[372] "Unknown."

[373] "Skeptical."

[374] "Man, man, man."

[375] "Men, men, men."

[376] It is interesting to read De Morgan's argument against Saint-Martin's authorship of this work. It is attributed to Saint-Martin both by the Biographie Universelle and by the British Museum Catalogue, and De Morgan says by "various catalogues and biographies."

[377] "To explain things by man and not man by things. On Errors and Truth, by a Ph.... Inc...."

[378] "If we would preserve ourselves from all illusions, and above all from the allurements of pride, by which man is so often seduced, we should never take man, but always God, for our term of comparison."

[379] "And here is found already an explanation of the numbers four and nine which caused some perplexity in the work cited above. Man is lost in passing from four to nine."

[380] Williams also took part in the preparation of some tables for the government to assist in the determination of longitude. He had published a work two years before the one here cited, on the same subject,—An entire new work and method to discover the variation of the Earth's Diameters, London, 1786.

[381] This is Gabriel Mouton (1618-1694), a vicar at Lyons, who suggested as a basis for a natural system of measures the mille, a minute of a degree of the meridian. This appeared in his Observationes diametrorum solis et lunae apparentium, meridianarumque aliquot altitudinum cum tabula declinationum solis.... Lyons, 1670.

[382] Jacques Cassini (1677-1756), one of the celebrated Cassini family of astronomers. After the death of his father he became director of the observatory at Paris. The basis for a metric unit was set forth by him in his Traite de la grandeur et de la figure de la terre, Paris, 1720. He was a prolific writer on astronomy.

[383] Alexis Jean Pierre Paucton (1732-1798). He was, for a time, professor of mathematics at Strassburg, but later (1796) held office in Paris. His leading contribution to metrology was his Metrologie ou Traite des mesures, Paris, 1780.

[384] He was an obscure writer, born at Deptford.

[385] He was also a writer of no scientific merit, his chief contributions being religious tracts. One of his productions, however, went through many editions, even being translated into French; Three dialogues between a Minister and one of his Parishioners; on the true principles of Religion and salvation for sinners by Jesus Christ. The twentieth edition appeared at Cambridge in 1786.

[386] This was the Reflections on the Revolution in France, and on the proceedings in certain societies in London relative to that event (London, 1790) by Edmund Burke (1729-1797). Eleven editions of the work appeared the first year.

[387] Paine (1736-1809) was born in Norfolkshire, of Quaker parents. He went to America at the beginning of the Revolution and published, in January 1776, a violent pamphlet entitled Common Sense. He was a private soldier under Washington, and on his return to England after the war he published The Rights of Man. He was indicted for treason and was outlawed to France. He was elected to represent Calais at the French convention, but his plea for moderation led him perilously near the guillotine. His Age of Reason (1794) was dedicated to Washington. He returned to America in 1802 and remained there until his death.

[388] Part I appeared in 1791 and was so popular that eight editions appeared in that year. It was followed in 1792 by Part II, of which nine editions appeared in that year. Both parts were immediately republished in Paris, and there have been several subsequent editions.

[389] Mary Wollstonecraft (1759-1797) was only thirty-three when this work came out. She had already published An historical and moral View of the Origin and Progress of the French Revolution (1790), and Original Stories from Real Life (1791). She went to Paris in 1792 and remained during the Reign of Terror.

[390] Samuel Parr (1747-1827) was for a time head assistant at Harrow (1767-1771), afterwards headmaster in other schools. At the time this book was written he was vicar of Hatton, where he took private pupils (1785-1798) to the strictly limited number of seven. He was a violent Whig and a caustic writer.

[391] On Mary Wollstonecraft's return from France she married (1797) William Godwin (1756-1836). He had started as a strong Calvinistic Nonconformist minister, but had become what would now be called an anarchist, at least by conservatives. He had written an Inquiry concerning Political Justice (1793) and a novel entitled Caleb Williams, or Things as they are (1794), both of which were of a nature to attract his future wife.

[392] This child was a daughter. She became Shelley's wife, and Godwin's influence on Shelley was very marked.

[393] This was John Nichols (1745-1826), the publisher and antiquary. He edited the Gentleman's Magazine (1792-1826) and his works include the Literary Anecdotes of the Eighteenth Century (1812-1815), to which De Morgan here refers.

[394] William Bellenden, a Scotch professor at the University of Paris, who died about 1633. His textbooks are now forgotten, but Parr edited an edition of his works in 1787. The Latin preface, Praefatio ad Bellendum de Statu, was addressed to Burke, North, and Fox, and was a satire on their political opponents.

[395] As we have seen, he had been head-master before he began taking "his handful of private pupils."

[396] The story has evidently got mixed up in the telling, for Tom Sheridan (1721-1788), the great actor, was old enough to have been Dr. Parr's father. It was his son, Richard Brinsley Sheridan (1751-1816), the dramatist and politician, who was the pupil of Parr. He wrote The Rivals (1775) and The School for Scandal (1777) soon after Parr left Harrow.

[397] Horner (1785-1864) was a geologist and social reformer. He was very influential in improving the conditions of child labor.

[398] William Cobbett (1762-1835), the journalist, was a character not without interest to Americans. Born in Surrey, he went to America at the age of thirty and remained there eight years. Most of this time he was occupied as a bookseller in Philadelphia, and while thus engaged he was fined for libel against the celebrated Dr. Rush. On his return to England he edited the Weekly Political Register (1802-1835), a popular journal among the working classes. He was fined and imprisoned for two years because of his attack (1810) on military flogging, and was also (1831) prosecuted for sedition. He further showed his paradox nature by his History of the Protestant Reformation (1824-1827), an attack on the prevailing Protestant opinion. He also wrote a Life of Andrew Jackson (1834). After repeated attempts he succeeded in entering parliament, a result of the Reform Bill.

[399] Robinson (1735-1790) was a Baptist minister who wrote several theological works and a number of hymns. His work at Cambridge so offended the students that they at one time broke up the services.

[400] This work had passed through twelve editions by 1823.

[401] Dyer (1755-1841), the poet and reformer, edited Robinson's Ecclesiastical Researches (1790). He was a life-long friend of Charles Lamb, and in their boyhood they were schoolmates at Christ's Hospital. His Complaints of the Poor People of England (1793) made him a worthy companion of the paradoxers above mentioned.

[402] These were John Thelwall (1764-1834) whose Politics for the People or Hogswash (1794) took its title from the fact that Burke called the people the "swinish multitude." The book resulted in sending the author to the Tower for sedition. In 1798 he gave up politics and started a school of elocution which became very famous. Thomas Hardy (1752-1832), who kept a bootmaker's shop in Piccadilly, was a fellow prisoner with Thelwall, being arrested for high treason. He was founder (1792) of The London Corresponding Society, a kind of clearing house for radical associations throughout the country. Horne Tooke was really John Horne (1736-1812), he having taken the name of his friend William Tooke in 1782. He was a radical of the radicals, and organized a number of reform societies. Among these was the Constitutional Society that voted money (1775) to assist the American revolutionists, appointing him to give the contribution to Franklin. For this he was imprisoned for a year. With his fellow rebels in the Tower in 1794, however, he was acquitted. As a philologist he is known for his early advocacy of the study of Anglo-Saxon and Gothic, and his Diversions of Purley (1786) is still known to readers.

[403] This was the admiral, Adam Viscount Duncan (1731-1804), who defeated the Dutch off Camperdown in 1797.

[404] He was created Duke of Clarence and St. Andrews in 1789 and was Admiral of the Fleet escorting Louis XVIII on his return to France in 1814. He became Lord High Admiral in 1827, and reigned as William IV from 1830 to 1837.

[405] This was Charles Abbott (1762-1832) first Lord Tenterden. He succeeded Lord Ellenborough as Chief Justice (1818) and was raised to the peerage in 1827. He was a strong Tory and opposed the Catholic Relief Bill, the Reform Bill, and the abolition of the death penalty for forgery.

[406] Edward Law (1750-1818), first Baron Ellenborough. He was chief counsel for Warren Hastings, and his famous speech in defense of his client is well known. He became Chief Justice and was raised to the peerage in 1802. He opposed all efforts to modernize the criminal code, insisting upon the reactionary principle of new death penalties.

[407] Edmund Law (1703-1787), Bishop of Carlisle (1768), was a good deal more liberal than his son. His Considerations on the Propriety of requiring subscription to the Articles of Faith (1774) was published anonymously. In it he asserts that not even the clergy should be required to subscribe to the thirty-nine articles.

[408] Joe Miller (1684-1738), the famous Drury Lane comedian, was so illiterate that he could not have written the Joe Miller's Jests, or the Wit's Vade-Mecum that appeared the year after his death. It was often reprinted and probably contained more or less of Miller's own jokes.

[409] The sixth duke (1766-1839) was much interested in parliamentary reform. He was a member of the Society of Friends of the People. He was for fourteen years a member of parliament (1788-1802) and was later Lord Lieutenant of Ireland (1806-1807). He afterwards gave up politics and became interested in agricultural matters.

[410] George Jeffreys (c. 1648-1689), the favorite of James II, who was active in prosecuting the Rye House conspirators. He was raised to the peerage in 1684 and held the famous "bloody assize" in the following year, being made Lord Chancellor as a result. He was imprisoned in the Tower by William III and died there.

[411] The Every Day Book, forming a Complete History of the Year, Months, and Seasons, and a perpetual Key to the Almanack, 1826-1827.

[412] The first and second editions appeared in 1820. Two others followed in 1821.

[413] The three trials of W. H., for publishing three parodies; viz the late John Wilkes' Catechism, the Political Litany, and the Sinecurists Creed; on three ex-officio informations, at Guildhall, London, ... Dec. 18, 19, & 20, 1817,... London, 1818.

[414] The Political Litany appeared in 1817.

[415] That is, Castlereagh's.

[416] The well-known caricaturist (1792-1878), then only twenty-nine years old.

[417] Robert Stewart (1769-1822) was second Marquis of Londonderry and Viscount Castlereagh. As Chief Secretary for Ireland he was largely instrumental in bringing about the union of Ireland and Great Britain. He was at the head of the war department during most of the Napoleonic wars, and was to a great extent responsible for the European coalition against the Emperor. He suicided in 1822.

[418] John Murray (1778-1843), the well-known London publisher. He refused to finish the publication of Don Juan, after the first five cantos, because of his Tory principles.

[419] Only the first two cantos appeared in 1819.

[420] Proclus (412-485), one of the greatest of the neo-Platonists, studied at Alexandria and taught philosophy at Athens. He left commentaries on Plato and on part of Euclid's Elements.

[421] Thomas Taylor (1758-1835), called "the Platonist," had a liking for mathematics, and was probably led by his interest in number mysticism to a study of neo-Platonism. He translated a number of works from the Latin and Greek, and wrote two works on theoretical arithmetic (1816, 1823).

