[337]Charles Hutton (1737-1823), professor of mathematics at Woolwich (1772-1807). HisMathematical Tables(1785) andMathematical and Philosophical Dictionary(1795-1796) are well known.[338]James Epps (1773-1839) contributed a number of memoirs on the use and corrections of instruments. He was assistant secretary of the Astronomical Society.[339]John Hutchinson (1674-1737) was one of the first to try to reconcile the new science of geology with Genesis. He denied the Newtonian hypothesis as dangerous to religion, and because it necessitated a vacuum. He was a mystic in his interpretation of the Scriptures, and created a sect that went under the name of Hutchinsonians.[340]John Rowning, a Lincolnshire rector, died in 1771. He wrote on physics, and published a memoir onA machine for finding the roots of equations universally(1770).[341]It is always difficult to sanction this spelling of the name of this Jesuit father who is so often mentioned in the analytic treatment of conics. He was born in Ragusa in 1711, and the original spelling was Ruđer Josip Bošković. When he went to live in Italy, as professor of mathematics at Rome (1740) and at Pavia, the name was spelled Ruggiero Giuseppe Boscovich, although Boscovicci would seem to a foreigner more natural. His astronomical work was notable, and in hisDe maculis solaribus(1736) there is the first determination of the equator of a planet by observing the motion of spots on its surface. Boscovich came near having some contact with America, for he was delegated to observe in California the transit of Venus in 1755, being prevented by the dissolution of his order just at that time. He died in 1787, at Milan.[342]James Granger (1723-1776) who wrote theBiographical History of England, London, 1769. His collection of prints was remarkable, numbering some fourteen thousand.[343]He was curator of experiments for the Royal Society. He wrote a large number of books and monographs on physics. He died about 1713.[344]Lee seems to have made no impression on biographers.[345]This work appeared at London in 1852.[346]Of course this is no longer true. The most scholarly work to-day is that of Rudio,Archimedes, Huygens, Lambert, Legendre, vier Abhandlungen über die Kreismessung ... mit einer Uebersicht über die Geschichte des Problems von der Quadratur des Zirkels, von den ältesten Zeiten bis auf unsere Tage, Leipsic, 1892.[347]Joseph Jérome le François de Lalande (1732-1807), professor of astronomy in the Collège de France (1753) and director of the Paris Observatory (1761). His writings on astronomy and hisBibliographie astronomique, avec l'histoire de l'astronomie depuis 1781 jusqu'en 1802(Paris, 1803) are well known.[348]De Morgan refers to hisHistoire de l'Astronomie au 18e siècle, which appeared in 1827, five years after Delambre's death. Jean Baptiste Joseph Delambre (1749-1822) was a pupil of and a collaborator with Lalande, following his master as professor of astronomy in the Collège de France. His work on the measurements for the metric system is well known, and his four histories of astronomy,ancienne(1817),au moyen âge(1819),moderne(1821), andau 18e siècle(posthumous, 1827) are highly esteemed.[349]Jean-Joseph Rive (1730-1792), a priest who left his cure under grave charges, and a quarrelsome character. His attack on Montucla was a case of the pot calling the kettle black; for while he was a brilliant writer he was a careless bibliographer.[350]Isaac Barrow (1630-1677) was quite as well known as a theologian as he was from his Lucasian professorship of mathematics at Cambridge.[351]"Besides we can see by this that Barrow was a poor philosopher; for he believed in the immortality of the soul and in a Divinity other than universal nature."[352]TheRécréations mathématiques et physiques(Paris, 1694) of Jacques Ozanam (1640-1717) is a work that is still highly esteemed. Among various other works he wrote aDictionnaire mathématique ou Idée générale des mathématiques(1690) that was not without merit. TheRécréationswent through numerous editions (Paris, 1694, 1696, 1741, 1750, 1770, 1778, and the Montucla edition of 1790; London, 1708, the Montucla-Hutton edition of 1803 and the Riddle edition of 1840; Dublin, 1790).[353]Hendryk van Etten, thenom de plumeof Jean Leurechon (1591-1670), rector of the Jesuit college at Bar, and professor of philosophy and mathematics. He wrote on astronomy (1619) and horology (1616), and is known for hisSelecta Propositiones in tota sparsim mathematica pulcherrime propositae in solemni festo SS. Ignatii et Francesci Xaverii, 1622. The book to which De Morgan refers is hisRécréation mathématicque, composée de plusieurs problèmes plaisants et facetieux, Lyons, 1627, with an edition at Pont-à-Mousson, 1629. There were English editions published at London in 1633, 1653, and 1674, and Dutch editions in 1662 and 1672.I do not understand how De Morgan happened to miss owning the work by Claude Gaspar Bachet de Meziriac (1581-1638),Problèmes plaisans et délectables, which appeared at Lyons in 1612, 8vo, with a second edition in 1624. There was a fifth edition published at Paris in 1884.