| 1876
...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... | |
| J. G - 1878 - 372 pages
...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... | |
| James Maurice Wilson - Geometry - 1878
...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... | |
| Wm. H. H. Phillips - Geometry - 1878 - 209 pages
...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
...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... | |
| Euclid - Geometry - 1890 - 400 pages
...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, Robert Simson - Geometry - 1892 - 518 pages
...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, H. S. Hall, F. H. Stevens - Euclid's Elements - 1904 - 456 pages
...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 - Geometry - 1905 - 42 pages
...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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