[422] There was an earlier edition, 1788-89.

[423] Georgius Gemistus, or Georgius Pletho (Plethon), lived in the fourteenth and fifteenth centuries. He was a native of Constantinople, but spent most of his time in Greece. He devoted much time to the propagation of the Platonic philosophy, but also wrote on divinity, geography, and history.

[424] Hannah More (1745-1833), was, in her younger days, a friend of Burke, Reynolds, Dr. Johnson, and Garrick. At this time she wrote a number of poems and aspired to become a dramatist. Her Percy (1777), with a prologue and epilogue by Garrick, had a long run at Covent Garden. Somewhat later she came to believe that the playhouse was a grave public evil, and refused to attend the revival of her own play with Mrs. Siddons in the leading part. After 1789 she and her sisters devoted themselves to starting schools for poor children, teaching them religion and housework, but leaving them illiterate.

[425] These were issued at the rate of three each month,—a story, a ballad, and a Sunday tract. They were collected and published in one volume in 1795. It is said that two million copies were sold the first year. There were also editions in 1798, 1819, 1827, and 1836-37.

[426] That is, Dr. Johnson (1709-1784). The Rambler was published in 1750-1752, and was an imitation of Addison's Spectator.

[427] Dr. Moore, referred to below.

[428] Dr. John Moore (1729-1802), physician and novelist, is now best known for his Journal during a Residence in France from the beginning of August to the middle of December, 1792, a work quoted frequently by Carlyle in his French Revolution.

[429] Sir John Moore (1761-1809), Lieutenant General in the Napoleonic wars. He was killed in the battle of Corunna. The poem by Charles Wolfe (1791-1823), The Burial of Sir John Moore (1817), is well known.

[430] Referring to the novels of Thomas Love Peacock (1785-1866), who succeeded James Mill as chief examiner of the East India Company, and was in turn succeeded by John Stuart Mill.

[431] Frances Burney, Madame d'Arblay (1752-1840), married General d'Arblay, a French officer and companion of Lafayette, in 1793. She was only twenty-five when she acquired fame by her Evelina, or a Young Lady's Entrance into the World. Her Letters and Diaries appeared posthumously (1842-45).

[432] Henry Peter, Baron Brougham and Vaux (1778-1868), well known in politics, science, and letters. He was one of the founders of the Edinburgh Review, became Lord Chancellor in 1830, and took part with men like William Frend, De Morgan's father-in-law, in the establishing of London University. He was also one of the founders of the Society for the Diffusion of Useful Knowledge. He was always friendly to De Morgan, who entered the faculty of London University, whose work on geometry was published by the Society mentioned, and who was offered the degree of doctor of laws by the University of Edinburgh while Lord Brougham was Lord Rector. The Edinburgh honor was refused by De Morgan who said he "did not feel like an LL.D."

[433] Maria Edgeworth (1767-1849).

[434] Sydney Owenson (c. 1783-1859) married Sir Thomas Morgan, a well-known surgeon, in 1812. Her Irish stories were very popular with the patriots but were attacked by the Quarterly Review. The Wild Irish Girl (1806) went through seven editions in two years.

[435] 1775-1817.

[436] 1771-1832.

[437] The famous preacher (1732-1808). He was the first chairman of the Religious Tract Society. He is also known as one of the earliest advocates of vaccination, in his Cow-pock Inoculation vindicated and recommended from matters of fact, 1806.

[438] Sir Rowland Hill (1795-1879), the father of penny postage.

[439] Beilby Porteus (1731-1808), Bishop of Chester (1776) and Bishop of London (1787). He encouraged the Sunday-school movement and the dissemination of Hannah More's tracts. He was an active opponent of slavery, but also of Catholic emancipation.

[440] Henrietta Maria Bowdler (1754-1830), generally known as Mrs. Harriet Bowdler. She was the author of many religious tracts and poems. Her Poems and Essays (1786) were often reprinted. The story goes that on the appearance of her Sermons on the Doctrines and duties of Christianity (published anonymously), Bishop Porteus offered the author a living under the impression that it was written by a man.

[441] William Frend (1757-1841), whose daughter Sophia Elizabeth became De Morgan's wife (1837), was at one time a clergyman of the Established Church, but was converted to Unitarianism (1787). He came under De Morgan's definition of a true paradoxer, carrying on a zealous warfare for what he thought right. As a result of his Address to the Inhabitants of Cambridge (1787), and his efforts to have abrogated the requirement that candidates for the M.A. must subscribe to the thirty-nine articles, he was deprived of his tutorship in 1788. A little later he was banished (see De Morgan's statement in the text) from Cambridge because of his denunciation of the abuses of the Church and his condemnation of the liturgy. His eccentricity is seen in his declining to use negative quantities in the operations of algebra. He finally became an actuary at London and was prominent in radical associations. He was a mathematician of ability, having been second wrangler and having nearly attained the first place, and he was also an excellent scholar in Latin, Greek, and Hebrew.

[442] George Peacock (1791-1858), Fellow of Trinity College, Cambridge, Lowndean professor of astronomy, and Dean of Ely Cathedral (1839). His tomb may be seen at Ely where he spent the latter part of his life. He was one of the group that introduced the modern continental notation of the calculus into England, replacing the cumbersome notation of Newton, passing from "the dotage of fluxions to the deism of the calculus."

[443] Robert Simson (1687-1768); professor of mathematics at Glasgow. His restoration of Apollonius (1749) and his translation and restoration of Euclid (1756, and 1776—posthumous) are well known.

[444] Francis Maseres (1731-1824), a prominent lawyer. His mathematical works had some merit.

[445] These appeared annually from 1804 to 1822.

[446] Henry Gunning (1768-1854) was senior esquire bedell of Cambridge. The Reminiscences appeared in two volumes in 1854.

[447] John Singleton Copley, Baron Lyndhurst (1772-1863), the son of John Singleton Copley the portrait painter, was born in Boston. He was educated at Trinity College, Cambridge, and became a lawyer. He was made Lord Chancellor in 1827.

[448] Sir William Rough (c. 1772-1838), a lawyer and poet, became Chief Justice of Ceylon in 1836. He was knighted in 1837.

[449] Herbert Marsh, afterwards Bishop of Peterborough, a relation of my father.—S. E. De M.

He was born in 1757 and died in 1839. On the trial of Frend he publicly protested against testifying against a personal confidant, and was excused. He was one of the first of the English clergy to study modern higher criticism of the Bible, and amid much opposition he wrote numerous works on the subject. He was professor of theology at Cambridge (1707), Bishop of Llandaff (1816), and Bishop of Peterborough.

[450] George Butler (1774-1853), Headmaster of Harrow (1805-1829), Chancellor of Peterborough (1836), and Dean of Peterborough (1842).

[451] James Tate (1771-1843), Headmaster of Richmond School (1796-1833) and Canon of St. Paul's Cathedral (1833). He left several works on the classics.

[452] Francis Place (1771-1854), at first a journeyman breeches maker, and later a master tailor. He was a hundred years ahead of his time as a strike leader, but was not so successful as an agitator as he was as a tailor, since his shop in Charing Cross made him wealthy. He was a well-known radical, and it was largely due to his efforts that the law against the combinations of workmen was repealed in 1824. His chief work was The Principles of Population (1822).

[453] Speed (1552-1629) was a tailor until Grevil (Greville) made him independent of his trade. He was not only an historian of some merit, but a skilful cartographer. His maps of the counties were collected in the Theatre of the Empire of Great Britaine, 1611. About this same time he also published Genealogies recorded in Sacred Scripture, a work that had passed through thirty-two editions by 1640.

[454] The history of Great Britaine under the conquests of ye Romans, Saxons, Danes, and Normans.... London, 1611, folio. The second edition appeared in 1623; the third, to which De Morgan here refers, posthumously in 1632; and the fourth in 1650.

[455] William Nicolson (1655-1727) became Bishop of Carlisle in 1702, and Bishop of Derry in 1718. His chief work was the Historical Library (1696-1724), in the form of a collection of documents and chronicles. It was reprinted in 1736 and in 1776.

[456] Sir Fulk Grevil, or Fulke Greville (1554-1628), was a favorite of Queen Elizabeth, Chancellor of the Exchequer under James I, a patron of literature, and a friend of Sir Philip Sidney.

[457] See note 443 on page 197.

[458] See note 444 on page 197.

[459] See note 439 on page 193.

[460] Edward Waring (1736-1796) was Lucasian professor of mathematics at Cambridge. He published several works on analysis and curves. The work referred to was the Miscellanea Analytica de aequationibus algebraicis et curvarum proprietatibus, Cambridge, 1762.

[461] A Dissertation on the use of the Negative Sign in Algebra...; to which is added, Machin's Quadrature of the Circle, London, 1758.

[462] The paper was probably one on complex numbers, or possibly one on quaternions, in which direction as well as absolute value is involved.

[463] De Morgan quotes from one of the Latin editions. Descartes wrote in French, the title of his first edition being: Discours de la methode pour bien conduire sa raison et chercher la verite dans les sciences, plus la dioptrique, les meteores et la geometrie qui sont des essais de cette methode, Leyden, 1637, 4to.

[464] "I have observed that algebra indeed, as it is usually taught, is so restricted by definite rules and formulas of calculation, that it seems rather a confused kind of an art, by the practice of which the mind is in a certain manner disturbed and obscured, than a science by which it is cultivated and made acute."

[465] It appeared in 93 volumes, from 1758 to 1851.

[466] The principles of the doctrine of life-annuities; explained in a familiar manner ... with a variety of new tables ..., London, 1783.

[467] I suppose the one who wrote Conjectures on the physical causes of Earthquakes and Volcanoes, Dublin, 1820.

[468] Scriptores Logarithmici; or, a Collection of several curious tracts on the nature and construction of Logarithms ... together with same tracts on the Binomial Theorem ..., 6 vols., London, 1791-1807.

[469] Charles Babbage (1792-1871), whose work on the calculating machine is well known. Maseres was, it is true, ninety-two at this time, but Babbage was thirty-one instead of twenty-nine. He had already translated Lacroix's Treatise on the differential and integral calculus (1816), in collaboration with Herschel and Peacock. He was Lucasian professor of mathematics at Cambridge from 1828 to 1839.

[470] The great and new Art of weighing Vanity, or a discovery of the ignorance of the great and new artist in his pseudo-philosophical writings. The "great and new artist" was Sinclair.

[471] George Sinclair, probably a native of East Lothian, who died in 1696. He was professor of philosophy and mathematics at Glasgow, and was one of the first to use the barometer in measuring altitudes. The work to which De Morgan refers is his Hydrostaticks (1672). He was a firm believer in evil spirits, his work on the subject going through four editions: Satan's Invisible World Discovered; or, a choice collection of modern relations, proving evidently against the Saducees and Athiests of this present age, that there are Devils, Spirits, Witches, and Apparitions, Edinburgh, 1685.