[354]His title page closes with "Paris, Chez Ch. Ant. Jombert.... M DCC LIV."This was Charles-Antoine Jombert (1712-1784), a printer and bookseller with some taste for painting and architecture. He wrote several works and edited a number of early treatises.[355]The late Professor Newcomb made the matter plain even to the non-mathematical mind, when he said that "ten decimal places are sufficient to give the circumference of the earth to the fraction of an inch, and thirty decimal places would give the circumference of the whole visible universe to a quantity imperceptible with the most powerful microscope."[356]Antinewtonianismi pars prima, in qua Newtoni de coloribus systema ex propriis principiis geometrice evertitur, et nova de coloribus theoria luculentissimis experimentis demonstrantur.... Naples, 1754;pars secunda, Naples, 1756.[357]Celestino Cominale (1722-1785) was professor of medicine at the University of Naples.[358]The work appeared in the years from 1844 to 1849.[359]There was a Vienna edition in 1758, 4to, and another in 1759, 4to. This edition is described on the title page asEditio Veneta prima ipso auctore praesente, et corrigente.[360]The first edition was entitledDe solis ac lunae defectibus libri V. P. Rogerii Josephi Boscovich ... cum ejusdem auctoris adnotationibus, London, 1760. It also appeared in Venice in 1761, and in French translation by the Abbé de Baruel in 1779, and was a work of considerable influence.[361]Paulian (1722-1802) was professor of physics at the Jesuit college at Avignon. He wrote several works, the most popular of which, theDictionnaire de physique(Avignon, 1761), went through nine editions by 1789.[362]This is correct.[363]Probably referring to the fact that Hill (1795-1879), who had done so much for postal reform, was secretary to the postmaster general (1846), and his name was a synonym for the post office directory.[364]Richard Lovett (1692-1780) was a good deal of a charlatan. He claimed to have studied electrical phenomena, and in 1758 advertised that he could effect marvelous cures, especially of sore throat, by means of electricity. Before publishing the works mentioned by De Morgan he had issued others of similar character, includingThe Subtile Medium proved(London, 1756) andThe Reviewers Reviewed(London, 1760).[365]Jean Sylvain Bailly (1736-1793), member of theAcadémie françaiseand of theAcadémie des sciences, first deputy elected to represent Paris in theEtats-généraux(1789), president of the first National Assembly, and mayor of Paris (1789-1791). For his vigor as mayor in keeping the peace, and for his manly defence of the Queen, he was guillotined. He was an astronomer of ability, but is best known for his histories of the science.[366]These were theHistoire de l'Astronomie ancienne(1775),Histoire de l'Astronomie moderne(1778-1783),Histoire de l'Astronomie indienne et orientale(1787), andLettres sur l'origine des peuples de l'Asie(1775).[367]"The sick old man of Ferney, V., a boy of a hundred years." Voltaire was born in 1694, and hence was eighty-three at this time.[368]In Palmézeaux'sVie de Bailly, in Bailly'sOuvrage Posthume(1810), M. de Sales is quoted as saying that theLettres sur l'Atlantidewere sent to Voltaire and that the latter did not approve of the theory set forth.[369]The British Museum catalogue gives two editions, 1781 and 1782.[370]A mystic and a spiritualist. His chief work was the one mentioned here.[371]Jacob Behmen, or Böhme (1575-1624), known as "the German theosophist," was founder of the sect of Boehmists, a cult allied to the Swedenborgians. He was given to the study of alchemy, and brought the vocabulary of the science into his mystic writings. His sect was revived in England in the eighteenth century through the efforts of William Law. Saint-Martin translated into French two of his Latin works under the titlesL'Aurore naissante, ou la Racine de la philosophie(1800), andLes trois principes de l'essence divine(1802). The originals had appeared nearly two hundred years earlier,—Aurorain 1612, andDe tribus principiisin 1619.[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 theBiographie Universelleand by theBritish 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'sDiameters, London, 1786.[381]This is Gabriel Mouton (1618-1694), a vicar at Lyons, who suggested as a basis for a natural system of measures themille, a minute of a degree of the meridian. This appeared in hisObservationes 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 hisTraité 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 hisMétrologie ou Traité 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 theReflections 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 entitledCommon Sense. He was a private soldier under Washington, and on his return to England after the war he publishedThe 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. HisAge 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 publishedAn historical and moral View of the Origin and Progress of the French Revolution(1790), andOriginal 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 anInquiry concerning Political Justice(1793) and a novel entitledCaleb 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 theGentleman's Magazine(1792-1826) and his works include theLiterary 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 wroteThe Rivals(1775) andThe 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 theWeekly 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 hisHistory of the Protestant Reformation(1824-1827), an attack on the prevailing Protestant opinion. He also wrote aLife 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'sEcclesiastical Researches(1790). He was a life-long friend of Charles Lamb, and in their boyhood they were schoolmates at Christ's Hospital. HisComplaints of the Poor People of England(1793) made him a worthy companion of the paradoxers above mentioned.