If the product of two quantities is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means. A Text-book of Geometry - Page 128by George Albert Wentworth - 1888 - 386 pagesFull view - About this book
| Fletcher Durell, Edward Rutledge Robbins - Algebra - 1897 - 482 pages
...Then ma :mb = nc: nd, And ma : pb = me : pd. 290. Equal Products made into a Proportion ; that is, if **the product of two quantities is equal to the product of two** other quantities, either two may be made the means, and the other two the extremes of a proportion.... | |
| George Albert Wentworth - 1898 - 424 pages
...of the two numbers that represent them when the quantities are expressed in a common unit. 338. If **the product of two quantities is equal to the product...either two may be made the extremes of a proportion** and the other two the means. For, if ad = be, then, divide by bd. — = ;~; , bd bd ac or - = - •... | |
| George Albert Wentworth - Algebra - 1898 - 516 pages
...of the two numbers that represent them when the quantities are expressed in a common unit. 338. If **the product of two quantities is equal to the product...either two may be made the extremes of a proportion** and the other two the means. For, if ad = be, then, divide by bd, -— = -—, od bd « с b = d .'.... | |
| George Albert Wentworth - Algebra - 1898 - 434 pages
...the two numbers that represent them when the quantities are expressed in a common unit. 338. If tbс **product of two quantities is equal to the product...either two may be made the extremes of a proportion** and the other two the means. For, if ad = be, then, divide by bd, — = — i н с or - = -r bd .'.... | |
| George Albert Wentworth - Algebra - 1898 - 428 pages
...of the two numbers that represent them when the quantities are expressed in a common unit. 338. If **the product of two quantities is equal to the product of two others, either two may be made** th6 extremes of a proportion and the other two the means. For, if ad = be, , . . , ' . . ad bc then'... | |
| James Howard Gore - Geometry - 1898 - 232 pages
...quantities is equal to the square root of their product. PROPOSITION II. THEOREM. 201. CONVERSELY, if **the product of two quantities is equal to the product of two others,** one pair may be made the extremes, and the other pair the means, of a proportion. Let ad = be. Dividing... | |
| Webster Wells - Geometry - 1898 - 284 pages
...Vac. Proof. From (1), b**= ac. (§ 232) .-. b = Vac. PROP. II. THEOREM. 234. (Converse of Prop. I.) If **the product of two quantities is equal to the product of two others,** one pair may be made the extremes, and the other pair the means, of a proportion. Given ad — be.... | |
| George Albert Wentworth - 1898 - 436 pages
...quantities are expressed in a common unit. 338. If the product of two quantities is equal to the prodvet **of two others, either two may be made the extremes of a proportion** and the other two the means. For. if ad = be, then, divide by bd, — = — > bd bd ac or - = -•... | |
| George Albert Wentworth - Geometry - 1899 - 498 pages
...b* = ac. § 327 Whence, extracting the square root, & = Vac. QED PROPOSITION III. THEOREM. 329. If **the product of two quantities is equal to the product...two others, either two may be made the extremes of** the proportion in which the other two are made the means. Let ad = be. To prove that a:b = c:d. Divide... | |
| George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...6 2 = ac. § 327 Whence, extracting the square root, Z< = V«CQED PROPOSITION III. THEOREM. 329. If **the product of two quantities is equal to the product...two others, either two may be made the extremes of** the proportion in which the other two are made the means. Let ad = be. To prove that a:b = c:d. Divide... | |
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