[472] This was probably William Sanders, Regent of St. Leonard's College, whose Theses philosophicae appeared in 1674, and whose Elementa geometriae came out a dozen years later.

[473] Ars nova et magna gravitatis et levitatis; sive dialogorum philosophicorum libri sex de aeris vera ac reali gravitate, Rotterdam, 1669, 4to.

[474] Volume I, Nos. 1 and 2, appeared in 1803.

[475] His daughter, Mrs. De Morgan, says in her Memoir of her husband: "My father had been second wrangler in a year in which the two highest were close together, and was, as his son-in-law afterwards described him, an exceedingly clear thinker. It is possible, as Mr. De Morgan said, that this mental clearness and directness may have caused his mathematical heresy, the rejection of the use of negative quantities in algebraical operations; and it is probable that he thus deprived himself of an instrument of work, the use of which might have led him to greater eminence in the higher branches." Memoir of Augustus De Morgan, London, 1882, p. 19.

[476] "If it is not true it is a good invention." A well-known Italian proverb.

[477] See page 86, note 132.

[478] He was born at Paris in 1713, and died there in 1765.

[479] Recherches sur les courbes a double courbure, Paris, 1731. Clairaut was then only eighteen, and was in the same year made a member of the Academie des sciences. His Elemens de geometrie appeared in 1741. Meantime he had taken part in the measurement of a degree in Lapland (1736-1737). His Traite de la figure de la terre was published in 1741. The Academy of St. Petersburg awarded him a prize for his Theorie de la lune (1750). His various works on comets are well known, particularly his Theorie du mouvement des cometes (1760) in which he applied the "problem of three bodies" to Halley's comet as retarded by Jupiter and Saturn.

[480] Joseph Privat, Abbe de Molieres (1677-1742), was a priest of the Congregation of the Oratorium. In 1723 he became a professor in the College de France. He was well known as an astronomer and a mathematician, and wrote in defense of Descartes's theory of vortices (1728, 1729). He also contributed to the methods of finding prime numbers (1705).

[481] "Deserves not only to be printed, but to be admired as a marvel of imagination, of understanding, and of ability."

[482] Blaise Pascal (1623-1662), the well-known French philosopher and mathematician. He lived for some time with the Port Royalists, and defended them against the Jesuits in his Provincial Letters. Among his works are the following: Essai pour les coniques (1640); Recit de la grande experience de l'equilibre des liqueurs (1648), describing his experiment in finding altitudes by barometric readings; Histoire de la roulette (1658); Traite du triangle arithmetique (1665); Aleae geometria (1654).

[483] This proposition shows that if a hexagon is inscribed in a conic (in particular a circle) and the opposite sides are produced to meet, the three points determined by their intersections will be in the same straight line.

[484] Jacques Curabelle, Examen des Oeuvres du Sr. Desargues, Paris, 1644. He also published without date a work entitled: Foiblesse pitoyable du Sr. G. Desargues employee contre l'examen fait de ses oeuvres.

[485] See page 119, note 233.

[486] Until "this great proposition called Pascal's should see the light."

[487] The story is that his father, Etienne Pascal, did not wish him to study geometry until he was thoroughly grounded in Latin and Greek. Having heard the nature of the subject, however, he began at the age of twelve to construct figures by himself, drawing them on the floor with a piece of charcoal. When his father discovered what he was doing he was attempting to demonstrate that the sum of the angles of a triangle equals two right angles. The story is given by his sister, Mme. Perier.

[488] Sir John Wilson (1741-1793) was knighted in 1786 and became Commissioner of the Great Seal in 1792. He was a lawyer and jurist of recognized merit. He stated his theorem without proof, the first demonstration having been given by Lagrange in the Memoirs of the Berlin Academy for 1771,—Demonstration d'un theoreme nouveau concernant les nombres premiers. Euler also gave a proof in his Miscellanea Analytica (1773). Fermat's works should be consulted in connection with the early history of this theorem.

[489] He wrote, in 1760, a tract in defense of Waring, a point of whose algebra had been assailed by a Dr. Powell. Waring wrote another tract of the same date.—A. De M.

William Samuel Powell (1717-1775) was at this time a fellow of St. John's College, Cambridge. In 1765 he became Vice Chancellor of the University. Waring was a Magdalene man, and while candidate for the Lucasian professorship he circulated privately his Miscellanea Analytica. Powell attacked this in his Observations on the First Chapter of a Book called Miscellanea (1760). This attack was probably in the interest of another candidate, a man of his own college (St. John's), William Ludlam.

[490] William Paley (1743-1805) was afterwards a tutor at Christ's College, Cambridge. He never contributed anything to mathematics, but his Evidences of Christianity (1794) was long considered somewhat of a classic. He also wrote Principles of Morality and Politics (1785), and Natural Theology (1802).

[491] Edward, first Baron Thurlow (1731-1806) is known to Americans because of his strong support of the Royal prerogative during the Revolution. He was a favorite of George III, and became Lord Chancellor in 1778.

[492] George Wilson Meadley (1774-1818) published his Memoirs of ... Paley in 1809. He also published Memoirs of Algernon Sidney in 1813. He was a merchant and banker, and had traveled extensively in Europe and the East. He was a convert to unitarianism, to which sect Paley had a strong leaning.

[493] Watson (1737-1816) was a strange kind of man for a bishopric. He was professor of chemistry at Cambridge (1764) at the age of twenty-seven. It was his experiments that led to the invention of the black-bulb thermometer. He is said to have saved the government L100,000 a year by his advice on the manufacture of gunpowder. Even after he became professor of divinity at Cambridge (1771) he published four volumes of Chemical Essays (vol. I, 1781). He became Bishop of Llandaff in 1782.

[494] James Adair (died in 1798) was counsel for the defense in the trial of the publishers of the Letters of Junius (1771). As King's Serjeant he assisted in prosecuting Hardy and Horne Tooke.

[495] Morgan (1750-1833) was actuary of the Equitable Assurance Society of London (1774-1830), and it was to his great abilities that the success of that company was due at a time when other corporations of similar kind were meeting with disaster. The Royal Society awarded him a medal (1783) for a paper on Probability of Survivorship. He wrote several important works on insurance and finance.

[496] Dr. Price (1723-1791) was a non-conformist minister and a writer on ethics, economics, politics, and insurance. He was a defender of the American Revolution and a personal friend of Franklin. In 1778 Congress invited him to America to assist in the financial administration of the new republic, but he declined. His famous sermon on the French Revolution is said to have inspired Burke's Reflections on the Revolution in France.

[497] Elizabeth Gurney (1780-1845), a Quaker, who married Joseph Fry (1800), a London merchant. She was the prime mover in the Association for the Improvement of the Female Prisoners in Newgate, founded in 1817. Her influence in prison reform extended throughout Europe, and she visited the prisons of many countries in her efforts to improve the conditions of penal servitude. The friendship of Mrs. Fry with the De Morgans began in 1837. Her scheme for a female benefit society proved worthless from the actuarial standpoint, and would have been disastrous to all concerned if it had been carried out, and it was therefore fortunate that De Morgan was consulted in time. Mrs. De Morgan speaks of the consultation in these words: "My husband, who was very sensitive on such points, was charmed with Mrs. Fry's voice and manner as much as by the simple self-forgetfulness with which she entered into this business; her own very uncomfortable share of it not being felt as an element in the question, as long as she could be useful in promoting good or preventing mischief. I can see her now as she came into our room, took off her little round Quaker cap, and laying it down, went at once into the matter. 'I have followed thy advice, and I think nothing further can be done in this case; but all harm is prevented.' In the following year I had an opportunity of seeing the effect of her most musical tones. I visited her at Stratford, taking my little baby and nurse with me, to consult her on some articles on prison discipline, which I had written for a periodical. The baby—three months old—was restless, and the nurse could not quiet her, neither could I entirely, until Mrs. Fry began to read something connected with the subject of my visit, when the infant, fixing her large eyes on the reader, lay listening till she fell asleep." Memoirs, p. 91.

[498] Mrs. Fry certainly believed that the writer was the old actuary of the Equitable, when she first consulted him upon the benevolent Assurance project; but we were introduced to her by our old and dear friend Lady Noel Byron, by whom she had been long known and venerated, and who referred her to Mr. De Morgan for advice. An unusual degree of confidence in, and appreciation of each other, arose on their first meeting between the two, who had so much that was externally different, and so much that was essentially alike, in their natures.—S. E. De M.

Anne Isabella Milbanke (1792-1860) married Lord Byron in 1815, when both took the additional name of Noel, her mother's name. They were separated in 1816.

[499] An obscure writer not mentioned in the ordinary biographies.

[500] Not mentioned in the ordinary biographies, and for obvious reasons.

[501] "Before" and "after."

[502] On Bishop Wilkins see note 171 on page 100.

[503] Provision for a journey.

[504] See note 179 on page 103.

[505] Thomas Bradwardine (1290-1349), known as Doctor Profundus, proctor and professor of theology at Oxford, and afterwards Chancellor of St. Paul's and confessor to Edward III. The English ascribed their success at Crecy to his prayers.

[506] He was consecrated Archbishop of Canterbury by the Pope at Avignon, July 13, 1349, and died of the plague at London in the same year.

[507] "One paltry little year."

[508] The title is carelessly copied, as is so frequently the case in catalogues, even of the Libri class. It should read: Arithmetica thome brauardini Olivier Senant Venum exponuntur ab Oliuiario senant in vico diui Jacobi sub signo beate Barbare sedente. The colophon reads: Explicit arithmetica speculatiua thōe brauardini bn reuisa et correcta a Petro sanchez Ciruelo aragonensi mathematicas legēte Parisius, īpressa per Thomā anguelart. There were Paris editions of 1495, 1496, 1498, s. a. (c. 1500), 1502, 1504, 1505, s. a. (c. 1510), 1512, 1530, a Valencia edition of 1503, two Wittenberg editions of 1534 and 1536, and doubtless several others. The work is not "very rare," although of course no works of that period are common. See the editor's Rara Arithmetica, page 61.

[509] This is his Tractatus de proportionibus, Paris, 1495; Venice, 1505; Vienna, 1515, with other editions.

[510] The colophon of the 1495 edition reads: Et sic explicit Geometria Thome brauardini cū tractatulo de quadratura circuli bene reuisa a Petro sanchez ciruelo: operaqz Guidonis mercatoris diligētissime impresse parisi^o in cāpo gaillardi. Anno dni. 1495. die. 20, maij.

