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On Quaternions

(98 views)
On Quaternions
$3,800
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Description: FIRST APPEARANCE of the first presentation of Hamilton's Quaternions, "a turning point in the development of mathematics" that "made possible the creation of the general theory of relativity" (Pickering; PMM). "The achievement in pure mathematics for which [Hamilton] is best remembered now is the invention of quaternions, a linear algebra of rotations in space of three dimensions. Quaternions were the first non-commutative number system system to be investigated in detail, and Hamilton's discovery that a consistent and useful system of algebra could be constructed without obeisanse to the commutative law of multiplication was comparable in importance to the invention of non-Euclidian geometry. Quaternions led to vector analysis, and were eventually superceded by the later, which has become of the greatest importance in mathematical physics and was developed by Ritman and Christoffel into tensor analysis. This made possible the creation of the general theory of relativity" (PMM 334). Hamilton's invention "was the first example of a coherent, significant mathematical system that preserved all of the laws of ordinary arithmetic, with the exception of commutativity... [His] ideas had an enormous influence on the gradual introduction and use of vectors in physics. Hamilton used the name scalar for the real part a of the quaternion, and the term vector for the imaginary part bi + cj + dk, and defined what are now known as the scalar (or dot) and vector (or cross) products. It was through successive work in the 19th century of the Britons Peter Guthrie Tait, James Clerk Maxwell, and Oliver Heaviside and the American Josiah Willard Gibbs that an autonomous theory of vectors was first established while developing on Hamilton's initial ideas" (Britannica). Recently, quaternions have found new life in the modeling of the three-dimensional rotations involved in modern computer graphics. "Hamilton's achievement in constructing quaternions is of considerable historical interest. It marked a turning point in the development of mathematics, involving as it did the introduction of noncommuting quantities into the subject matter of the field as well as an exemplary set of new entities and operations, the quaternion systerial agency, harnessing and directing that agency--domesticating it" (Andrew Pickering, "Concepts and the Mangle of Practice: Constructing Quaternions"). Hamilton first presented his remarkable invention of Quaternions in a lecture given at the Royal Irish Academy on November 13, 1843. Though Hamilton?s lecture is recorded in the Proceedings of the Academy for that date, his work on Quaternions did not appear in print until July of 1844 in the present volume. He later expanded and developed his invention in his more famous 1853 book Lectures on Quaternions (listed in PMM). In: The London, Edinburgh, and Dublin Philosophical Magazine, vol.XXV, 3rd Series, no.163, 166 & 169. London: Richard and John E. Taylor, 1844. Octavo, early contemporary half calf over marbled boards. Some rubbing to spine and extremities. Internally fine.

Artist or Maker: Hamilton, William

 
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