[402]These were John Thelwall (1764-1834) whosePolitics 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 hisDiversions 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. HisConsiderations 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 theJoe Miller's Jests, or the Wit's Vade-Mecumthat 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]ThePolitical Litanyappeared 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'sElements.[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. HerPercy(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). TheRamblerwas published in 1750-1752, and was an imitation of Addison'sSpectator.[427]Dr. Moore, referred to below.[428]Dr. John Moore (1729-1802), physician and novelist, is now best known for hisJournal during a Residence in France from the beginning of August to the middle of December, 1792, a work quoted frequently by Carlyle in hisFrench 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 herEvelina, or a Young Lady's Entrance into the World. HerLetters and Diariesappeared 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 theEdinburgh 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 theQuarterly 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 hisCow-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. HerPoems and Essays(1786) were often reprinted. The story goes that on the appearance of herSermons 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 hisAddress 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 "thedotage of fluxions to thedeism 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. TheReminiscencesappeared 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 wasThe 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 theTheatre of the Empire of Great Britaine, 1611. About this same time he also publishedGenealogies 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 theHistorical 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 note443on page197.[458]See note444on page197.[459]See note439on page193.[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 theMiscellanea 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 méthode pour bien conduire sa raison et chercher la vérité dans les sciences, plus la dioptrique, les météores et la géométrie qui sont des essais de cette méthode, 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 wroteConjectures on the physical causes of Earthquakes and Volcanoes, Dublin, 1820.[468]Scriptores Logarithmici; or, a Collection of several curioustracts 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'sTreatise 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 hisHydrostaticks(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, whoseTheses philosophicaeappeared in 1674, and whoseElementa geometriaecame 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 herMemoirof 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 page86, note132.[478]He was born at Paris in 1713, and died there in 1765.[479]Recherches sur les courbes à double courbure, Paris, 1731. Clairaut was then only eighteen, and was in the same year made a member of the Académie des sciences. HisElémens de géométrieappeared in 1741. Meantime he had taken part in the measurement of a degree in Lapland (1736-1737). HisTraité de la figure de la terrewas published in 1741. The Academy of St. Petersburg awarded him a prize for hisThéorie de la lune(1750). His various works on comets are well known, particularly hisThéorie du mouvement des comètes(1760) in which he applied the "problem of three bodies" to Halley's comet as retarded by Jupiter and Saturn.[480]Joseph Privat, Abbé de Molières (1677-1742), was a priest of the Congregation of the Oratorium. In 1723 he became a professor in the Collège 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 hisProvincial Letters. Among his works are the following:Essai pour les coniques(1640);Recit de la grande expérience de l'équilibre des liqueurs(1648), describing his experiment in finding altitudes by barometric readings;Histoire de la roulette(1658);Traité du triangle arithmétique(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 Œuvres du Sr. Desargues, Paris, 1644. He also published without date a work entitled:Foiblesse pitoyable du Sr. G. Desargues employée contre l'examen fait de ses œuvres.[485]See page119, note233.