This Petro Ciruelo was born in Arragon, and died in 1560 at Salamanca. He studied mathematics and philosophy at Paris, and took the doctor's degree there. He taught at the University of Alcala and became canon of the Cathedral at Salamanca. Besides his editions of Bradwardine he wrote several works, among them the Liber arithmeticae practicae qui dicitur algorithmus (Paris, 1495) and the Cursus quatuor mathematicarum artium liberalium (Alcala, 1516).

[511] Star polygons, a subject of considerable study in the later Middle Ages. See note 35 on page 44.

[512] "A new theory that adds lustre to the fourteenth century."

[513] There is nothing in the edition of 1495 that leads to this conclusion.

[514] The full title is: Nouvelle theorie des paralleles, avec un appendice contenant la maniere de perfectionner la theorie des paralleles de A. M. Legendre. The author had no standing as a scientist.

[515] Adrien Marie Legendre (1752-1833) was one of the great mathematicians of the opening of the nineteenth century. His Elements de geometrie (1794) had great influence on the geometry of the United States. His Essai sur la theorie des nombres (1798) is one of the classics upon the subject. The work to which Kircher refers is the Nouvelle theorie des paralleles (1803), in which the attempt is made to avoid using Euclid's postulate of parallels, the result being merely the substitution of another assumption that was even more unsatisfactory. The best presentations of the general theory are W. B. Frankland's Theories of Parallelism, Cambridge, 1910, and Engel and Staeckel's Die Theorie der Parallellinien von Euclid bis auf Gauss, Leipsic, 1895. Legendre published a second work on the theory the year of his death, Reflexions sur ... la theorie des paralleles (1833). His other works include the Nouvelles methodes pour la determination des orbites des cometes (1805), in which he uses the method of least squares; the Traite des fonctions elliptiques et des integrales (1827-1832), and the Exercises de calcul integral (1811, 1816, 1817).

[516] Johann Joseph Ignatz von Hoffmann (1777-1866), professor of mathematics at Aschaffenburg, published his Theorie der Parallellinien in 1801. He supplemented this by his Kritik der Parallelen-Theorie in 1807, and his Das eilfte Axiom der Elemente des Euclidis neu bewiesen in 1859. He wrote other works on mathematics, but none of his contributions was of any importance.

[517] Johann Karl Friedrich Hauff (1766-1846) was successively professor of mathematics at Marburg, director of the polytechnic school at Augsburg, professor at the Gymnasium at Cologne, and professor of mathematics and physics at Ghent. The work to which Kircher refers is his memoirs on the Euclidean Theorie der Parallelen in Hindenburg's Archiv, vol. III (1799), an article of no merit in the general theory.

[518] Wenceslaus Johann Gustav Karsten (1732-1787) was professor of logic at Rostock (1758) and Butzow (1760), and later became professor of mathematics and physics at Halle. His work on parallels is the Versuch einer voellig berichtigten Theorie der Parallellinien (1779). He also wrote a work entitled Anfangsgruende der mathematischen Wissenschaften (1780), but neither of these works was more than mediocre.

[519] Johann Christoph Schwab (not Schwal) was born in 1743 and died in 1821. He was professor at the Karlsschule at Stuttgart. De Morgan's wish was met, for the catalogues give "c. fig. 8," so that it evidently had eight illustrations instead of eight volumes. He wrote several other works on the principles of geometry, none of any importance.

[520] Gaetano Rossi of Catanzaro. This was the libretto writer (1772-1855), and hence the imperfections of the work can better be condoned. De Morgan should have given a little more of the title: Solusione esatta e regolare ... del ... problema della quadratura del circolo. There was a second edition, London, 1805.

[521] This identifies Rossi, for Josephine Grassini (1773-1850) was a well-known contralto, prima donna at Napoleon's court opera.

[522] William Spence (1783-1860) was an entomologist and economist of some standing, a fellow of the Royal Society, and one of the founders of the Entomological Society of London. The work here mentioned was a popular one, the first edition appearing in 1807, and four editions being justified in a single year. He also wrote Agriculture the Source of Britain's Wealth (1808) and Objections against the Corn Bill refuted (1815), besides a work in four volumes on entomology (1815-1826) in collaboration with William Kirby.

[523] "That used to be so, but we have changed all that."

[524] "Meet the coming disease."

[525] George Douglas (or Douglass) was a Scotch writer. He got out an edition of the Elements of Euclid in 1776, with an appendix on trigonometry and a set of tables. His work on Mathematical Tables appeared in 1809, and his Art of Drawing in Perspective, from mathematical principles, in 1810.

[526] See note 443, on page 197.

[527] John Playfair (1748-1848) was professor of mathematics (1785) and natural philosophy (1805) at the University of Edinburgh. His Elements of Geometry went through many editions.

[528] "Tell Apella" was an expression current in classical Rome to indicate incredulity and to show the contempt in which the Jew was held. Horace says: Credat Judaeus Apella, "Let Apella the Jew believe it." Our "Tell it to the marines," is a similar phrase.

[529] As De Morgan says two lines later, "No mistake is more common than the natural one of imagining that the"—University of Virginia is at Richmond. The fact is that it is not there, and that it did not exist in 1810. It was not chartered until 1819, and was not opened until 1825, and then at Charlottesville. The act establishing the Central College, from which the University of Virginia developed, was passed in 1816. The Jean Wood to whom De Morgan refers was one John Wood who was born about 1775 in Scotland and who emigrated to the United States in 1800. He published a History of the Administration of J. Adams (New York, 1802) that was suppressed by Aaron Burr. This act called forth two works, a Narrative of the Suppression, by Col. Burr, of the 'History of the Administration of John Adams' (1802), in which Wood was sustained; and the Antidote to John Wood's Poison (1802), in which he was attacked. The work referred to in the "printed circular" may have been the New theory of the diurnal rotation of the earth (Richmond, Va., 1809). Wood spent the last years of his life in Richmond, Va., making county maps. He died there in 1822. A careful search through works relating to the University of Virginia fails to show that Wood had any connection with it.

[530] There seems to be nothing to add to Dobson's biography beyond what De Morgan has so deliciously set forth.

[531] "Give to each man his due."

[532] Hester Lynch Salusbury (1741-1821), the friend of Dr. Johnson, married Henry Thrale (1763), a brewer, who died in 1781. She then married Gabriel Piozzi (1784), an Italian musician. Her Anecdotes of the late Samuel Johnson (1786) and Letters to and from Samuel Johnson (1788) are well known. She also wrote numerous essays and poems.

[533] Samuel Pike (c. 1717-1773) was an independent minister, with a chapel in London and a theological school in his house. He later became a disciple of Robert Sandeman and left the Independents for the Sandemanian church (1765). The Philosophia Sacra was first published at London in 1753. De Morgan here cites the second edition.

[534] Pike had been dead over forty years when Kittle published this second edition. Kittle had already published a couple of works: King Solomon's portraiture of Old Age (Edinburgh, 1813), and Critical and Practical Lectures on the Apocalyptical Epistles to the Seven Churches of Asia Minor (London, 1814).

[535] See note 334, on page 152.

[536] William Stukely (1687-1765) was a fellow of the Royal Society and of the College of Physicians and Surgeons. He afterwards (1729) entered the Church. He was prominent as an antiquary, especially in the study of the Roman and Druidic remains of Great Britain. He was the author of numerous works, chiefly on paleography.

[537] William Jones (1726-1800), who should not be confused with his namesake who is mentioned in note 281 on page 135. He was a lifelong friend of Bishop Horne, and his vicarage at Nayland was a meeting place of an influential group of High Churchmen. Besides the Physiological Disquisitions (1781) he wrote The Catholic Doctrine of the Trinity (1756) and The Grand Analogy (1793).

[538] Robert Spearman (1703-1761) was a pupil of John Hutchinson, and not only edited his works but wrote his life. He wrote a work against the Newtonian physics, entitled An Enquiry after Philosophy and Theology (Edinburgh, 1755), besides the Letters to a Friend concerning the Septuagint Translation (Edinburgh, 1759) to which De Morgan refers.

[539] A writer of no importance, at least in the minds of British biographers.

[540] Alexander Catcott (1725-1779), a theologian and geologist, wrote not only a work on the creation (1756) but a Treatise on the Deluge (1761, with a second edition in 1768). Sir Charles Lyell considered the latter work a valuable contribution to geology.

[541] James Robertson (1714-1795), professor of Hebrew at the University of Edinburgh. Probably De Morgan refers to his Grammatica Linguae Hebraeae (Edinburgh, 1758; with a second edition in 1783). He also wrote Clavis Pentateuchi (1770).

[542] Benjamin Holloway (c. 1691-1759), a geologist and theologian. He translated Woodward's Naturalis Historia Telluris, and was introduced by Woodward to Hutchinson. The work referred to by De Morgan appeared at Oxford in two volumes in 1754.

[543] His work was The Christian plan exhibited in the interpretation of Elohim: with observations upon a few other matters relative to the same subject, Oxford, 1752, with a second edition in 1755.

[544] Duncan Forbes (1685-1747) studied Oriental languages and Civil law at Leyden. He was Lord President of the Court of Sessions (1737). He wrote a number of theological works.

[545] Should be 1756.

[546] Edward Henry Bickersteth (1825-1906), bishop of Exeter (1885-1900); published The Rock of Ages; or scripture testimony to the one Eternal Godhead of the Father, and of the Son, and of the Holy Ghost at Hampstead in 1859. A second edition appeared at London in 1860.

[547] Thomas Sadler (1822-1891) took his Ph.D. at Erlangen in 1844, and became a Unitarian minister at Hampstead, where Bickersteth's work was published. Besides writing the Gloria Patri (1859), he edited Crabb Robinson's Diaries.

[548] This was his Virgil's Bucolics and the two first Satyrs of Juvenal, 1634.

[549] Possibly in his Twelve Questions or Arguments drawn out of Scripture, wherein the commonly received Opinion touching the Deity of the Holy Spirit is clearly and fully refuted, 1647. This was his first heretical work, and it was followed by a number of others that were written during the intervals in which the Puritan parliament allowed him out of prison. It was burned by the hangman as blasphemous. Biddle finally died in prison, unrepentant to the last.

[550] The first edition of the anonymous [Greek: Haireseon anastasis] (by Vicars?) appeared in 1805.

[551] Possibly by Thomas Pearne (c. 1753-1827), a fellow of St. Peter's College, Cambridge, and a Unitarian minister.

[552] Thomas Wentworth, Earl of Strafford, was borne in London in 1593, and was executed there in 1641. He was privy councilor to Charles I, and was Lord Deputy of Ireland. On account of his repressive measures to uphold the absolute power of the king he was impeached by the Long Parliament and was executed for treason. The essence of his defence is in the sentence quoted by De Morgan, to which Pym replied that taken as a whole, the acts tended to show an intention to change the government, and this was in itself treason.

[553] The name assumed by a writer who professed to give a mathematical explanation of the Trinity, see farther on.—S. E. De M.

