 | Association for the improvement of geometrical teaching - 1876 - 66 페이지
...other antecedent is greater than, equal to, or less than that of its consequent. Or in other words : The ratio of A to B is equal to that of P to Q,,when wA is greater than, equal to, or less than ?zB, according as mP is greater than, equal to or... | |
 | James Maurice Wilson - 1878 - 450 페이지
...to, or less than «Q, whatever whole numbers m and « may be. It is an immediate consequence that : The ratio of A to B is equal to that of P to Q ; when, m being any number whatever, and « another number determined so that either a»A is between... | |
 | J. G - 1878 - 408 페이지
...And then follows as an "immediate consequence" its application to incommensurable magnitudes : — The ratio of A to B is equal to that of P to Q, when, m being any number whatever, and n another number determined so that m A is between n B and (n... | |
 | William Henry Harrison Phillips - 1878 - 236 페이지
...1. Four magnitudes, A and B of one kind, and C and D of the same or another kind, are proportional, when the ratio of A to B is equal to that of C to D ; that is, when TJ. = :pr (II., 7). Thus A and B may be two lines, C and D, two triangles. The... | |
 | Mathematical association - 1883 - 86 페이지
...equal to, or less than »Q, whatever whole numbers m and n may be. It is an immediate consequence that: The ratio of A to B is equal to that of P to Q ; when, m being any number whatever, and » another number determined so that either /»A is between... | |
 | Association for the Improvement of Geometrical Teaching - 1888 - 208 페이지
...equal to, or less than wQ, whatever whole numbers m and n may be. It is an immediate consequence that : The ratio of A to B is equal to that of P to Q, when, m being any number whatever, and » another number determined so that either mA. is between «B... | |
 | Euclid - 1890 - 442 페이지
...between them. Euclid's definition, expressed in the notation already indicated, is the same as this — The ratio of A to B is equal to that of P to Q when m A >, =, or < n B according as mP >, =, or < nQ, whatever numbers m and n may be. It is an immediate... | |
 | Euclid - 1892 - 460 페이지
...distributed among those of B in the same manner as the multiples of C are distributed among those of D. 5. When the ratio of A to B is equal to that of C to D the four magnitudes are called proportionals. This is ex' presjied by saying " A is to B as... | |
 | Euclid - 1904 - 488 페이지
...proportion, when the ratio of the first to the second is equal to the ratio of the third to the fourth. When the ratio of a to b is equal to that of x to y, the four magnitudes are called proportionals. This is expressed by saying " a is to b as x... | |
 | Cora Lenore Williams - 1905 - 56 페이지
...order as the multiples of the antecedent of the second ratio among those of its consequent. Def. 53. When the ratio of A to B is equal to that of P to Q the four magnitudes, A, B, P, Q, are said to be proportionals, or to form a proportion. The proportion is denoted thus:... | |
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B, according as mP is greater than, equal to, or less than »Q, whatever whole numbers m and n may be. It is an immediate consequence that: The ratio of A to B is equal to that of P to Q ; when, m being any number whatever, and... 