[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 théorème nouveau concernant les nombres premiers. Euler also gave a proof in hisMiscellanea 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 hisMiscellanea Analytica. Powell attacked this in hisObservations 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 hisEvidences of Christianity(1794) was long considered somewhat of a classic. He also wrotePrinciples of Morality and Politics(1785), andNatural 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 hisMemoirs of ... Paleyin 1809. He also publishedMemoirs of Algernon Sidneyin 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 £100,000 a year by his advice on the manufacture of gunpowder. Even after he became professor of divinity at Cambridge (1771) he published four volumes ofChemical 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 theLetters 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 onProbability 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'sReflections 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 note171on page100.[503]Provision for a journey.[504]See note179on page103.[505]Thomas Bradwardine (1290-1349), known asDoctor 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 Crécy 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 bnreuisa 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'sRara Arithmetica, page 61.[509]This is hisTractatus 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 parisioin 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 Alcalà and became canon of the Cathedral at Salamanca. Besides his editions of Bradwardine he wrote several works, among them theLiber arithmeticae practicae qui dicitur algorithmus(Paris, 1495) and theCursus quatuor mathematicarum artium liberalium(Alcalà, 1516).[511]Star polygons, a subject of considerable study in the later Middle Ages. See note35on page44.[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 théorie des parallèles, avec un appendice contenant la manière de perfectionner la théorie des parallèles 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. HisEléments de géométrie(1794) had great influence on the geometry of the United States. HisEssai sur la théorie des nombres(1798) is one of the classics upon the subject. The work to which Kircher refers is theNouvelle théorie des parallèles(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'sTheories of Parallelism, Cambridge, 1910, and Engel and Stäckel'sDie Theorie der Parallellinien von Euclid bis auf Gauss, Leipsic, 1895. Legendre published a second work on the theory the year of his death,Réflexions sur ... la théorie des parallèles(1833). His other works include theNouvelles méthodes pour la détermination des orbites des comètes(1805), in which he uses the method of least squares; theTraité des fonctions elliptiques et des intégrales(1827-1832), and theExercises de calcul intégral(1811, 1816, 1817).
[337]Charles Hutton (1737-1823), professor of mathematics at Woolwich (1772-1807). HisMathematical Tables(1785) andMathematical and Philosophical Dictionary(1795-1796) are well known.
[338]James Epps (1773-1839) contributed a number of memoirs on the use and corrections of instruments. He was assistant secretary of the Astronomical Society.
[339]John Hutchinson (1674-1737) was one of the first to try to reconcile the new science of geology with Genesis. He denied the Newtonian hypothesis as dangerous to religion, and because it necessitated a vacuum. He was a mystic in his interpretation of the Scriptures, and created a sect that went under the name of Hutchinsonians.
[340]John Rowning, a Lincolnshire rector, died in 1771. He wrote on physics, and published a memoir onA machine for finding the roots of equations universally(1770).
[341]It is always difficult to sanction this spelling of the name of this Jesuit father who is so often mentioned in the analytic treatment of conics. He was born in Ragusa in 1711, and the original spelling was Ruđer Josip Bošković. When he went to live in Italy, as professor of mathematics at Rome (1740) and at Pavia, the name was spelled Ruggiero Giuseppe Boscovich, although Boscovicci would seem to a foreigner more natural. His astronomical work was notable, and in hisDe maculis solaribus(1736) there is the first determination of the equator of a planet by observing the motion of spots on its surface. Boscovich came near having some contact with America, for he was delegated to observe in California the transit of Venus in 1755, being prevented by the dissolution of his order just at that time. He died in 1787, at Milan.
[342]James Granger (1723-1776) who wrote theBiographical History of England, London, 1769. His collection of prints was remarkable, numbering some fourteen thousand.
[343]He was curator of experiments for the Royal Society. He wrote a large number of books and monographs on physics. He died about 1713.
[344]Lee seems to have made no impression on biographers.
[345]This work appeared at London in 1852.
[346]Of course this is no longer true. The most scholarly work to-day is that of Rudio,Archimedes, Huygens, Lambert, Legendre, vier Abhandlungen über die Kreismessung ... mit einer Uebersicht über die Geschichte des Problems von der Quadratur des Zirkels, von den ältesten Zeiten bis auf unsere Tage, Leipsic, 1892.