[554] Sabellius (fl. 230 A.D.) was an early Christian of Libyan origin. He taught that Father, Son, and Holy Spirit were different names for the same person.

[555] Sir Richard Phillips was born in London in 1767 (not 1768 as stated above), and died there in 1840. He was a bookseller and printer in Leicester, where he also edited a radical newspaper. He went to London to live in 1795 and started the Monthly Magazine there in 1796. Besides the works mentioned by De Morgan he wrote on law and economics.

[556] It was really eighteen months.

[557] While he was made sheriff in 1807 he was not knighted until the following year.

[558] James Mitchell (c. 1786-1844) was a London actuary, or rather a Scotch actuary living a good part of his life in London. Besides the work mentioned he compiled a Dictionary of Chemistry, Mineralogy, and Geology (1823), and wrote On the Plurality of Worlds (1813) and The Elements of Astronomy (1820).

[559] Richarda Smith, wife of Sir George Biddell Airy (see note 129, page 85) the astronomer. In 1835 Sir Robert Peel offered a pension of L300 a year to Airy, who requested that it be settled on his wife.

[560] Mary Fairfax (1780-1872) married as her second husband Dr. William Somerville. In 1826 she presented to the Royal Society a paper on The Magnetic Properties of the Violet Rays of the Solar Spectrum, which attracted much attention. It was for her Mechanism of the Heavens (1831), a popular translation of Laplace's Mecanique Celeste, that she was pensioned.

[561] Dominique Francois Jean Arago (1786-1853) the celebrated French astronomer and physicist.

[562] For there is a well-known series

1 + 1/2^2 + 1/3^2 + ... = [pi]^2/6.

If, therefore, the given series equals 1, we have

2 = 1/6 [pi]^2

or [pi]^2 = 12,

whence [pi] = 2 [root]3.

But c = [pi]d, and twice the diagonal of a cube on the diameter is 2d [root]3.

[563] There was a second edition in 1821.

[564] London, 1830.

[565] He was a resident of Chatham, and seems to have published no other works.

[566] Richard Whately (1787-1863) was, as a child, a calculating prodigy (see note 132, page 86), but lost the power as is usually the case with well-balanced minds. He was a fellow of Oriel College, Oxford, and in 1825 became principal of St. Alban Hall. He was a friend of Newman, Keble, and others who were interested in the religious questions of the day. He became archbishop of Dublin in 1831. He was for a long time known to students through his Logic (1826) and Rhetoric (1828).

[567] William King, D.C.L. (1663-1712), student at Christ Church, Oxford, and celebrated as a wit and scholar. His Dialogues of the Dead (1699) is a satirical attack on Bentley.

[568] Thomas Ebrington (1760-1835) was a fellow of Trinity College, Dublin, and taught divinity, mathematics, and natural philosophy there. He became provost of the college in 1811, bishop of Limerick in 1820, and bishop of Leighlin and Ferns in 1822. His edition of Euclid was reprinted a dozen times. The Reply to John Search's Considerations on the Law of Libel appeared at Dublin in 1834.

[569] Joseph Blanco White (1775-1841) was the son of an Irishman living in Spain. He was born at Seville and studied for orders there, being ordained priest in 1800. He lost his faith in the Roman Catholic Church, and gave up the ministry, escaping to England at the time of the French invasion. At London he edited Espanol, a patriotic journal extensively circulated in Spain, and for this service he was pensioned after the expulsion of the French. He then studied at Oriel College, Oxford, and became intimate with men like Whately, Newman, and Keble. In 1835 he became a Unitarian. Among his theological writings is his Evidences against Catholicism (1825). The "rejoinder" to which De Morgan refers consisted of two letters: The law of anti-religious Libel reconsidered (Dublin, 1834) and An Answer to some Friendly Remarks on "The Law of Anti-Religious Libel Reconsidered" (Dublin, 1834).

[570] The work was translated from the French.

[571] J. Hoene Wronski (1778-1853) served, while yet a mere boy, as an artillery officer in Kosciusko's army (1791-1794). He was imprisoned after the battle of Maciejowice. He afterwards lived in Germany, and (after 1810) in Paris. For the bibliography of his works see S. Dickstein's article in the Bibliotheca Mathematica, vol. VI (2), page 48.

[572] Perhaps referring to his Introduction a la philosophie des mathematiques (1811).

[573] Read "equation of the."

[574] Thomas Young (1773-1829), physician and physicist, sometimes called the founder of physiological optics. He seems to have initiated the theory of color blindness that was later developed by Helmholtz. The attack referred to was because of his connection with the Board of Longitude, he having been made (1818) superintendent of the Nautical Almanac and secretary of the Board. He opposed introducing into the Nautical Almanac anything not immediately useful to navigation, and this antagonized many scientists.

[575] Isaac Milner (1750-1820) was professor of natural philosophy at Cambridge (1783) and later became, as De Morgan states, president of Queens' College (1788). In 1791 he became dean of Carlisle, and in 1798 Lucasian professor of mathematics. His chief interest was in chemistry and physics, but he contributed nothing of importance to these sciences or to mathematics.

[576] Thomas Perronet Thompson (1783-1869), fellow of Queens' College, Cambridge, saw service in Spain and India, but after 1822 lived in England. He became major general in 1854, and general in 1868. Besides some works on economics and politics he wrote a Geometry without Axioms (1830) that De Morgan includes later on in his Budget. In it Thompson endeavored to prove the parallel postulate.

[577] De Morgan's father-in-law. See note 441, page 196.

[578] Johann Friedrich Herbart (1776-1841), successor of Kant as professor of philosophy at Koenigsberg (1809-1833), where he established a school of pedagogy. From 1833 until his death he was professor of philosophy at Goettingen. The title of the pamphlet is: De Attentionis mensura causisque primariis. Psychologiae principia statica et mechanica exemplo illustraturus.... Regiomonti,... 1822. The formulas in question are given on pages 15 and 17, and De Morgan has omitted the preliminary steps, which are, for the first one:

[beta] ([phi] - z) [delta]t = [delta]z

unde [beta]t= Const / ([phi] - z).

Pro t = 0 etiam z = 0; hinc [beta]t = log [phi]/([phi] - z).

z = [phi] (1 - [epsilon]^{-[beta]t});

et [delta]z/[delta]t = [beta][phi][epsilon]^{-[beta]t}

These are, however, quite elementary as compared with other portions of the theory.

[579] See note 371, page 168.

[580] William Law (1686-1761) was a clergyman, a fellow of Emanuel College, Cambridge, and in later life a convert to Behmen's philosophy. He was so free in his charities that the village in which he lived became so infested by beggars that he was urged by the citizens to leave. He wrote A serious call to a devout and holy life (1728).

[581] He was a curate at Cheshunt, and wrote the Spiritual voice to the Christian Church and to the Jews (London, 1760), A second warning to the world by the Spirit of Prophecy (London, 1760), and Signs of the Times; or a Voice to Babylon (London, 1773).

[582] His real name was Thomas Vaughan (1622-1666). He was a fellow of Jesus College, Oxford, taking orders, but was deprived of his living on account of drunkenness. He became a mystic philosopher and gave attention to alchemy. His works had a large circulation, particularly on the continent. He wrote Magia Adamica (London, 1650), Euphrates; or the Waters of the East (London, 1655), and The Chymist's key to shut, and to open; or the True Doctrine of Corruption and Generation (London, 1657).

[583] Emanuel Swedenborg, or Svedberg (1688-1772) the mystic. It is not commonly known to mathematicians that he was one of their guild, but he wrote on both mathematics and chemistry. Among his works are the Regelkonst eller algebra (Upsala, 1718) and the Methodus nova inveniendi longitudines locorum, terra marique, ope lunae (Amsterdam, 1721, 1727, and 1766). After 1747 he devoted his attention to mystic philosophy.

[584] Pierre Simon Laplace (1749-1827), whose Exposition du systeme du monde (1796) and Traite de mecanique celeste (1799) are well known.

[585] See note 117, page 76.

[586] John Dalton (1766-1844), who taught mathematics and physics at New College, Manchester (1793-1799) and was the first to state the law of the expansion of gases known by his name and that of Gay-Lussac. His New system of Chemical Philosophy (Vol. I, pt. i, 1808; pt. ii, 1810; vol. II, 1827) sets forth his atomic theory.

[587] Howison was a poet and philosopher. He lived in Edinburgh and was a friend of Sir Walter Scott. This work appeared in 1822.

[588] He was a shoemaker, born about 1765 at Haddiscoe, and his "astro-historical" lectures at Norwich attracted a good deal of attention at one time. He traced all geologic changes to differences in the inclination of the earth's axis to the plane of its orbit. Of the works mentioned by De Morgan the first appeared at Norwich in 1822-1823, and there was a second edition in 1824. The second appeared in 1824-1825. The fourth was Urania's Key to the Revelation; or the analyzation of the writings of the Jews..., and was first published at Norwich in 1823, there being a second edition at London in 1833. His books were evidently not a financial success, for Mackey died in an almshouse at Norwich.

[589] Godfrey Higgins (1773-1833), the archeologist, was interested in the history of religious beliefs and in practical sociology. He wrote Horae Sabbaticae (1826), The Celtic Druids (1827 and 1829), and Anacalypsis, an attempt to draw aside the veil of the Saitic Isis; or an Inquiry into the Origin of Languages, Nations, and Religions (posthumously published, 1836), and other works. See also page 274, infra.

[590] The work also appeared in French. Wirgman wrote, or at least began, two other works: Divarication of the New Testament into Doctrine and History; part I, The Four Gospels (London, 1830), and Mental Philosophy; part I, Grammar of the five senses; being the first step to infant education (London, 1838).

[591] He was born at Shandrum, County Limerick, and supported himself by teaching writing and arithmetic. He died in an almshouse at Cork.

[592] George Boole (1815-1864), professor of mathematics at Queens' College, Cork. His Laws of Thought (1854) was the first work on the algebra of logic.

[593] Oratio Grassi (1582-1654), the Jesuit who became famous for his controversy with Galileo over the theory of comets. Galileo ridiculed him in Il Saggiatore, although according to the modern view Grassi was the more nearly right. It is said that the latter's resentment led to the persecution of Galileo.

[594] De Morgan might have found much else for his satire in the letters of Walsh. He sought, in his Theory of Partial Functions, to substitute "partial equations" for the differential calculus. In his diary there is an entry: "Discovered the general solution of numerical equations of the fifth degree at 114 Evergreen Street, at the Cross of Evergreen, Cork, at nine o'clock in the forenoon of July 7th, 1844; exactly twenty-two years after the invention of the Geometry of Partial Equations, and the expulsion of the differential calculus from Mathematical Science."

[595] "It has been ordered, sir, it has been ordered."

