 | Association for the improvement of geometrical teaching - 1876 - 66 페이지
...- ;z) A (w being greater than n) (Eue. v. 6.) 7. m. n A = mn.K =. nm.K — n.mh. (Eue. v. 3 ) DEF. 3. The ratio of one magnitude to another of the same kind is the relation of the former to the latter in respect of quantuplicity. The ratio of A to B is denoted thus A : B,... | |
 | William Guy Peck - 1876 - 376 페이지
...by less than any assignable quantity are said to be equal to each other. PROPOSITION I. THEOREM. If the ratio of one magnitude to another of the same kind is equal to —, to within less than —, for all values of m, the 1 m m' JJ true value of the ratio is... | |
 | James Maurice Wilson - 1878 - 450 페이지
...(mn)A(m being greater than «) (Euc. v. 6). 7. «.«A = '««.A = ««. A=«.*»A (.£«<:. v. 3). . 2?^ 3. The ratio of one magnitude to another of the same kind is the relation of the former to the latter in respect of quantuplidty. The ratio of A to B is denoted thus, A : B,... | |
 | Mathematical association - 1883 - 86 페이지
...common multiple, and conversely that magnitudes which have a common multiple are commensurable. DEF. 4. The ratio of one magnitude to another of the same kind is the relation of the former to the latter in respect of quantuplidty. The ratio of A to B is denoted thus, A : B,... | |
 | Association for the Improvement of Geometrical Teaching - 1888 - 208 페이지
...two or more magnitudes have a common multiple or measure they are said to be commensurable. DBF. 4. The ratio of one magnitude to another of the same kind is a certain relation of the former to the latter in retpect of quantity, the comparison being made by... | |
 | Euclid - 1892 - 460 페이지
...(m+n + ...) A. (o) If m > n, then mA - «A = (m - n) A. (6) m . »A = urn . A = nm . A = n . i«A. 3. The Ratio of one magnitude to another of the same...second in respect of quantuplicity. The ratio of A to B is denoted thus, A : B; and A is called the antecedent, B the consequent of the ratio. The term quantuplicity... | |
 | Charles Godfrey, Arthur Warry Siddons - 1903 - 384 페이지
...the ratio of two lengths. In the case of other magnitudes, ratio may be defined as follows : — DBF. The ratio of one magnitude to another of the same kind is the quotient obtained by dividing the numerical measure of the first by that of the second, the unit being... | |
 | Association for the Improvement of Geometrical Teaching - 1903 - 342 페이지
...nA.=(m — «) A, (;« being greater than «). 7. »z.«A=;««. A=«#zA=«./«A. DEF. 3. — 77/c ratio of one magnitude to another of the same kind is the relation of the former to the latter in respect of quanta plicity. The quant uplirity of A with respect to B... | |
 | Euclid - 1904 - 488 페이지
...second an exact number of times. Thus — is a submultiple of a, if m is any whole number. Definition 3. The ratio of one magnitude to another of the same...the relation which the first bears to the second in regard to quantity ; this is measured by the fraction which the first is of the second. Thus if two... | |
 | Cora Lenore Williams - 1905 - 122 페이지
...The converse proposition necessarily follows: A > = or < B according as m A > = or < m B. Def. 51. The ratio of one magnitude to another of the same...the relation which the first bears to the second. The ratio of magnitude A to magnitude B is denoted thus, A: B, and A is called the antecedent, B, the... | |
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The ratio of one magnitude to another of the same kind is the quotient obtained by dividing the numerical measure of the first by that of the second, the unit being the same in each case. 