[347]Joseph Jérome le François de Lalande (1732-1807), professor of astronomy in the Collège de France (1753) and director of the Paris Observatory (1761). His writings on astronomy and hisBibliographie astronomique, avec l'histoire de l'astronomie depuis 1781 jusqu'en 1802(Paris, 1803) are well known.
[348]De Morgan refers to hisHistoire de l'Astronomie au 18e siècle, which appeared in 1827, five years after Delambre's death. Jean Baptiste Joseph Delambre (1749-1822) was a pupil of and a collaborator with Lalande, following his master as professor of astronomy in the Collège de France. His work on the measurements for the metric system is well known, and his four histories of astronomy,ancienne(1817),au moyen âge(1819),moderne(1821), andau 18e siècle(posthumous, 1827) are highly esteemed.
[349]Jean-Joseph Rive (1730-1792), a priest who left his cure under grave charges, and a quarrelsome character. His attack on Montucla was a case of the pot calling the kettle black; for while he was a brilliant writer he was a careless bibliographer.
[350]Isaac Barrow (1630-1677) was quite as well known as a theologian as he was from his Lucasian professorship of mathematics at Cambridge.
[351]"Besides we can see by this that Barrow was a poor philosopher; for he believed in the immortality of the soul and in a Divinity other than universal nature."
[352]TheRécréations mathématiques et physiques(Paris, 1694) of Jacques Ozanam (1640-1717) is a work that is still highly esteemed. Among various other works he wrote aDictionnaire mathématique ou Idée générale des mathématiques(1690) that was not without merit. TheRécréationswent through numerous editions (Paris, 1694, 1696, 1741, 1750, 1770, 1778, and the Montucla edition of 1790; London, 1708, the Montucla-Hutton edition of 1803 and the Riddle edition of 1840; Dublin, 1790).
[353]Hendryk van Etten, thenom de plumeof Jean Leurechon (1591-1670), rector of the Jesuit college at Bar, and professor of philosophy and mathematics. He wrote on astronomy (1619) and horology (1616), and is known for hisSelecta Propositiones in tota sparsim mathematica pulcherrime propositae in solemni festo SS. Ignatii et Francesci Xaverii, 1622. The book to which De Morgan refers is hisRécréation mathématicque, composée de plusieurs problèmes plaisants et facetieux, Lyons, 1627, with an edition at Pont-à-Mousson, 1629. There were English editions published at London in 1633, 1653, and 1674, and Dutch editions in 1662 and 1672.
I do not understand how De Morgan happened to miss owning the work by Claude Gaspar Bachet de Meziriac (1581-1638),Problèmes plaisans et délectables, which appeared at Lyons in 1612, 8vo, with a second edition in 1624. There was a fifth edition published at Paris in 1884.
[354]His title page closes with "Paris, Chez Ch. Ant. Jombert.... M DCC LIV."
This was Charles-Antoine Jombert (1712-1784), a printer and bookseller with some taste for painting and architecture. He wrote several works and edited a number of early treatises.
[355]The late Professor Newcomb made the matter plain even to the non-mathematical mind, when he said that "ten decimal places are sufficient to give the circumference of the earth to the fraction of an inch, and thirty decimal places would give the circumference of the whole visible universe to a quantity imperceptible with the most powerful microscope."
[356]Antinewtonianismi pars prima, in qua Newtoni de coloribus systema ex propriis principiis geometrice evertitur, et nova de coloribus theoria luculentissimis experimentis demonstrantur.... Naples, 1754;pars secunda, Naples, 1756.
[357]Celestino Cominale (1722-1785) was professor of medicine at the University of Naples.
[358]The work appeared in the years from 1844 to 1849.
[359]There was a Vienna edition in 1758, 4to, and another in 1759, 4to. This edition is described on the title page asEditio Veneta prima ipso auctore praesente, et corrigente.
[360]The first edition was entitledDe solis ac lunae defectibus libri V. P. Rogerii Josephi Boscovich ... cum ejusdem auctoris adnotationibus, London, 1760. It also appeared in Venice in 1761, and in French translation by the Abbé de Baruel in 1779, and was a work of considerable influence.
[361]Paulian (1722-1802) was professor of physics at the Jesuit college at Avignon. He wrote several works, the most popular of which, theDictionnaire de physique(Avignon, 1761), went through nine editions by 1789.