[596] Bartholomew Prescot was a Liverpool accountant. De Morgan gives this correct spelling on page 278. He died after 1849. His Inverted Scheme of Copernicus appeared in Liverpool in 1822.

[597] Robert Taylor (1784-1844) had many more ups and downs than De Morgan mentions. He was a priest of the Church of England, but resigned his parish in 1818 after preaching against Christianity. He soon recanted and took another parish, but was dismissed by the Bishop almost immediately on the ground of heresy. As stated in the text, he was convicted of blasphemy in 1827 and was sentenced to a year's imprisonment, and again for two years on the same charge in 1831. He then married a woman who was rich in money and in years, and was thereupon sued for breach of promise by another woman. To escape paying the judgment that was rendered against him he fled to Tours where he took up surgery.

[598] Herbert Marsh, Bishop of Peterborough. See note 449 on page 199.

[599] "Argument from the prison."

[600] Richard Carlile (1790-1843), one of the leading radicals of his time. He published Hone's parodies (see note 250, page 124) after they had been suppressed, and an edition of Thomas Paine (1818). He was repeatedly imprisoned, serving nine years in all. His continued conflict with the authorities proved a good advertisement for his bookshop.

[601] Wilhelm Ludwig Christmann (1780-1835) was a protestant clergyman and teacher of mathematics. For a while he taught under Pestalozzi. Disappointed in his ambition to be professor of mathematics at Tubingen, he became a confirmed misanthrope and is said never to have left his house during the last ten years of his life. He wrote several works: Ein Wort ueber Pestalozzi und Pestalozzismus (1812); Ars cossae promota (1814); Philosophia cossica (1815); Aetas argentea cossae (1819); Ueber Tradition und Schrift, Logos und Kabbala (1829), besides the one mentioned above. The word coss in the above titles was a German name for algebra, from the Italian cosa (thing), the name for the unknown quantity. It appears in English in the early name for algebra, "the cossic art."

[602] See note 174, page 101.

[603] See note 589, page 257.

[604] He seems to have written nothing else.

[605] See note 596 on page 270. The name is here spelled correctly.

[606] Joseph Jacotot (1770-1840), the father of this Fortune Jacotot, was an infant prodigy. At nineteen he was made professor of the humanities at Dijon. He served in the army, and then became professor of mathematics at Dijon. He continued in his chair until the restoration of the Bourbons, and then fled to Louvain. It was here that he developed the method with which his name is usually connected. He wrote a Mathematiques in 1827, which went through four editions. The Epitome is by his son, Fortune.

[607] He wrote on educational topics and a Sacred History that went through several editions.

[608] "All is in all."

[609] "Know one thing and refer everything else to it," as it is often translated.

[610] A writer of no reputation.

[611] Sir John Lubbock (1803-1865), banker, scientist, publicist, astronomer, one of the versatile men of his time.

[612] See note 165, page 99.

[613] "Those about to die salute you."

[614] Georges Louis Leclerc Buffon (1707-1788), the well-known biologist. He also experimented with burning mirrors, his results appearing in his Invention des miroirs ardens pour bruler a une grande distance (1747). The reference here may be to his Resolution des problemes qui regardent le jeu du franc carreau (1733). The prominence of his Histoire naturelle (36 volumes, 1749-1788) has overshadowed the credit due to him for his translation of Newton's work on Fluxions.

[615] See page 285. This article was a supplement to No. 14 in the Athenaeum Budget.—A. De M.

[616] There are many similar series and products. Among the more interesting are the following:

[pi] 2.2.4.4.6.6.8... —— = ————————, 2 1.3.3.5.5.7.7...

[pi]-3 = 1 1 1 ——— = ——- - ——- + ——- - ..., 4 2.3.4 4.5.6 6.7.8

[pi] 1 1 1 1 1 —— = sqrt - . (1 - —- + ——- - ——- + ——- - ...), 6 3 3.3 3^2.5 3^3.7 3^4.9

[pi] 1 1 1 1 —— = 4 ( - - ——- + ——- - ——- + ...) 4 5 3.5^3 5.5^5 7.5^7

1 1 1 - ( —- - ———- + ———- - ...). 239 3.239^3 5.239^5

[617] "To a privateer, a privateer and a half."

[618] Joshua Milne (1776-1851) was actuary of the Sun Life Assurance Society. He wrote A Treatise on the Valuation of Annuities and Assurances on Lives and Survivorships; on the Construction of tables of mortality; and on the Probabilities and Expectations of Life, London, 1815. Upon the basis of the Carlisle bills of mortality of Dr. Heysham he reconstructed the mortality tables then in use and which were based upon the Northampton table of Dr. Price. His work revolutionized the actuarial science of the time. In later years he devoted his attention to natural history.

[619] See note 576, page 252. He also wrote the Theory of Parallels. The proof of Euclid's axiom looked for in the properties of the equiangular spiral (London, 1840), which went through four editions, and the Theory of Parallels. The proof that the three angles of a triangle are equal to two right angles looked for in the inflation of the sphere (London, 1853), of which there were three editions.

[620] For the latest summary, see W. B. Frankland, Theories of Parallelism, an historical critique, Cambridge, 1910.

[621] Joseph Louis Lagrange (1736-1813), author of the Mecanique analytique (1788), Theorie des functions analytiques (1797), Traite de la resolution des equations numeriques de tous degres (1798), Lecons sur le calcul des fonctions (1806), and many memoirs. Although born in Turin and spending twenty of his best years in Germany, he is commonly looked upon as the great leader of French mathematicians. The last twenty-seven years of his life were spent in Paris, and his remarkable productivity continued to the time of his death. His genius in the theory of numbers was probably never excelled except by Fermat. He received very high honors at the hands of Napoleon and was on the first staff of the Ecole polytechnique (1797).

[622] "I shall have to think it over again."

[623] Henry Goulburn (1784-1856) held various government posts. He was under-secretary for war and the colonies (1813), commissioner to negotiate peace with America (1814), chief secretary to the Lord Lieutenant of Ireland (1821), and several times Chancellor of the Exchequer. On the occasion mentioned by De Morgan he was standing for parliament, and was successful.

[624] On Drinkwater Bethune see note 165, page 99.

[625] Charles Henry Cooper (1808-1866) was a biographer and antiquary. He was town clerk of Cambridge (1849-1866) and wrote the Annals of Cambridge (1842-1853). His Memorials of Cambridge (1874) appeared after his death. Thompson Cooper was his son, and the two collaborated in the Athenae Cantabrigiensis (1858).

[626] William Yates Peel (1789-1858) was a brother of Sir Robert Peel, he whose name degenerated into the familiar title of the London "Bobby" or "Peeler." Yates Peel was a member of parliament almost continuously from 1817 to 1852. He represented Cambridge at Westminster from 1831 to 1835.

[627] Henry John Temple, third Viscount of Palmerston (1784-1865), was member for Cambridge in 1811, 1818, 1820, 1826 (defeating Goulburn), and 1830. He failed of reelection in 1831 because of his advocacy of reform. This must have been the time when Goulburn defeated him. He was Foreign Secretary (1827) and Secretary of State for Foreign Affairs (1830-1841, and 1846-1851). It is said of him that he "created Belgium, saved Portugal and Spain from absolutism, rescued Turkey from Russia and the highway to India from France." He was Prime Minister almost continuously from 1855 to 1865, a period covering the Indian Mutiny and the American Civil War.

[628] William Cavendish, seventh Duke of Devonshire (1808-1891). He was member for Cambridge from 1829 to 1831, but was defeated in 1831 because he had favored parliamentary reform. He became Earl of Burlington in 1834, and Duke of Devonshire in 1858. He was much interested in the promotion of railroads and in the iron and steel industries.

[629] Richard Sheepshanks (1794-1855) was a brother of John Sheepshanks the benefactor of art. (See note 314, p. 147.) He was a fellow of Trinity College, Cambridge, a fellow of the Royal Society and secretary of the Astronomical Society. Babbage (See note 469, p. 207) suspected him of advising against the government support of his calculating machine and attacked him severely in his Exposition of 1851, in the chapter on The Intrigues of Science. Babbage also showed that Sheepshanks got an astronomical instrument of French make through the custom house by having Troughton's (See note 332, page 152) name engraved on it. Sheepshanks admitted this second charge, but wrote a Letter in Reply to the Calumnies of Mr. Babbage, which was published in 1854. He had a highly controversial nature.

[630] See note 469, page 207. The work referred to is Passages from the Life of a Philosopher, London, 1864.

[631] Drinkwater Bethune. See note 165, page 99.

[632] Simeon-Denis Poisson (1781-1840) was professor of calculus and mechanics at the Ecole polytechnique. He was made a baron by Napoleon, and was raised to the peerage in 1837. His chief works are the Traite de mecanique (1811) and the Traite mathematique de la chaleur (1835).

[633] "As to M. Poisson, I really wish I had a thousandth part of his mathematical knowledge that I might prove my system to the incredulous."

[634] This list includes most of the works of Antoine-Louis-Guenard Demonville. There was also the Nouveau systeme du monde ... et hypotheses conformes aux experiences sur les vents, sur la lumiere et sur le fluide electro-magnetique, Paris, 1830.

[635] Paris, 1835.

[636] Paris, 1833.

[637] The second part appeared in 1837. There were also editions in 1850 and 1852, and one edition appeared without date.

[638] Paris, 1842.

[639] Parsey also wrote The Art of Miniature Painting on Ivory (1831), Perspective Rectified (1836), and The Science of Vision (1840), the third being a revision of the second.

[640] William Ritchie (1790-1837) was a physicist who had studied at Paris under Biot and Gay-Lussac. He contributed several papers on electricity, heat, and elasticity, and was looked upon as a good experimenter. Besides the geometry he wrote the Principles of the Differential and Integral Calculus (1836).

[641] Alfred Day (1810-1849) was a man who was about fifty years ahead of his time in his attempt to get at the logical foundations of geometry. It is true that he laid himself open to criticism, but his work was by no means bad. He also wrote A Treatise on Harmony (1849, second edition 1885), The Rotation of the Pendulum (1851), and several works on Greek and Latin Grammar.

[642] Walter Forman wrote a number of controversial tracts. His first seems to have been A plan for improving the Revenue without adding to the burdens of the people, a letter to Canning in 1813. He also wrote A New Theory of the Tides (1822). His Letter to Lord John Russell, on Lord Brougham's most extraordinary conduct; and another to Sir J. Herschel, on the application of Kepler's third law appeared in 1832.

[643] Lord John Russell (1792-1878) first Earl Russell, was one of the strongest supporters of the reform measures of the early Victorian period. He became prime minister in 1847, and again in 1865.

[644] Lauder seems never to have written anything else.

[645] See note 22, page 40.

[646] The names of Alphonso Cano de Molina, Yvon, and Robert Sara have no standing in the history of the subject beyond what would be inferred from De Morgan's remark.

