 | Charles Davies - Geometry - 1872 - 464 pages
...this case, the square of the mean w equal to the product of the extremes. PROPOSITION II. THEOREM. If the product of two quantities is equal to the product of two other quantit1es, two nf them may be made the means, and the other two the extremes of a proportion.... | |
 | William Frothingham Bradbury - Geometry - 1873 - 288 pages
...14, If the product of two quantities is equal to the product of two others, the factors of eгther product may be made the extremes, and the factors of the other the means of a proportion. Let ad = Ъ с а с Dividing by 6 d "b~"d that is a : b = с : d THEOREM III. 15 « If four quantities are... | |
 | Elias Loomis - Algebra - 1873 - 396 pages
...c : d. Then | = |,Art.292. Multiplying each of these equals by bd, we have ad=bc. 300. Conversely, if the product of two quantities is equal to the product of two other quantities, the first two may be made the extremes, and the other two the means of a proportion.... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...this case, the square of the mean is equal to the product of the extremes. PROPOSITION n. THEOREM. If the product of two quantities is equal to the product of two other quantities, two of them may be made the means, and the other two the extremes of a proportion.... | |
 | William Frothingham Bradbury - 1875 - 280 pages
...extremes is equal to the product of the means. Let a : Ъ = с : d а с ie T= о а THEOREM II. 203i If the product of two quantities is equal to the product...factors of either product may be made the extremes, and Ihe factors of the oiher the means of a proportion. Let ad = b с Dividing by bd, Y — ~, ie a : Ь... | |
 | William Guy Peck - Algebra - 1875 - 348 pages
...extremes. Conversely, if we divide both members of (2) by ca, we have, - = -; or, a : b :: c : d; hence, ac If the product of two quantities is equal to the product of two other quantities, the first two may be made the means, and the second two the extremes, of a proportion.... | |
 | William Guy Peck - Conic sections - 1876 - 412 pages
...we then have the square of the mean equal to the product of the extremes. PROPOSITION III. THEOREM. If the product of two quantities is equal to the product of two other quantities, the first two may be made the means and the other two the extremes of a proportion.... | |
 | William Frothingham Bradbury - Algebra - 1877 - 302 pages
...product of the extremes is equal to the product of the means. Let a : 6 = c : d i=5 THEOREM II. 203. If the product of two quantities is equal to the product...the means of a proportion. Let ad = bc Dividing by bd, - = ie a : b = c : d THEOREM III. 204. If four quantities are in proportion, they will be in proportion... | |
 | William Frothingham Bradbury - Algebra - 1877 - 280 pages
...of llie extremes is equal to the product of the means. Let a : b = с : d a с b=d THEOREM II. 203i If the product of two quantities is equal to the product of two others, the factors of eitlier product may be made the extremes, and the factors of the other the means of a proportion. Let... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...this proposition, A x C=B x B, which is equal to B'. PROPOSITION ii. THEOREM. (Converse of Prop. I.) If the product of two quantities is equal to the product of two others, the one pair may be made the extremes, and the other t/ie means of a proportion. Thus, suppose we have... | |
| |
If the product of two quantities is equal to the product of two others, the... 
