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
| George Albert Wentworth - Geometry - 1877 - 426 pages
...means). Whence, extracting the square root, PROPOSITION III. 261. lf the product of two quantities be **equal to the product of two others, either two may be made the extremes** nf a proportion in which the other two are made the means. Let ad = be. We are to prove a : b : : с... | |
| Elias Loomis - Conic sections - 1877 - 458 pages
...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... | |
| James Bates Thomson - Algebra - 1878 - 322 pages
...By Art. 363, | = * Clearing of fractions, at = 6s. Again, 9:6:: 6-4, and 4 xg = 62. THEOREM III. If **the product of two quantities is equal to the product of two others,** the four quantities are proportional j the factors of either product being taken for the extremes,... | |
| William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...we have, £ = £, or, A:B = C:DL, £ = 5, or, A:C=B:DIL, ~ = ~, or, B : A = D : C III. CA Hence, if **the product of two quantities is equal to the product of two** other quantities, one pair of factors may be made the extremes, and the other pair the means, of a... | |
| William Frothingham Bradbury - Geometry - 1880 - 260 pages
...equal to the product of the meaiis ia merely clearing the equation of fractions. THEOREM II. 14i If **the product of two quantities is equal to the product of two others,** the factors of either product may be made the extremes, and the factors of the other the means of a... | |
| George Albert Wentworth - Geometry, Modern - 1881 - 266 pages
...extracting the square root, b = V/ac. QED PROPOSITION III. 261. If the product of two quantities be **equal to the product of two others, either two may...which the other two are made the means. Let ad = be.** We are to prove a : b : : с : d. Divide both members of the given equation by 6 d. Then ļ_. bd or,... | |
| George Albert Wentworth - Algebra - 1881 - 400 pages
...if ab :: c: d, then f = ^ 6 a By multiplying by bd, ad = bc. 342. If the product of two numbers be **equal to the product of two others, either two may be made the extremes of a proportion** and the other two the means. For, if ad = be, by dividing by bd, 2_ = _£ od ba ac PS' 343. The equation... | |
| William James Milne - Algebra - 1881 - 360 pages
...What does ad, the first member of the equation, form in the proportion? What be? PRINCIPLE 3. — 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.... | |
| George Albert Wentworth - Geometry, Modern - 1879 - 262 pages
...the square root, b = \l ac. QE o. PROPOSITION III. 261. If the product of two quantities be equal lo **the product of two others, either two may be made...which the other two are made the means. Let ad = be.** We are to prove a : b : : c : d. .. , Divide both members of the given equation by b d. Then or. ac... | |
| National cyclopaedia - 1884 - 670 pages
...term) can be obtained as easily ; for be . ad , ad a=— ,6 = — , and c = — . dcb Conversely, if **the product of two quantities is equal to the product of two others,** these four are proportionals ; example, 4 times 6 = 3 times 8 ; whence we see that 3 is to 4 as 6 is... | |
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