[647] Claude Mydorge (1585-1647), an intimate friend of Descartes, was a dilletante in mathematics who read much but accomplished little. His Recreations mathematiques is his chief work. Boncompagni published the "Problemes de Mydorge" in his Bulletino.

[648] Claude Hardy was born towards the end of the 16th century and died at Paris in 1678. In 1625 he edited the Data Euclidis, publishing the Greek text with a Latin translation. He was a friend of Mydorge and Descartes, but an opponent of Fermat.

[649] That is, in the Bibliotheca Realis of Martin Lipen, or Lipenius (1630-1692), which appeared in six folio volumes, at Frankfort, 1675-1685.

[650] See note 29, page 43.

[651] Baldassare Boncompagni (1821-1894) was the greatest general collector of mathematical works that ever lived, possibly excepting Libri. His magnificent library was dispersed at his death. His Bulletino (1868-1887) is one of the greatest source books on the history of mathematics that we have. He also edited the works of Leonardo of Pisa.

[652] He seems to have attracted no attention since De Morgan's search, for he is not mentioned in recent bibliographies.

[653] Joseph-Louis Vincens de Mouleon de Causans was born about the beginning of the l8th century. He was a Knight of Malta, colonel in the infantry, prince of Conti, and governor of the principality of Orange. His works on geometry are the Prospectus apologetique pour la quadrature du cercle (1753), and La vraie geometrie transcendante (1754).

[654] See note 119, page 80.

[655] See note 120, page 81.

[656] Lieut. William Samuel Stratford (1791-1853), was in active service during the Napoleonic wars but retired from the army in 1815. He was first secretary of the Astronomical Society (1820) and became superintendent of the Nautical Almanac in 1831. With Francis Baily he compiled a star catalogue, and wrote on Halley's (1835-1836) and Encke's (1838) comets.

[657] See Sir J. Herschel's Astronomy, p. 369.—A. De M.

[658] Captain Ross had just stuck a bit of brass there.—A. De M.

Sir James Clark Ross (1800-1862) was a rear admiral in the British navy and an arctic and antarctic explorer of prominence. De Morgan's reference is to Ross's discovery of the magnetic pole on June 1, 1831. In 1838 he was employed by the Admiralty on a magnetic survey of the United Kingdom. He was awarded the gold medal of the geographical societies of London and Paris in 1842.

[659] John Partridge (1644-1715), the well-known astrologer and almanac maker. Although bound to a shoemaker in his early boyhood, he had acquired enough Latin at the age of eighteen to read the works of the astrologers. He then mastered Greek and Hebrew and studied medicine. In 1680 he began the publication of his almanac, the Merlinus Liberatus, a book that acquired literary celebrity largely through the witty comments upon it by such writers as Swift and Steele.

[660] See note 642 on page 296.

[661] William Woodley also published several almanacs (1838, 1839, 1840) after his rejection by the Astronomical Society in 1834.

[662] It appeared at London.

[663] The first edition appeared in 1830, also at London.

[664] See note 441, page 196.

[665] Thomas Kerigan wrote The Young Navigator's Guide to the siderial and planetary parts of Nautical Astronomy (London, 1821, second edition 1828), a work on eclipses (London, 1844), and the work on tides (London, 1847) to which De Morgan refers.

[666] Jean Sylvain Bailly, who was guillotined. See note 365, page 166.

[667] See note 670, page 309.

[668] Laurent seems to have had faint glimpses of the modern theory of matter. He is, however, unknown.

[669] See note 133, page 87.

[670] Francis Baily (1774-1844) was a London stockbroker. His interest in science in general and in astronomy in particular led to his membership in the Royal Society and to his presidency of the Astronomical Society. He wrote on interest and annuities (1808), but his chief works were on astronomy.

[671] If the story is correctly told Baily must have enjoyed his statement that Gauss was "the oldest mathematician now living." As a matter of fact he was then only 58, three years the junior of Baily himself. Gauss was born in 1777 and died in 1855, and Baily was quite right in saying that he was "generally thought to be the greatest" mathematician then living.

[672] Margaret Cooke, who married Flamsteed in 1692.

[673] John Brinkley (1763-1835), senior wrangler, first Smith's prize-man (1788), Andrews professor of astronomy at Dublin, first Astronomer Royal for Ireland (1792), F.R.S. (1803), Copley medallist, president of the Royal Society and Bishop of Cloyne. His Elements of Astronomy appeared in 1808.

[674] See note 248, page 124.

[675] See note 276, page 133.

[676] See note 352, page 161.

[677] "It becomes the doctors of the Sorbonne to dispute, the Pope to decree, and the mathematician to go to Paradise on a perpendicular line."

[678] See note 124, page 83.

[679] See note 621, page 288.

[680] Sylvain van de Weyer, who was born at Louvain in 1802. He was a jurist and statesman, holding the portfolio for foreign affairs (1831-1833), and being at one time ambassador to England.

[681] Henry Crabb Robinson (1775-1867), correspondent of the Times at Altona and in the Peninsula, and later foreign editor. He was one of the founders of the Athenaeum Club and of University College, London. He seems to have known pretty much every one of his day, and his posthumous Diary attracted attention when it appeared.

[682] Was this Whewell, who was at Trinity from 1812 to 1816 and became a fellow in 1817?

[683] Tom Cribb (1781-1848) the champion pugilist. He had worked as a coal porter and hence received his nickname, the Black Diamond.

[684] John Finleyson, or Finlayson, was born in Scotland in 1770 and died in London in 1854. He published a number of pamphlets that made a pretense to being scientific. Among his striking phrases and sentences are the statements that the stars were made "to amuse us in observing them"; that the earth is "not shaped like a garden turnip as the Newtonians make it," and that the stars are "oval-shaped immense masses of frozen water." The first edition of the work here mentioned appeared at London in 1830.

[685] Richard Brothers (1757-1824) was a native of Newfoundland. He went to London when he was about 30, and a little later set forth his claim to being a descendant of David, prince of the Hebrews, and ruler of the world. He was confined as a criminal lunatic in 1795 but was released in 1806.

[686] Charles Grey (1764-1845), second Earl Grey, Viscount Howick, was then Prime Minister. The Reform Bill was introduced and defeated in 1831. The following year, with the Royal guarantees to allow him to create peers, he finally carried the bill in spite of "the number of the beast."

[687] The letters of obscure men, the Epistolae obscurorum virorum ad venerabilem virum Magistrum Ortuinum Gratium Dauentriensem, by Joannes Crotus, Ulrich von Hutten, and others appeared at Venice about 1516.

[688] The lamentations of obscure men, the Lamentationes obscurorum virorum, non prohibete per sedem Apostolicam. Epistola D. Erasmi Roterodami: quid de obscuris sentiat, by G. Ortwinus, appeared at Cologne in 1518.

[689] The criticism was timely when De Morgan wrote it. At present it would have but little force with respect to the better class of algebras.

[690] Thomas Ignatius Maria Forster (1789-1860) was more of a man than one would infer from this satire upon his theory. He was a naturalist, astronomer, and physiologist. In 1812 he published his Researches about Atmospheric Phenomena, and seven years later (July 3, 1819) he discovered a comet. With Sir Richard Phillips he founded a Meteorological Society, but it was short lived. He declined a fellowship in the Royal Society because he disapproved of certain of its rules, so that he had a recognized standing in his day. The work mentioned by De Morgan is the second edition, the first having appeared at Frankfort on the Main in 1835 under the title, Recueil des ouvrages et des pensees d'un physicien et metaphysicien.

[691] Zadkiel, whose real name was Richard James Morrison (1795-1874), was in his early years an officer in the navy. In 1831 he began the publication of the Herald of Astrology, which was continued as Zadkiel's Almanac. His name became familiar throughout Great Britain as a result.

[692] See note 566, page 246.

[693] Sumner (1780-1862) was an Eton boy. He went to King's College, Cambridge, and was elected fellow in 1801. He took many honors, and in 1807 became M.A. He was successively Canon of Durham (1820), Bishop of Chester (1828), and Archbishop of Canterbury (1848). Although he voted for the Catholic Relief Bill (1829) and the Reform Bill (1832), he opposed the removal of Jewish disabilities.

[694] Charles Richard Sumner (1790-1874) was not only Bishop of Winchester (1827), but also Bishop of Llandaff and Dean of St. Paul's, London (1826). He lost the king's favor by voting for the Catholic Relief Bill.

[695] John Bird Sumner, brother of Charles Richard.

[696] Thomas Musgrave (1788-1860) became Fellow of Trinity in 1812, and senior proctor in 1831. He was also Dean of Bristol.

[697] Charles Thomas Longley (1794-1868) was educated at Westminster School and at Christ Church, Oxford. He became M.A. in 1818 and D.D. in 1829. Besides the bishoprics mentioned he was Bishop of Ripon (1836-1856), and before that was headmaster of Harrow (1829-1836).

[698] Thomson (1819-1890) was scholar and fellow of Queen's College, Oxford. He became chaplain to the Queen in 1859.

[699] This is worthy of the statistical psychologists of the present day.

[700] The famous Moon Hoax was written by Richard Adams Locke, who was born in New York in 1800 and died in Staten Island in 1871. He was at one time editor of the Sun, and the Hoax appeared in that journal in 1835. It was reprinted in London (1836) and Germany, and was accepted seriously by most readers. It was published in book form in New York in 1852 under the title The Moon Hoax. Locke also wrote another hoax, the Lost Manuscript of Mungo Park, but it attracted relatively little attention.

[701] It is true that Jean-Nicolas Nicollet (1756-1843) was at that time in the United States, but there does not seem to be any very tangible evidence to connect him with the story. He was secretary and librarian of the Paris observatory (1817), member of the Bureau of Longitudes (1822), and teacher of mathematics in the Lycee Louis-le-Grand. Having lost his money through speculations he left France for the United States in 1831 and became connected with the government survey of the Mississippi Valley.

[702] This was Alexis Bouvard (1767-1843), who made most of the computations for Laplace's Mecanique celeste (1793). He discovered eight new comets and calculated their orbits. In his tables of Uranus (1821) he attributed certain perturbations to the presence of an undiscovered planet, but unlike Leverrier and Adams he did not follow up this clue and thus discover Neptune.

[703] Patrick Murphy (1782-1847) awoke to find himself famous because of his natural guess that there would be very cold weather on January 20, although that is generally the season of lowest temperature. It turned out that his forecasts were partly right on 168 days and very wrong on 197 days.

