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
| Charles Davies, William Guy Peck - Mathematics - 1855 - 628 pages
...definition, that the product of the extremes is equal to the product of the menus ; and conversely, if **the product of two quantities is equal to the product of two others,** the first two may be taken as the structed with a groove in each leg, so that extremes, and the last... | |
| Elias Loomis - Algebra - 1855 - 356 pages
...expression becomes abd bcd ~b~=~d' or ad=bc. Thus, if 3 : 4 : : 9 : 12, .hen 3X12=4X9. (213.) Conversely, if **the product of two quantities is equal to the product of two others,** the first two quantities may be made the extremes, and the other two the means of a proportion. Let-... | |
| Thomas Sherwin - Algebra - 1855 - 262 pages
...If we divide both members by b and d, we have — = —, or bdi a : b = c : d. Therefore, •• If **the product of two quantities is equal to the product of two** other quantities, the two factors of one product may be made the means, and the two factors of the... | |
| Thomas Sherwin - Algebra - 1855 - 318 pages
...product of the extremes. 2. Suppose we have ad=bc. Dividing both members by b XLIX. PROPORTIONS. 221 If **the product of two quantities is equal to the product of two** otner quantities, the two factors of either product may be made the means, and the two factors of the... | |
| Elias Loomis - Algebra - 1856 - 280 pages
...equation of fractions, we have ad— bc. Thus, if 3:4:: 9:12, then 3x12=4x9. (184.) Conversely, if **the product of two quantities is equal to the product of two others,** the first two quantities may be made the extremes, and the other two the means of a proportion. Let... | |
| John Fair Stoddard, William Downs Henkle - Algebra - 1859 - 538 pages
...4 > Are ax, abx, bx in proportion ? 5, Are ax, xVab, bx in proportion ? PROPOSITION (38 4i) 3. When **the product of two quantities is equal to the product of two** other quantities, the four quantities may be expressed in the form of three different, proportions.... | |
| James B. Dodd - Algebra - 1859 - 368 pages
...square root of their product. Thus from the equation ax=b2, we find b = (ax)*. THEOREM IV. (153.) When **the 'product of two quantities is equal to the product of two** other quantities, either pair of factors may be made the extremes, and the other the means, of a Proportion.... | |
| Charles Davies - Algebra - 1859 - 324 pages
...that A x D = В x (7, we shall also have, -j = -~ ; А ъ and hence, A : В : : С : D. That is : 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.... | |
| Thomas Sherwin - 1862 - 252 pages
...ad—be. If we divide both members by 6 and d, we have — = —, or a : b = c : d. Therefore, bd If **the product of two quantities is equal to the product of two** other quantities, the two factors of one product may be made the means, and the two factors of the... | |
| Horatio Nelson Robinson - Algebra - 1863 - 432 pages
...the product of the means divided by the other extreme. (2) 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 tico for the extremes of a proportion.... | |
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