...rewriting of the logical foundations of algebra was badly needed.12 In the same year John Warren published A Treatise on the Geometrical Representation of the Square Roots of Negative Quantities. Hamilton read it in 1829 at Graves's instigation. Warren's book described the so-called Argand diagram...

...coordinate plane. Based on the work of Argand, the English mathematician John Warren in 1828 published A Treatise on the Geometrical Representation of the Square Roots of Negative Numbers, which inspired the Irish physicistastronomer-mathematician WR Hamilton to show, in 1837, that...

...1828 this happened again - even on both sides of the Channel -with the publications of John Warren, A Treatise on the Geometrical Representation of the Square Roots of Negative Quantities, and CV Mourey, La vraie theorie des quantites negatives et des quantites pretendues imaginaires. Warren...

...Warnock, Geoffrey J. 1982 Berkeley, (2nd edn). Basil Blackwell, Oxford. (1st edn: 1953.) Warren, John 1828 A treatise on the geometrical representation of the square roots of negative quantities. J. Smith, Cambridge. Weyl, Hermann 1944b David Hilbert and his mathematical work. Bulletin of the American...

...allowed to substitute, in any other part of that calculation, either of the two [John Warren (1796-1852) A treatise on the geometrical representation of the square roots of negative quantities, Cambridge: 1828.] equated symbols for the other; and every other equation between two symbols of one...

...1685, A Treatise of Algebra, both historical and practical, London: John Playford. Warren, John. 1828, A Treatise on the Geometrical Representation of the Square Roots of Negative Quantities, Cambridge: J. Smith. Warren, John. 1829a. "Consideration of the objections raised against the geometrical...

...attempts to develop geometrical accounts of the algebra of negative and imaginary numbers. Consider A Treatise on the Geometrical Representation of the Square Roots of Negative Quantities, an elegant book by John Warren of Cambridge University, published in 1828. Warren noted that in his...

...with Hamilton about the problem. In 1828 he suggested that Hamilton read Warren's recently published Treatise on the Geometrical Representation of the Square Roots of Negative Quantities, which expressed the complex numbers as points in the plane. Hamilton was dissatisfied with a geometric...

...communicate this result to algebraists. This paper, therefore, is intended as a continuation of my " Treatise on the geometrical representation of the square roots of negative quantities;" and the object of it is to extend the geometrical representation to the powers of quantities, whose...