[704] He seems to have written nothing else. If one wishes to enter into the subject of the mathematics of the Great Pyramid there is an extensive literature awaiting him. Richard William Howard Vyse (1784-1853) published in 1840 his Operations carried on at the Pyramids of Gizeh in 1837, and in this he made a beginning of a scientific metrical study of the subject. Charles Piazzi Smyth (1819-1900), astronomer Royal for Scotland (1845-1888) was much carried away with the number mysticism of the Great Pyramid, so much so that he published in 1864 a work entitled Our Inheritance in the Great Pyramid, in which his vagaries were set forth. Although he was then a Fellow of the Royal Society (1857), his work was so ill received that when he offered a paper on the subject it was rejected (1874) and he resigned in consequence of this action. The latest and perhaps the most scholarly of all investigators of the subject is William Matthew Flinders Petrie (born in 1853), Edwards professor of Egyptology at University College, London, whose Pyramids and Temples of Gizeh (1883) and subsequent works are justly esteemed as authorities.

[705] As De Morgan subsequently found, this name reversed becomes Oliver B...e, for Oliver Byrne, one of the odd characters among the minor mathematical writers of the middle of the last century. One of his most curious works is The first six Books of the Elements of Euclid; in which coloured diagrams and symbols are used instead of letters (1847). There is some merit in speaking of the red triangle instead of the triangle ABC, but not enough to give the method any standing. His Dual Arithmetic (1863-1867) was also a curious work.

[706] Brenan also wrote on English composition (1829), a work that went through fourteen editions by 1865; a work entitled The Foreigner's English Conjugator (1831), and a work on the national debt.

[707] See note 211, page 112.

[708] See note 592, page 261.

[709] Sir William Rowan Hamilton (1805-1865), the discoverer of quaternions (1852), was an infant prodigy, competing with Zerah Colburn as a child. He was a linguist of remarkable powers, being able, at thirteen years of age, to boast that he knew as many languages as he had lived years. When only sixteen he found an error in Laplace's Mecanique celeste. When only twenty-two he was appointed Andrews professor of astronomy, and he soon after became Astronomer Royal of Ireland. He was knighted in 1835. His earlier work was on optics, his Theory of Systems of Rays appearing in 1823. In 1827 he published a paper on the principle of Varying Action. He also wrote on dynamics.

[710] "Let him not leave the kingdom,"—a legal phrase.

[711] Probably De Morgan is referring to Johann Bernoulli III (1744-1807), who edited Lambert's Logische und philosophische Abhandlungen, Berlin, 1782. He was astronomer of the Academy of Sciences at Berlin.

[712] Jacob Bernoulli (1654-1705) was one of the two brothers who founded the famous Bernoulli family of mathematicians, the other being Johann I. His Ars conjectandi (1713), published posthumously, was the first distinct treatise on probabilities.

[713] Johann Heinrich Lambert (1728-1777) was one of the most learned men of his time. Although interested chiefly in mathematics, he wrote also on science, logic, and philosophy.

[714] Joseph Diez Gergonne (1771-1859), a soldier under Napoleon, and founder of the Annales de mathematiques (1810).

[715] Gottfried Ploucquet (1716-1790) was at first a clergyman, but afterwards became professor of logic at Tuebingen.

[716] "In the premises let the middle term be omitted; what remains indicates the conclusion."

[717] Probably Sir William Edmond Logan (1789-1875), who became so interested in geology as to be placed at the head of the geological survey of Canada (1842). The University of Montreal conferred the title LL.D. upon him, and Napoleon III gave him the cross of the Legion of Honor.

[718] "So strike that he may think himself to die."

[719] "Witticism or piece of stupidity."

[720] A very truculently unjust assertion: for Sir W. was as great a setter up of some as he was a puller down of others. His writings are a congeries of praises and blames, both cruel smart, as they say in the States. But the combined instigation of prose, rhyme, and retort would send Aristides himself to Tartarus, if it were not pretty certain that Minos would grant a stet processus under the circumstances. The first two verses are exaggerations standing on a basis of truth. The fourth verse is quite true: Sir W. H. was an Edinburgh Aristotle, with the difference of ancient and modern Athens well marked, especially the perfervidum ingenium Scotorum.—A. De M.

[721] See note 576, p. 252. There was also a Theory of Parallels that differed from these, London, 1853, second edition 1856, third edition 1856.

[722] The work was written by Robert Chambers (1802-1871), the Edinburgh publisher, a friend of Scott and of many of his contemporaries in the literary field. He published the Vestiges of the Natural History of Creation in 1844, not 1840.

[723] Everett (1784-1872) was at that time a good Wesleyan, but was expelled from the ministry in 1849 for having written Wesleyan Takings and as under suspicion for having started the Fly Sheets in 1845. In 1857 he established the United Methodist Free Church.

[724] Smith was a Primitive Methodist preacher. He also wrote an Earnest Address to the Methodists (1841) and The Wealth Question (1840?).

[725] He wrote the Nouveau traite de Balistique, Paris, 1837.

[726] Joseph Denison, known to fame only through De Morgan. See also page 353.

[727] The radical (1784?-1858), advocate of the founding of London university (1826), of medical reform (1827-1834), and of the repeal of the duties on newspapers and corn, and an ardent champion of penny postage.

[728] I. e., Roman Catholic Priest.

[729] Murphy (1806-1843) showed extraordinary powers in mathematics even before the age of thirteen. He became a fellow of Caius College, Cambridge, in 1829, dean in 1831, and examiner in mathematics in London University in 1838.

[730] See note 442, page 196.

[731] Sir John Bowring (1792-1872), the linguist, writer, and traveler, member of many learned societies and a writer of high reputation in his time. His works were not, however, of genuine merit.

[732] Joseph Hume (1777-1855) served as a surgeon with the British army in India early in the nineteenth century. He returned to England in 1808 and entered parliament as a radical in 1812. He was much interested in all reform movements.

[733] Sir Robert Harry Inglis (1786-1855), a strong Tory, known for his numerous addresses in the House of Commons rather than for any real ability.

[734] Sir Robert Peel (1788-1850) began his parliamentary career in 1809 and was twice prime minister. He was prominent in most of the great reforms of his time.

[735] See note 627, page 290.

[736] John Taylor (1781-1864) was a publisher, and published several pamphlets opposed to Peel's currency measures. De Morgan refers to his work on the Junius question. This was done early in his career, and resulted in A Discovery of the author of the Letters of Junius (1813), and The Identity of Junius with a distinguished living character established (1816), this being Sir Philip Francis.

[737] See note 665, page 308.

[738] See page 348.

[739] See note 348, page 160.

[740] Sir Nicholas Harris Nicolas (1799-1848) was a reformer in various lines,—the Record Commission, the Society of Antiquaries, and the British Museum,—and his work was not without good results.

[741] See note 98, page 69.

[742] In the Companion to the Almanac for 1845 is a paper by Prof. De Morgan, "On the Ecclesiastical Calendar," the statements of which, so far as concerns the Gregorian Calendar, are taken direct from the work of Clavius, the principal agent in the arrangement of the reformed reckoning. This was followed, in the Companion to the Almanac for 1846, by a second paper, by the same author, headed "On the Earliest Printed Almanacs," much of which is written in direct supplement to the former article.—S. E. De Morgan.

[743] It may be necessary to remind some English readers that in Latin and its derived European languages, what we call Easter is called the passover (pascha). The Quartadecimans had the name on their side: a possession which often is, in this world, nine points of the law.—A. De M.

[744] Socrates Scholasticus was born at Constantinople c. 379, and died after 439. His Historia Ecclesiastica (in Greek) covers the period from Constantine the Great to about 439, and includes the Council of Nicaea. The work was printed in Paris 1544.

[745] Theodoretus or Theodoritus was born at Antioch and died about 457. He was one of the greatest divines of the fifth century, a man of learning, piety, and judicial mind, and a champion of freedom of opinion in all religious matters.

[746] He died in 417. He was a man of great energy and of high attainments.

[747] He died in 461, having reigned as pope for twenty-one years. It was he who induced Attila to spare Rome in 452.

[748] He succeeded Leo as pope in 461, and reigned for seven years.

[749] Victorinus or Victorius Marianus seems to have been born at Limoges. He was a mathematician and astronomer, and the cycle mentioned by De Morgan is one of 532 years, a combination of the Metonic cycle of 19 years with the solar cycle of 28 years. His canon was published at Antwerp in 1633 or 1634, De doctrina temporum sive commentarius in Victorii Aquitani et aliorum canones paschales.

[750] He went to Rome about 497, and died there in 540. He wrote his Liber de paschate in 525, and it was in this work that the Christian era was first used for calendar purposes.

[751] See note 259, page 126.

[752] Johannes de Sacrobosco (Holy wood), or John of Holywood. The name was often written, without regard to its etymology, Sacrobusto. He was educated at Oxford and taught in Paris until his death (1256). He did much to make the Hindu-Arabic numerals known to European scholars.

[753] See note 36, page 44.

[754] See note 45, page 48.

[755] The Julian year is a year of the Julian Calendar, in which there is leap year every fourth year. Its average length is therefore 365 days and a quarter.—A. De M.

[756] Ugo Buoncompagno (1502-1585) was elected pope in 1572.

[757] He was a Calabrian, and as early as 1552 was professor of medicine at Perugia. In 1576 his manuscript on the reform of the calendar was presented to the Roman Curia by his brother, Antonius. The manuscript was not printed and it has not been preserved.

[758] The title of this work, which is the authority on all points of the new Calendar, is Kalendarium Gregorianum Perpetuum. Cum Privilegio Summi Pontificis Et Aliorum Principum. Romae, Ex Officina Dominici Basae. MDLXXXII. Cum Licentia Superiorum (quarto, pp. 60).—A. De M.

[759] Manuels-Roret. Theorie du Calendrier et collection de tous les Calendriers des Annees passees et futures.... Par L. B. Francoeur,... Paris, a la librairie encyclopedique de Roret, rue Hautefeuille, 10 bis. 1842. (12mo.) In this valuable manual, the 35 possible almanacs are given at length, with such preliminary tables as will enable any one to find, by mere inspection, which almanac he is to choose for any year, whether of old or new style. [1866. I may now refer to my own Book of Almanacs, for the same purpose].—A. De M.

Louis Benjamin Francoeur (1773-1849), after holding positions in the Ecole polytechnique (1804) and the Lycee Charlemagne (1805), became professor of higher algebra in the University of Paris (1809). His Cours complet des mathematiques pures was well received, and he also wrote on mechanics, astronomy, and geodesy.

[760] Albertus Pighius, or Albert Pigghe, was born at Kempen c. 1490 and died at Utrecht in 1542. He was a mathematician and a firm defender of the faith, asserting the supremacy of the Pope and attacking both Luther and Calvin. He spent some time in Rome. His greatest work was his Hierarchiae ecclesiasticae assertio (1538).

[761] This was A. F. Vogel. The work was his translation from the German edition which appeared at Leipsic the same year, Entdeckung einer numerischen General-Aufloesung aller hoeheren endlichen Gleichungen von jeder beliebigen algebraischen und transcendenten Form.

[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'Algebre Superieure, 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."