[362]This is correct.
[363]Probably referring to the fact that Hill (1795-1879), who had done so much for postal reform, was secretary to the postmaster general (1846), and his name was a synonym for the post office directory.
[364]Richard Lovett (1692-1780) was a good deal of a charlatan. He claimed to have studied electrical phenomena, and in 1758 advertised that he could effect marvelous cures, especially of sore throat, by means of electricity. Before publishing the works mentioned by De Morgan he had issued others of similar character, includingThe Subtile Medium proved(London, 1756) andThe Reviewers Reviewed(London, 1760).
[365]Jean Sylvain Bailly (1736-1793), member of theAcadémie françaiseand of theAcadémie des sciences, first deputy elected to represent Paris in theEtats-généraux(1789), president of the first National Assembly, and mayor of Paris (1789-1791). For his vigor as mayor in keeping the peace, and for his manly defence of the Queen, he was guillotined. He was an astronomer of ability, but is best known for his histories of the science.
[366]These were theHistoire de l'Astronomie ancienne(1775),Histoire de l'Astronomie moderne(1778-1783),Histoire de l'Astronomie indienne et orientale(1787), andLettres sur l'origine des peuples de l'Asie(1775).
[367]"The sick old man of Ferney, V., a boy of a hundred years." Voltaire was born in 1694, and hence was eighty-three at this time.
[368]In Palmézeaux'sVie de Bailly, in Bailly'sOuvrage Posthume(1810), M. de Sales is quoted as saying that theLettres sur l'Atlantidewere sent to Voltaire and that the latter did not approve of the theory set forth.
[369]The British Museum catalogue gives two editions, 1781 and 1782.
[370]A mystic and a spiritualist. His chief work was the one mentioned here.
[371]Jacob Behmen, or Böhme (1575-1624), known as "the German theosophist," was founder of the sect of Boehmists, a cult allied to the Swedenborgians. He was given to the study of alchemy, and brought the vocabulary of the science into his mystic writings. His sect was revived in England in the eighteenth century through the efforts of William Law. Saint-Martin translated into French two of his Latin works under the titlesL'Aurore naissante, ou la Racine de la philosophie(1800), andLes trois principes de l'essence divine(1802). The originals had appeared nearly two hundred years earlier,—Aurorain 1612, andDe tribus principiisin 1619.
[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 theBiographie Universelleand by theBritish 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'sDiameters, London, 1786.
[381]This is Gabriel Mouton (1618-1694), a vicar at Lyons, who suggested as a basis for a natural system of measures themille, a minute of a degree of the meridian. This appeared in hisObservationes 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 hisTraité 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 hisMétrologie ou Traité 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 theReflections 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 entitledCommon Sense. He was a private soldier under Washington, and on his return to England after the war he publishedThe 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. HisAge 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 publishedAn historical and moral View of the Origin and Progress of the French Revolution(1790), andOriginal 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 anInquiry concerning Political Justice(1793) and a novel entitledCaleb 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 theGentleman's Magazine(1792-1826) and his works include theLiterary 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 wroteThe Rivals(1775) andThe 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 theWeekly 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 hisHistory of the Protestant Reformation(1824-1827), an attack on the prevailing Protestant opinion. He also wrote aLife 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'sEcclesiastical Researches(1790). He was a life-long friend of Charles Lamb, and in their boyhood they were schoolmates at Christ's Hospital. HisComplaints of the Poor People of England(1793) made him a worthy companion of the paradoxers above mentioned.
[402]These were John Thelwall (1764-1834) whosePolitics 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 hisDiversions 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. HisConsiderations 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 theJoe Miller's Jests, or the Wit's Vade-Mecumthat 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]ThePolitical Litanyappeared 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'sElements.
[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. HerPercy(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). TheRamblerwas published in 1750-1752, and was an imitation of Addison'sSpectator.
[427]Dr. Moore, referred to below.
[428]Dr. John Moore (1729-1802), physician and novelist, is now best known for hisJournal during a Residence in France from the beginning of August to the middle of December, 1792, a work quoted frequently by Carlyle in hisFrench 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 herEvelina, or a Young Lady's Entrance into the World. HerLetters and Diariesappeared 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 theEdinburgh 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 theQuarterly 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 hisCow-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. HerPoems and Essays(1786) were often reprinted. The story goes that on the appearance of herSermons 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 hisAddress 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 "thedotage of fluxions to thedeism 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. TheReminiscencesappeared 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 wasThe 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 theTheatre of the Empire of Great Britaine, 1611. About this same time he also publishedGenealogies 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 theHistorical 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 note443on page197.
