| Jeremiah Day - Algebra - 1814 - 304 pages
...=-jtyeducing the fractions, ad=bc. Thus 12: 8:: IS: 10, therefore 12x10=8x15. 375. 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, when they are so arranged, that those .on one side... | |
| Jeremiah Day - Algebra - 1827 - 352 pages
...is, in both cases the same. And if no : b'. '.x : yy then a : b'.'.x : ny. 375. 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, when they are so arranged, that those on one side... | |
| Algebra - 1838 - 372 pages
...B, C, and D, are so related to each other that AxD=B*C, i „ , , BD we shall also have ~T=~r' A. O **and hence, A : B : : C : D; that is, if the product...extremes, and the other two the means of a proportion.** 180. If we have three proportional quantities A : B : : B : C, 1 ^ C wehave _=_; hence, &=AC; that... | |
| Bourdon (M., Louis Pierre Marie) - Algebra - 1839 - 368 pages
...product of the two means. 179. If four quantities, A, B, C, and D, are so related to each other that **we shall also have — =— , AC/ and hence, A : B...product of two quantities is equal to the product of two** otter quantities, two of them may be made the extremes, and the other two the means of a proportion.... | |
| Charles Davies - Algebra - 1839 - 264 pages
...B, C, D, are so related to each other that AxD=BxC, ,....., BD we shall also have — =— ; A. Lx **and hence, A : B~: : C : D. That is : If the product of two quantities is equal to** tJte product of two other quantities, two of them may be made the extremes, and the other two the means... | |
| Charles Davies - Algebra - 1840 - 264 pages
...quantities, A, B, C, D, are so related to each other that ta.ll.!! BD we shall also have — =— ; AO **and hence, A : B : : C : D. That is : If the product of two quantities is equal to the product of two** otlier quantities, two of them may be made the extremes, and the other two the means of a proportion.... | |
| Charles Davies - Algebra - 1841 - 264 pages
...D, are so related to each other that AxD=BxC, . . . . , BD we shall also have — =— ; -j' I ' ' **and hence, A : B : : C : D. That is : If the product...extremes, and the other two the means of a proportion.** ThuB, if we have 2x8=4x4, we also have 2 : 4 : : 4 : 8. 156. If we have three proportional quantities... | |
| Charles Davies - Algebra - 1842 - 368 pages
...quantities, A, B, C, and D, are so related to each other that we shall also have — =— ., jfi O **and hence, A : B : : C : D; that is, if the product...extremes, and the other two the means of a proportion.** we have -=^; , BC hence, B 2 =AC; that is, the square of the middle term is equal to the product of... | |
| Charles Davies - Algebra - 1842 - 284 pages
...Thus, if we have the proportion 3 : 6 : : 6 : 12, t we shall also have = 62 = 3xl2=36. QUEST. — 155. **If the product of two quantities is equal to the product of two other quantities,** may the four be placed in a proportion 1 How ? — 156. If three quantities are proportional, what... | |
| Thomas Sherwin - Algebra - 1842 - 326 pages
...Suppose we have ad = bc. Dividing both members by 6 and d, we have r = -, or a : b = c : d. Hence, oa **If the product of two quantities is equal to the product of** ttca other quantities, the two factors of either product may be made the means, and the two factors... | |
| |