 | American Association for the Advancement of Science - 1892 - 614 lapas
...beginning of the nineteenth, mathematical advancement was rapid under the powerful hands of Euler, Lagrange, Laplace and Legendre: To these great men...which one of higher multiplicity is used. The field of Quautics has been brilliantly cultivated by Cayley, Sylvester and others. The theory of Matrices has... | |
 | American Association for the Advancement of Science - 1892 - 604 lapas
...discussion of the Calculus of Imaginaries, which was afterwards systematized and developed by Gauss, Catichy and others, the treatment of Determinants, contributions...which one of higher multiplicity is used. The field of Quanties has been brilliantly cultivated by Cayley, Sylvester and others. The theory of Matrices has... | |
 | Arthur Cayley - 1896 - 676 lapas
...numbers (in the foregoing sense, number = quantity of the form a + /3t) form (what real numbers do not) a universe complete in itself, such that starting in it we are never led out of it. There may very well be, and perhaps are, numbers in a more general sense of the term (quaternions are... | |
 | Arthur Cayley - 1896 - 663 lapas
...numbers (in the foregoing sense, number = quantity of the form a + /3i) form (what real numbers do not) a universe complete in itself, such that starting in it we are never led out of it. There may very well be, and perhaps are, numbers in a more general sense of the term (quaternions are... | |
 | John Theodore Merz - 1912 - 848 lapas
...without the addition of the imaginary unit, but that with the introduction of a second unit "numbers form a universe complete in itself, such that, starting in it, we are never led out of it. There may very well be, and perhaps are, numbers in a more general sense of the term ; but in order... | |
 | Sir Thomas Percy Nunn - 1914 - 654 lapas
...word " number " in algebra always to mean "complex number," we can say with Cay ley that "numbers form a universe complete in itself, such that, starting in it, we are never led out of it ". These observations have an obvious geometrical intrepretation. Eeal numbers correspond to points... | |
 | Thomas Percy Nunn, Sir Thomas Percy Nunn - 1914 - 762 lapas
...of § 1) that complex numbers must be regarded as the typical numbers of algebra because they " form a universe complete in itself, such that, starting in it, we are never led out of it ". In Ex. XCVI we begin a series of investigations which illustrate this important statement. The statement... | |
 | Sir Thomas Percy Nunn, Thomas Percy Nunn - 1919 - 654 lapas
...of § 1) that complex numbers must be regarded as the typical numbers of algebra because they " form a universe complete in itself, such that, starting in it, we are never led out of it ". In^ Ex. XCVI we begin a series of investigations which .illustrate this important statement. The... | |
| |
We have in fact a double algebra as the instrument for the complete treatment of all higher analysis, except that in which one of higher multiplicity is used. The field of Quautics has been brilliantly cultivated by Cayley, Sylvester and others. 