 | Joseph Ray - Algebra - 1848 - 252 pages
...equul to 8X2, we infer that the proportion isfalie. .\,.t-'2l't. — PROPOSITION II. — Conversely, If the product of two quantities is equal to the product of two others, two of them may be made the means, and the other two the extremes of a proportion. Let bc=ad.... | |
 | Jeremiah Day, James Bates Thomson - Algebra - 1848 - 264 pages
...means in both cases is the same. So if na : b : : x : y, then a : b : : x : ny. 339. On the other hand, if the product of two quantities is equal to the product of two others, the four quantities will form a proportion if they are so arranged, that those on one side... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...: B : : B : C ; then, by the proposition, I BOOK H. PROPOSITION ii. THEOREM (Converse of Prop. /.). 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. Thus, suppose... | |
 | Bourdon (M., Louis Pierre Marie) - Algebra - 1850 - 386 pages
...other that A x D — В х С, ß D we shall also have, — - = -=;-, А, О and hence, A : В : : С : D; that is If the product of two quantities is equal...quantities, two of them may be made the extremes, and tht other two the means of a proportion. 180. If we have three proportional quantities, A : В : :... | |
 | Charles Davies - Algebra - 1850 - 292 pages
...If four quantities, A, B, C, D, are so related each other that we shall also have — — ~r<"' A. O and hence, A : B : : C : D. That is : If the product...the product of two other quantities, two of them may tie made the extremes, and the other two the means of a proportion. Thus, if we have = 4x4, we also... | |
 | Horatio Nelson Robinson - Algebra - 1850 - 256 pages
...first term. This is a part of the well known rule of three, in Arithmetic. PROPOSITION II. Conversely. If the product of two quantities is equal to the product of two others, then two of them may be taken for the means, and the other two for the extremes of a proportion.... | |
 | Charles Davies - Algebra - 1851 - 300 pages
...quantities, A, B, C, D, are so related to each other that AxD=BxC, we shall also have ~T=~F . A. O and hence, A : B : : C : D. That is : If the product of two quantities is equal n the product of two oilier quantities, two of them may te made the extremes, and the other two the... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...PROPOSITION II. THEOEEM. If the product of two magnitudes be equal to the product of two other magnitudes, two of them may be made the extremes and the other two the means of a proportion. If we have Mx Q=NxP; then win M : N : : P : Q. For, if P have not to §, the ratio which M has to JVj... | |
 | Joseph Ray - Algebra - 1848 - 250 pages
...equal to 8X2, we infer that the proportion is false. ART. 345. — PROPOSITION II. — Conversely, If the product of two quantities is equal to the product of two others, two of them may be made the means, and the other two the extremes of a proportion. Let bc=ad.... | |
 | Joseph Ray - Algebra - 1852 - 408 pages
...to 2X8, we infer that 2, 3, 5, and 8, are not in proportion. ART. 268. PROPOSITION II. Conversely, If the product of two quantities is equal to the product of two others, two of them may be made the means, and the other two the extremes of a proportion. Let be—... | |
| |
If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion. 
