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The present work is constructed on the same plan as my treatise on Plane Trigonometry, to which it is intended as a sequel; it contains all the propositions usually included under the head of Spherical Trigonometry, together with a large collection of examples for exercise. In the course of the work reference is made to preceding writers from whom assistance has been obtained; besides these writers I have consulted the treatises on Trigonometry by Lardner, Lefebure de Fourcy, and Snowball, and the treatise on Geometry published in the Library of Useful Knowledge. The examples have been chiefly selected from the University and College Examination Papers. In the account of Napier's Rules of Circular Parts an explanation has been given of a method of proof devised by Napier, which seems to have been overlooked by most modern writers on the subject. I have had the advantage of access to an unprinted Memoir on this point by the late R. L. Ellis of Trinity College; Mr Ellis had in fact rediscovered for himself Napier's own method. For the use of this Memoir and for some valuable references on the subject I am indebted to the Dean of Ely.Considerable labour has been bestowed on the text in order to render it comprehensive and accurate, and the examples have all been carefully verified; and thus I venture to hope that the work will be found useful by Students and Teachers. In the third edition I have made some additions which I hope will be found valuable. I have considerably enlarged the discussion on the connexion of Formul in Plane and Spherical Trigonometry; so as to include an account of the properties in Spherical Trigonometry which are analogous to those of the Nine Points Circle in Plane Geometry. The mode of investigation is more elementary than those hitherto employed; and perhaps some of the results are new. The fourteenth Chapter is almost entirely original, and may deserve attention from the nature of the propositions themselves and of the demonstrations which are given. Cambridge, July

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Isaac Todhunter (1820 - 1884), was an English mathematician who is best known today for the books he wrote on mathematics and its history. The son of George Todhunter, a Nonconformist minister, and Mary nee Hume, he was born at Rye, Sussex. He was educated at Hastings, where his mother had opened a school after the death of his father in 1826. He became an assistant master at a school at Peckham, attending at the same time evening classes at the University College, London where he was influenced by Augustus De Morgan. In 1842 he obtained a mathematical scholarship and graduated as B.A. at London University, where he was awarded the gold medal on the M.A. examination. About this time he became mathematical master at a school at Wimbledon. In 1844 Todhunter entered St John's College, Cambridge, where he was senior wrangler in 1848, and gained the first Smith's Prize and the Burney Prize; and in 1849 he was elected to a fellowship, and began his life of college lecturer and private tutor. In 1862 he was made a fellow of the Royal Society, and in 1865 a member of the Mathematical Society of London. In 1871 he gained the Adams Prize and was elected to the council of the Royal Society. He was elected honorary fellow of St John's in 1874, having resigned his fellowship on his marriage in 1864. In 1880 his eyesight began to fail, and shortly afterwards he was attacked with paralysis. He is buried in the Mill Road cemetery, Cambridge.

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