 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.  Elementary Algebra - Page 318by Frederick Howland Somerville - 1908 - 407 pagesFull view - About this book
 | Nicholas Tillinghast - Geometry, Plane - 1844 - 108 pages
...means is equal to the product of the extremes ; as, 6 : 4 : : 15 : 10, hence 10.6=15.4. Prop. 2. If the product of two numbers is equal to the product of two other numbers, the four may be arranged in a proportion; as, 8.3=12.2, hence 8: 12: : 2 : 3. Scholium. Remark that... | |
 | Bourdon (M., Louis Pierre Marie) - Arithmetic - 1858 - 262 pages
...multiplication, they must have been equal at first. Hence the property is proved. 161. Reciprocally. — If the product of two numbers is equal to the product of two other numbers, these four numbers form a proportion of which either pair of factors will constitute the means, the... | |
 | William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...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 proportion. EXERCISE 2. From AD = BC, write eight proportions. 5. Since the proportions II. and III. are true when... | |
 | Webster Wells - Algebra - 1879 - 468 pages
...x = a 344. If the product of two quantities be equal to the product of two others, one pair of them may be made the extremes, and the other pair the means, of a proportion. Thus, if ad = b с , , ad be ao In a similar manner, we might derive from the equation ad = bc, the... | |
 | Webster Wells - Algebra - 1885 - 324 pages
...296. (Converse of Art. 293.) If the product of tim quantities be 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 by bd, g * or£ = £ bd bd bd In a similar manner we may prove that : a : c =... | |
 | Webster Wells - 1885 - 368 pages
...296. (Converse of Art. 293.) If the product of two quantities be 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 by bd, g=«!с orf с bd bd bd • In a similar manner we may prove that : a... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...// the product of two factors is equal to the product of two other factors, either pair of factors may be made the extremes and the other pair the means of a proportion. Assume B x C = A x D; dividing each member by A x C, we have, I = -g, or A : B :: C : D; in like manner,... | |
 | Webster Wells - Algebra - 1885 - 370 pages
...of Art. 293.) If the product of two quantities be equal to the product of two others, one pair mail be made the extremes, and the other pair the means, of a proportion. Let ad = be. Dividing by bd, g = g,orf = i. bd bd bd In a similar manner we may prove that : a : с... | |
 | David Martin Sensenig - Algebra - 1889 - 388 pages
...other mean. II. If the product of two quantities equals the product of two other quantities, either pair may be made the extremes, and the other pair the means, of a proportion. Given mX n = pX Ч (A) Prove, 1. m :p: :q: n 5 • p : m : : n •9 2. m :q: :p: n в • p : n: :... | |
 | Webster Wells - Algebra - 1890 - 560 pages
...384. (Converse of Art. 381.) 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 bjMi M=S'c"HWhence, a : b = c : d. In like manner we may prove that a : c = 6... | |
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