[516]Johann Joseph Ignatz von Hoffmann (1777-1866), professor of mathematics at Aschaffenburg, published hisTheorie der Parallellinienin 1801. He supplemented this by hisKritik der Parallelen-Theoriein 1807, and hisDas eilfte Axiom der Elemente des Euclidis neu bewiesenin 1859. He wrote other works on mathematics, but none of his contributions was of any importance.[517]Johann Karl Friedrich Hauff (1766-1846) was successively professor of mathematics at Marburg, director of the polytechnic school at Augsburg, professor at the Gymnasium at Cologne, and professor of mathematics and physics at Ghent. The work to which Kircher refers is his memoirs on the EuclideanTheorie der Parallelenin Hindenburg'sArchiv, vol. III (1799), an article of no merit in the general theory.[518]Wenceslaus Johann Gustav Karsten (1732-1787) was professor of logic at Rostock (1758) and Butzow (1760), and later became professor of mathematics and physics at Halle. His work on parallels is theVersuch einer völlig berichtigten Theorie der Parallellinien(1779). He also wrote a work entitledAnfangsgründe der mathematischen Wissenschaften(1780), but neither of these works was more than mediocre.[519]Johann Christoph Schwab (not Schwal) was born in 1743 and died in 1821. He was professor at the Karlsschule at Stuttgart. De Morgan's wish was met, for the catalogues give "c. fig. 8," so that it evidently had eight illustrations instead of eight volumes. He wrote several other works on the principles of geometry, none of any importance.[520]Gaetano Rossi of Catanzaro. This was the libretto writer (1772-1855), and hence the imperfections of the work can better be condoned. De Morgan should have given a little more of the title:Solusione esatta e regolare ... del ... problema della quadratura del circolo. There was a second edition, London, 1805.[521]This identifies Rossi, for Joséphine Grassini (1773-1850) was a well-known contralto,prima donnaat Napoleon's court opera.[522]William Spence (1783-1860) was an entomologist and economist of some standing, a fellow of the Royal Society, and one of the founders of the Entomological Society of London. The work here mentioned was a popular one, the first edition appearing in 1807, and four editions being justified in a single year. He also wroteAgriculture the Source of Britain's Wealth(1808) andObjections against the Corn Bill refuted(1815), besides a work in four volumes on entomology (1815-1826) in collaboration with William Kirby.[523]"That used to be so, but we have changed all that."[524]"Meet the coming disease."[525]George Douglas (or Douglass) was a Scotch writer. He got out an edition of theElements of Euclidin 1776, with an appendix on trigonometry and a set of tables. His work onMathematical Tablesappeared in 1809, and hisArt of Drawing in Perspective, from mathematical principles, in 1810.[526]See note443, on page197.[527]John Playfair (1748-1848) was professor of mathematics (1785) and natural philosophy (1805) at the University of Edinburgh. HisElements of Geometrywent through many editions.[528]"Tell Apella" was an expression current in classical Rome to indicate incredulity and to show the contempt in which the Jew was held. Horace says:Credat Judæus Apella, "Let Apella the Jew believe it." Our "Tell it to the marines," is a similar phrase.[529]As De Morgan says two lines later, "No mistake is more common than the natural one of imagining that the"—University of Virginia is at Richmond. The fact is that it is not there, and that it did not exist in 1810. It was not chartered until 1819, and was not opened until 1825, and then at Charlottesville. The act establishing the Central College, from which the University of Virginia developed, was passed in 1816. The Jean Wood to whom De Morgan refers was one John Wood who was born about 1775 in Scotland and who emigrated to the United States in 1800. He published aHistory of the Administration of J. Adams(New York, 1802) that was suppressed by Aaron Burr. This act called forth two works, aNarrative of the Suppression, by Col. Burr, of the 'History of the Administration of John Adams'(1802), in which Wood was sustained; and theAntidote to John Wood's Poison(1802), in which he was attacked. The work referred to in the "printed circular" may have been theNew theory of the diurnal rotation of the earth(Richmond, Va., 1809). Wood spent the last years of his life in Richmond, Va., making county maps. He died there in 1822. A careful search through works relating to the University of Virginia fails to show that Wood had any connection with it.[530]There seems to be nothing to add to Dobson's biography beyond what De Morgan has so deliciously set forth.[531]"Give to each man his due."[532]Hester Lynch Salusbury (1741-1821), the friend of Dr. Johnson, married Henry Thrale (1763), a brewer, who died in 1781. She then married Gabriel Piozzi (1784), an Italian musician. HerAnecdotes of the late Samuel Johnson(1786) andLetters to and from Samuel Johnson(1788) are well known. She also wrote numerous essays and poems.[533]Samuel Pike (c. 1717-1773) was an independent minister, with a chapel in London and a theological school in his house. He later became a disciple of Robert Sandeman and left the Independents for the Sandemanian church (1765). ThePhilosophia Sacrawas first published at London in 1753. De Morgan here cites the second edition.