 | Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...sign of equality. Thus a:b::c:d means the same as a : b = c : d. 233. THEOREM. If four numbers are in proportion, the product of the extremes equals the product of the means. For if a : b = c : d, then - = -, and multiplying both sides of bd this equation by bd, we obtain ad... | |
 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...numerical method is still applicable, as will be shown subsequently. PROPOSITION I. — THEOREM. In every proportion the product of the extremes equals the product of the means. Suppose a : b = c : d, Then will axd = 6 x c. Proof. — From the given proportion We have £ = f .... | |
 | Leonard Eugene Dickson - Algebra - 1902 - 242 pages
...is 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... | |
 | 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 the product of the means. Thus, in the proportion, 17 : 51 = 14 : 42. 17 X 42 = 51 X 14, since both products equal 714. 56. Rule.... | |
 | 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... | |
 | Robert Judson Aley, David Andrew Rothrock - Algebra - 1904 - 344 pages
...theorems apply to proportions in which the terms of each ratio are considered abstract numbers. THEOREM I. In any proportion the product of the extremes equals the product of the means. Given A : В = C : A or, more simply, A_C B~uThen is AD = BO. Why? COROLLARY. The mean proportional... | |
 | 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.... | |
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In any proportion, the product of the extremes equals the product of the means. 
