 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 132by George Albert Wentworth - 1889 - 242 pagesFull view - About this book
 | James Bates Thomson - Algebra - 1878 - 322 pages
...e 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
...AC, 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
...extremes 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 - 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 ï_. 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
...3. 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
...fourth 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... | |
 | George Albert Wentworth - Algebra - 1886 - 284 pages
...a : b : : с : d, then а.1 od By multiplying by bd, ad= be. 287. 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, ^- = —, bd bd M 288. The equation... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...be a : b = b : c. Then by §242, 62=ac. Whence, b = Vac. PROPOSITION II. THEOREM. 244. CONVERSELY, if the product of two quantities is equal to the product of two others, one pair may be made the extremes, and the other pair the means, of a proportion. Let ad = be. Dividing... | |
| |
