thus if a : b : : b : c : : c : d : : d : e, we have a continued proportion. 65. Prop. 1. In a proportion the product of the extremes equals the product of the means. DEM. — If o : b : : c : d then ad = 6c. For a : 6 : : c : d is the same flt C as r = -a which cleared...

...read, 8 : 12 : : 2 : 3, where 8 and 3 are called the extreme, and 12 2 the mean terms. 102. In every proportion, the product of the extremes equals the product of the means ; thus, if 8 : 12 : : 2 : 3, then 8X3 8 2 = 12x2; for if - • = — and both fractions be brought...