| 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... | |
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