 | Engineering - 1902 - 514 pages
...of arithmetic. In our grandfathers' arithmetics, it was called "The rule of three." 55. Rule. — hi any proportion, the product of the extremes equals...means. Thus, in the proportion, 17 : 51 = 14 : 42. 17 X 42 = 51 X 14, since both products equal 714. 56. Rule. — The prodiict of t lie extremes divided by... | |
 | Leonard Eugene Dickson - Algebra - 1902 - 242 pages
...read я is to и as с is to d. The terms a and d are called the extremes, /< and с the means. In any proportion the product of the extremes equals the product of the means. Thus, from a : b = с : d we get Inversely, if ad = be, then a, b, c, d are in proportion. If three quantities... | |
 | International Correspondence Schools - Arithmetic - 1902 - 794 pages
...called " The rule of three." 320. Rule I. — In any proportion, the product of the extremes equals t/ic product of the means. Thus, in the proportion, 17 : 51 = 14 : 42. 17 x 42 = 51 X 14, since both products equal 714. 321. Rule II. — The product of tJie extremes divided... | |
 | Louis Parker Jocelyn - Algebra - 1902 - 460 pages
...da + о c + a и — aa — a b — ad — c. or b + ad + e 302. Prop. 1. When four numbers are in proportion, the product of the extremes equals the product of the means. Т» Т ia (' Dem. Let - = — • о а Then ad = be, by clearing of fractions. But ad is the product... | |
 | David Martin Sensenig, Robert Franklin Anderson - Arithmetic - 1902 - 376 pages
...proportion is in its simplest form when its ratios are in the simplest form. 334. PRIN. In a numerical proportion the product of the extremes equals the product of the means. Proof. Given x : 5 = 7 : 9, to prove that 9 X x = 5 X 7. x : 5 = 7 : 9 may be written f = | [§ 329,... | |
 | John Marvin Colaw - Algebra - 1903 - 444 pages
...transformation and solution of equations apply in dealing with proportions. PRINCIPLES OF PROPORTION 405. In any proportion the product of the extremes equals the product of the means. For, if a: b = c: d, a_c bd' It follows from the preceding that in the proportion a : b = b : c, b=-... | |
 | John Alton Avery - Geometry, Modern - 1903 - 136 pages
...the following propositions, the fractional form of the ratio is referred to. 144. Proposition I. In a proportion the product of the extremes equals the product of the means. SUG. Multiply each ratio by product of consequents. 145. Prop. II. If the product of two quantities... | |
 | International Correspondence Schools - Arithmetic - 1904 - 656 pages
...of arithmetic. In our grandfathers' arithmetics, it was called "The rule of three." 69. Rule. — In any proportion, the product of the extremes equals...means. Thus, in the proportion, 17 : 51 = 14 : 42 17 X 42 = 51 X 14, since both products equal 714. 70. Rule. — The product of the extremes divided by either... | |
 | Fletcher Durell - Geometry - 1911 - 553 pages
...proportion a : b = c : d. To prove a . c = b : d. Proof. a : b = c : d. Hyp. .-. ad^~bc, Art. 302. (in any proportion, the product of the extremes equals the product of the means) . Writing1 a and d as the extremes, and c and 5 as the means of a proportion, a : c— 1) : d, Art.... | |
 | Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...the proportion a : 6 = 6 : c. To prove b = V/rac~. Proof. a :b=b : c. Hyp. .-. 62 = ac, Art. 302. {in any proportion, the product of the extremes equals the product of the means). QED Ex. 1. Find the fourth proportional to 2, 3 and 6; also to 3, i, f. Ex. 2. Find the mean proportional... | |
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In any proportion, the product of the extremes equals the product of the means. Thus, in the proportion, 17 : 51 = 14 : 42. 
