## A Memoir on the Theory of Matrices (Cayley, pp. 17-46) + The Bakerian Lecture: On the stratifications and dark band in electrical discharges as observed in Torricellian vacua (Gassiot, pp.1-16) + Description of the Skull and Teeth of the Placodus Laticeps, Owen, with Indications of Other New Species of Placodus, and Evidence of the Saurian Nature of That Genus (Owen, pp. 169-184) with On the Megatherium (Megatherium americanum, cuvier and blumenbach). Part IV. —Bones of the anterior extremities (Owen, pp. 261-279) in Philosophical Transactions 148, 1858, Full Volume Parts I & II [INCLUDING MANY MORE PAPERS]

London: Royal Society, 1858. 1st Edition. Handsomely bound FIRST EDITION, FULL VOLUME INCLUSIVE OF MANY IMPORTANT PAPERS & 71 PLATES. Included are Cayley’s paper on matrices marks “an epoch in the development of the subject” (Ball, A Short Account of the History of Mathematics, 476). Gassiot’s paper “was particularly important in the demise of the contact theory of voltaic electricity” and is widely held to contain the roots of early television (Wiki; Shiers, Early TV). Two papers by the distinguished paleontologist Richard Owen (with a total of 8 plates). As well, there are 5 more papers by Cayley; several by Tyndall including one on ice; Matthiessen on metals (including his ‘rule’), work for which he would later win the Royal Medal. There are others by Plücker, Lister, Lyell, and others.

CAYLEY: Cayley’s memoir on matrices “the first paper on matrix algebra” (Higham, Cayley, Sylvester, and Early Matrix Theory, 2007). His “researches on matrices and non-commutative algebras mark an epoch in the development of the subject” (Ball, A Short Account of the History of Mathematics, 476). “The fundamental notions in metrical geometry are the distance by another, also involving "imaginary" elements, Cayley’s [matrix algebra provided the means for unifying Euclidean geometry and the common non-Euclidean geometries into one comprehensive theory" (Bell, Men of Mathematics). Defining matrices oddly literally, Sylvester was first to use the term matrix in 1850, but it is Cayley who quickly saw the import of the concept and in 1858 published “a landmark paper” [this paper] using his own abstract definition “as the basis of a brand new area of mathematics: the algebra of matrices” (Flood, Mathematics, 7). Here Cayley shows that the coefficient arrays studied earlier for quadratic forms and for linear transformations are special cases of his general concept – that like quaternions, matrices do not always give the same results when multiplied together in different orders; further he gave a matrix algebra defining addition, multiplication, scalar multiplication and inverses (ibid).

GASSIOT: In this paper and again in 1859, Gassiot reported experiments in which he observed deflections of cathode rays by electrostatic charges & magnetism. These findings (along with Plücker’s) provided the first evidence that ‘cathode rays’ carry an electric charge & might be particles. The roots of television can even be found in Gassiot’s research into electric discharges in rarefied gases. With Faraday & others, Gassiot’s work was part of the foundation of cathode-ray-tube technology which led much later to electron physics (Shiers). Note that we offer extracted first editions of Gassiot's papers separately.

OWEN: Owen “distinguished himself with his powers of organization and deduction. At the same time he showed himself to be a peerless anatomist with instincts for reconstruction almost on a par with the great Cuvier in Paris. He became such an expert on the anatomy of animals that he was granted first refusal on any animal that died at the London Zoological Gardens, and these he would invariably have delivered to his house for examination. Once his wife returned home to find a freshly deceased rhinoceros filling the front hallway” (Bryson, 88). The other Cayley papers are: A Memoir on the Automorphic Linear Transformation of a Bipartite Quadric; Supplementary Researches on the Partition of Numbers; A Fourth Memoir upon Quantics; A Fifth Memoir upon Quantics; On the Tangential of a Cubic. Item #1336

DETAILS: Complete Parts I & II. Quarto. 909pp. Full index. 71 plates. Ex-libris with one Royal College of Surgeons stamp on the title page and the occasional blind stamp (very difficult to see) within) Handsomely rebound in aged calf. 5 raised bands at the spine, each gilt-ruled with gilt-tooled fleur de lis. Red and black, gilt-lettered spine labels. Tightly bound. New endpapers. The front a rear prelims have some light spotting, but the volume is otherwise pristine throughout. Near fine condition.

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Price:
$1,200.00
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