[762] The latest edition of Burnside and Panton's Theory of Equations has this brief summary of the present status of the problem: "Demonstrations have been given by Abel and Wantzel (see Serret's Cours d'Algèbre Supérieure, Art. 516) of the impossibility of resolving algebraically equations unrestricted in form, of a degree higher than the fourth. A transcendental solution, however, of the quintic has been given by M. Hermite, in a form involving elliptic integrals."
[763] There was a second edition of this work in 1846. The author's Astronomy Simplified was published in 1838, and the Thoughts on Physical Astronomy in 1840, with a second edition in 1842.
[764] This was The Science of the Weather, by several authors... edited by B., Glasgow, 1867.
[765] This was Y. Ramachandra, son of Sundara Lāla. He was a teacher of science in Delhi College, and the work to which De Morgan refers is A Treatise on problems of Maxima and Minima solved by Algebra, which appeared at Calcutta in 1850. De Morgan's edition was published at London nine years later.
[766] Abraham de Moivre (1667-1754), French refugee in London, poor, studying under difficulties, was a man with tastes in some respects like those of De Morgan. For one thing, he was a lover of books, and he had a good deal of interest in the theory of probabilities to which De Morgan also gave much thought. His introduction of imaginary quantities into trigonometry was an event of importance in the history of mathematics, and the theorem that bears his name, (cos φ + i sin φ)n = cos nφ + i sin nφ, is one of the most important ones in all analysis.
[767] John Dolland (1706-1761), the silk weaver who became the greatest maker of optical instruments in his time.
[768] Thomas Simpson (1710-1761), also a weaver, taking his leisure from his loom at Spitalfields to teach mathematics. His New Treatise on Fluxions (1737) was written only two years after he began working in London, and six years later he was appointed professor of mathematics at Woolwich. He wrote many works on mathematics and Simpson's Formulas for computing trigonometric tables are still given in the text-books.
[769] Nicholas Saunderson (1682-1739), the blind mathematician. He lost his eyesight through smallpox when only a year old. At the age of 25 he began lecturing at Cambridge on the principles of the Newtonian philosophy. His Algebra, in two large volumes, was long the standard treatise on the subject.
[770] He was not in the class with the others mentioned.
[771] Not known in the literature of mathematics.