[458]See note444on page197.
[459]See note439on page193.
[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 theMiscellanea 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 méthode pour bien conduire sa raison et chercher la vérité dans les sciences, plus la dioptrique, les météores et la géométrie qui sont des essais de cette méthode, 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 wroteConjectures on the physical causes of Earthquakes and Volcanoes, Dublin, 1820.
[468]Scriptores Logarithmici; or, a Collection of several curioustracts 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'sTreatise 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 hisHydrostaticks(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, whoseTheses philosophicaeappeared in 1674, and whoseElementa geometriaecame 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 herMemoirof 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 page86, note132.
[478]He was born at Paris in 1713, and died there in 1765.
[479]Recherches sur les courbes à double courbure, Paris, 1731. Clairaut was then only eighteen, and was in the same year made a member of the Académie des sciences. HisElémens de géométrieappeared in 1741. Meantime he had taken part in the measurement of a degree in Lapland (1736-1737). HisTraité de la figure de la terrewas published in 1741. The Academy of St. Petersburg awarded him a prize for hisThéorie de la lune(1750). His various works on comets are well known, particularly hisThéorie du mouvement des comètes(1760) in which he applied the "problem of three bodies" to Halley's comet as retarded by Jupiter and Saturn.
[480]Joseph Privat, Abbé de Molières (1677-1742), was a priest of the Congregation of the Oratorium. In 1723 he became a professor in the Collège 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 hisProvincial Letters. Among his works are the following:Essai pour les coniques(1640);Recit de la grande expérience de l'équilibre des liqueurs(1648), describing his experiment in finding altitudes by barometric readings;Histoire de la roulette(1658);Traité du triangle arithmétique(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 Œuvres du Sr. Desargues, Paris, 1644. He also published without date a work entitled:Foiblesse pitoyable du Sr. G. Desargues employée contre l'examen fait de ses œuvres.
[485]See page119, note233.
[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 théorème nouveau concernant les nombres premiers. Euler also gave a proof in hisMiscellanea 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 hisMiscellanea Analytica. Powell attacked this in hisObservations 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 hisEvidences of Christianity(1794) was long considered somewhat of a classic. He also wrotePrinciples of Morality and Politics(1785), andNatural 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 hisMemoirs of ... Paleyin 1809. He also publishedMemoirs of Algernon Sidneyin 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 £100,000 a year by his advice on the manufacture of gunpowder. Even after he became professor of divinity at Cambridge (1771) he published four volumes ofChemical 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 theLetters 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 onProbability 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'sReflections 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 note171on page100.
[503]Provision for a journey.
[504]See note179on page103.
[505]Thomas Bradwardine (1290-1349), known asDoctor 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 Crécy 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 bnreuisa 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'sRara Arithmetica, page 61.
[509]This is hisTractatus 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 parisioin 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 Alcalà and became canon of the Cathedral at Salamanca. Besides his editions of Bradwardine he wrote several works, among them theLiber arithmeticae practicae qui dicitur algorithmus(Paris, 1495) and theCursus quatuor mathematicarum artium liberalium(Alcalà, 1516).
[511]Star polygons, a subject of considerable study in the later Middle Ages. See note35on page44.
[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 théorie des parallèles, avec un appendice contenant la manière de perfectionner la théorie des parallèles 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. HisEléments de géométrie(1794) had great influence on the geometry of the United States. HisEssai sur la théorie des nombres(1798) is one of the classics upon the subject. The work to which Kircher refers is theNouvelle théorie des parallèles(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'sTheories of Parallelism, Cambridge, 1910, and Engel and Stäckel'sDie Theorie der Parallellinien von Euclid bis auf Gauss, Leipsic, 1895. Legendre published a second work on the theory the year of his death,Réflexions sur ... la théorie des parallèles(1833). His other works include theNouvelles méthodes pour la détermination des orbites des comètes(1805), in which he uses the method of least squares; theTraité des fonctions elliptiques et des intégrales(1827-1832), and theExercises de calcul intégral(1811, 1816, 1817).