[104] Referring to Hamilton's edition of the _Collected Works of Dugald Stewart_, 10 volumes, Edinburgh, 1854-58. It is not commonly remembered that Stewart (1753-1828) taught mathematics at the University of Edinburgh before he took up philosophy. [105] This was Hamilton's edition of the _Works of Thomas Reid_ (2 vols., Edinburgh, 1846-1863). Reid (1710-1796) included mathematics in his work in philosophy at Aberdeen. In 1764 he succeeded Adam Smith at Glasgow. [106] Edward Irving (1792-1834), the famous preacher. At first he assisted Dr. Chalmers at Glasgow, but in 1822 he went to London where he met with great success. A few years later he became mentally unbalanced and was finally expelled from his church (1832) for heresy. He was a great friend of Carlyle. [107] He also wrote a number of other paradoxes, including _An Essay towards a Science of Consciousness_ (1838), _Instinctive Natural Religion_ (1858), _Popular Treatise on the structure, diseases, and treatment of the human teeth_ (1837), and _On Headache_ (1859). [108] James Smith (1801-1857), known as Shepherd Smith, was a socialist and a mystic, with a philosophy that was wittily described as "Oriental pantheism translated into Scotch." He was editor of several journals. [109] Joanna Southcott (1750-1814) was known for her rhyming prophecies in which she announced herself as the woman spoken of in Revelations xii. She had at one time as many as 100,000 disciples, and she established a sect that long survived her. [110] Thales, c. 640-548 B. C. [111] Pythagoras, 580-501 B. C. [112] Anaxagoras, 499-428 B. C., the last of the Ionian school, teacher of Euripides and Pericles. Plutarch speaks of him as having squared the circle. [113] Oinopides of Chios, contemporary of Anaxagoras. Proclus tells us that Oinopides was the first to show how to let fall a perpendicular to a line from an external point. [114] Bryson and Antiphon, contemporaries of Socrates, invented the so-called method of exhaustions, one of the forerunners of the calculus. [115] He wrote, c. 440 B. C., the first elementary textbook on mathematics in the Greek language. The "lunes of Hippocrates" are well known in geometry. [116] Jabir ben Aflah. He lived c. 1085, at Seville, and wrote on astronomy and spherical trigonometry. The _Gebri filii Affla Hispalensis de astronomia libri_ IX was published at Nuremberg in 1533. [117] Hieronymus Cardanus, or Girolamo Cardano (1501-1576), the great algebraist. His _Artis magnae sive de regulis Algebrae_ was published at Nuremberg in 1545. [118] Nicolo Tartaglia (c. 1500-1557), the great rival of Cardan. [119] See note 5 {98}, Vol. I, page 69. [120] See note 10 {124}, Vol. I., page 83. [121] See note 9 {123}, Vol. I, page 83. [122] Pierre Herigone lived in Paris the first half of the 17th century. His _Cours mathematique_ (6 vols., 1634-1644) had some standing but was not at all original.