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MATHER 277 symmetry. One of the most remarkable achievements of the science was Leverrier's prediction in 1846 of the place and orbit of the planet Neptune from the motions of Uranus, announcing before its discovery by the tele- scope the existence, position, and magnitude of a body beyond the recognized limits of our system, merely as an inference from the per- turbations of the outermost planet known to us. Poisson, Airy, Plana, Hansen, Gauss, Adams, De Morgan, and Peirce are among the recent mathematicians who have solved im- portant problems in the physical application of analysis. Many new mathematical theories have been originated during the last half cen- tury. Among them may be mentioned the theory of determinants, the theory of invari- ants of Messrs. Cayley and Sylvester, that of clinants of Mr. Ellis, and many others. Some of them will probably pass into history only as evidences of the ingenuity of their authors, while others promise to be of great value. As they are of interest to professed mathematicians only, they require no further notice in this work. Among the greatest works in mathe- matical literature are the Principia of New- ton, the Mechanica of Euler, the Theorie des fonctions and the Mechanique analytique of Lagrange, the Application de ^analyse d la geo- metric of Monge, and the Mecanique celeste of Laplace. See Montucla, Histoire des mathe- matiques, continued by Lalande (4 vols., Paris, 1799-1802); Bossut, Essai sur Vhistoire des mathematiques (2 vols., Paris, 1802); Comte, Philosophie positive, vol. i., and Synthese posi- tive ; Libri-Carucci, Histoire des sciences ma- thematiques en Italic (4 vols., Paris, 1838-'41) ; Montferrier, Dictionnaire des sciences mathe- matiques (2d ed., 3 vols. 4to, Paris, 1844), and Encyclopedic mathematique tfaprh les prin- cipes de la philosophic des mathematiques de Home WronsU (4 vols. 8vo, Paris, 1856-'9) ; Fries, Die mathematische Naturphilosophie (Heidelberg, 1822) ; Poppe, Geschichte der Mathematilc (Tubingen, 1828) ; Ohm, Versuch eines vollcommenen, consequenten Systems der Mathematilc (3d ed., Nuremberg, 1853-'5) ; Bartholoma3i, Philosophie der Mathematilc (Jena, 1860) ; Davies, " Logic and Utility of Mathematics" (New York, 1851); and Davies and Peck, " Mathematical Dictionary " (New York, 1856). See also the works cited under the title GEOMETRY. MATHER. L Richard, an English clergyman, born at Lowton, Lancashire, in 1596, died in Dorchester, Mass., April 22, 1669. He re- ceived a good education, became a schoolmas- ter at Toxteth Park, near Liverpool, at the age of 15, was admitted to Brazenose college, Oxford, in 1618, was ordained a few months later, and became the minister of Toxteth, where he remained 15 years. He was sus- pended for nonconformity to the ceremonies of the established church in 1633, and, though soon restored by the influence of friends, was again silenced in 1634. He therefore emi- grated to New England, landing in Boston Aug. 17, 1635. In the following year he be- came pastor of the church in Dorchester, where he resided till his death. He was the author of several brief theological treatises and letters, chiefly on church government, and drew up in 1648, at the instance of the Cam- bridge synod, a model of discipline, which was accepted. He married in 1656 the widow of John Cotton. Of his six sons by his first wife, four were distinguished clergymen and authors: Samuel (1626-'7l), in Dublin, Ire- land; Nathaniel (1630-'97), in London; Elea- zar (1637-'69), in Northampton, Mass.; and Increase. His " Journal, Life, and Death " has been published for the Dorchester anti- quarian and historical society (Boston, 1850). II. Increase, an American clergyman, son of the preceding, born in Dorchester, Mass., June 21, 1639, died Aug. 23, 1723. He graduated at Harvard college in 1656, and in 1658 at Trinity college, Dublin. He afterward preached in Devonshire and the island of Guernsey. He returned to America in 1661, and was pastor of the North church, Boston, from 1664 till his death. He was a member of the synod of 1679, and drew up the propositions^ which were adopted concerning the proper subjects of baptism. In 1681 he was elected president of Harvard college. The reluctance of his church to relinquish him induced him to de- cline the office; but in 1685 he accepted it with a stipulation that he should retain his relation to his people. He continued in this station till 1701, when he retired in conse- quence of an act of the general court requiring the president to reside in Cambridge. He procured an act authorizing the college to create bachelors and doctors of divinity, and received in 1692 the first diploma for the de- gree of D. D. that was granted in America. When in 1683 Charles II. demanded that the charter of Massachusetts should be resigned into his hands, Mather was foremost in oppo- sing the measure ; and when that monarch annulled the charter in 1684, he was sent to England as agent for the colonies. He was in England during the revolution of 1688, and, finding it impossible to obtain a restoration of the old charter, accepted a new one, under which the appointment to all the offices re- served to the crown was confided to him. He returned in 1692, when the general court ap- pointed a day of thanksgiving for his safety and for the settlement of the dispute. He is said to have condemned the violent proceed- ings which followed relating to witchcraft. He was accustomed to spend 16 hours every day in his study, and always committed his sermons to memory. One tenth part of all his income was devoted to charity. He was the author of 92 distinct publications, now mostly very scarce. Two of these were writ- ten in Latin. His " Remarkable Providences " was republished in the " Library of Old Au- thors" (London, 1856), with an introduction