[534]Pike had been dead over forty years when Kittle published this second edition. Kittle had already published a couple of works:King Solomon's portraiture of Old Age(Edinburgh, 1813), andCritical and Practical Lectures on the Apocalyptical Epistles to the Seven Churches of Asia Minor(London, 1814).[535]See note334, on page152.[536]William Stukely (1687-1765) was a fellow of the Royal Society and of the College of Physicians and Surgeons. He afterwards (1729) entered the Church. He was prominent as an antiquary, especially in the study of the Roman and Druidic remains of Great Britain. He was the author of numerous works, chiefly on paleography.[537]William Jones (1726-1800), who should not be confused with his namesake who is mentioned in note281on page135. He was a lifelong friend of Bishop Horne, and his vicarage at Nayland was a meeting place of an influential group of High Churchmen. Besides thePhysiological Disquisitions(1781) he wroteThe Catholic Doctrine of the Trinity(1756) andThe Grand Analogy(1793).[538]Robert Spearman (1703-1761) was a pupil of John Hutchinson, and not only edited his works but wrote his life. He wrote a work against the Newtonian physics, entitledAn Enquiry after Philosophy and Theology(Edinburgh, 1755), besides theLetters to a Friend concerning the Septuagint Translation(Edinburgh, 1759) to which De Morgan refers.[539]A writer of no importance, at least in the minds of British biographers.[540]Alexander Catcott (1725-1779), a theologian and geologist, wrote not only a work on the creation (1756) but aTreatise on the Deluge(1761, with a second edition in 1768). Sir Charles Lyell considered the latter work a valuable contribution to geology.[541]James Robertson (1714-1795), professor of Hebrew at the University of Edinburgh. Probably De Morgan refers to hisGrammatica Linguae Hebrææ(Edinburgh, 1758; with a second edition in 1783). He also wroteClavis Pentateuchi(1770).[542]Benjamin Holloway (c. 1691-1759), a geologist and theologian. He translated Woodward'sNaturalis Historia Telluris, and was introduced by Woodward to Hutchinson. The work referred to by De Morgan appeared at Oxford in two volumes in 1754.[543]His work wasThe Christian plan exhibited in the interpretation of Elohim: with observations upon a few other matters relative to the same subject, Oxford, 1752, with a second edition in 1755.[544]Duncan Forbes (1685-1747) studied Oriental languages and Civil law at Leyden. He was Lord President of the Court of Sessions (1737). He wrote a number of theological works.[545]Should be 1756.[546]Edward Henry Bickersteth (1825-1906), bishop of Exeter (1885-1900); publishedThe Rock of Ages; or scripture testimony to the one Eternal Godhead of the Father, and of the Son, and of the Holy Ghostat Hampstead in 1859. A second edition appeared at London in 1860.[547]Thomas Sadler (1822-1891) took his Ph.D. at Erlangen in 1844, and became a Unitarian minister at Hampstead, where Bickersteth's work was published. Besides writing theGloria Patri(1859), he edited Crabb Robinson's Diaries.[548]This was hisVirgil's Bucolics and the two first Satyrs of Juvenal, 1634.[549]Possibly in hisTwelve Questions or Arguments drawn out of Scripture, wherein the commonly received Opinion touching the Deity of the Holy Spirit is clearly and fully refuted, 1647. This was his first heretical work, and it was followed by a number of others that were written during the intervals in which the Puritan parliament allowed him out of prison. It was burned by the hangman as blasphemous. Biddle finally died in prison, unrepentant to the last.[550]The first edition of theanonymousἉιρεσεων ἀναστασις(by Vicars?) appeared in 1805.[551]Possibly by Thomas Pearne (c. 1753-1827), a fellow of St. Peter's College, Cambridge, and a Unitarian minister.[552]Thomas Wentworth, Earl of Strafford, was borne in London in 1593, and was executed there in 1641. He was privy councilor to Charles I, and was Lord Deputy of Ireland. On account of his repressive measures to uphold the absolute power of the king he was impeached by the Long Parliament and was executed for treason. The essence of his defence is in the sentence quoted by De Morgan, to which Pym replied that taken as a whole, the acts tended to show an intention to change the government, and this was in itself treason.[553]The name assumed by a writer who professed to give a mathematical explanation of the Trinity, see farther on.—S. E. De M.[554]Sabellius (fl. 230 A.D.) was an early Christian of Libyan origin. He taught that Father, Son, and Holy Spirit were different names for the same person.[555]Sir Richard Phillips was born in London in 1767 (not 1768 as stated above), and died there in 1840. He was a bookseller and printer in Leicester, where he also edited a radical newspaper. He went to London to live in 1795 and started theMonthly Magazinethere in 1796. Besides the works mentioned by De Morgan he wrote on law and economics.[556]It was really eighteen months.[557]While he was made sheriff in 1807 he was not knighted until the following year.[558]James Mitchell (c. 1786-1844) was a London actuary, or rather a Scotch actuary living a good part of his life in London. Besides the work mentioned he compiled aDictionary of Chemistry, Mineralogy, and Geology(1823), and wroteOn the Plurality of Worlds(1813) andThe Elements of Astronomy(1820).[559]Richarda Smith, wife of Sir George Biddell Airy (see note129, page85) the astronomer. In 1835 Sir Robert Peel offered a pension of £300 a year to Airy, who requested that it be settled on his wife.[560]Mary Fairfax (1780-1872) married as her second husband Dr. William Somerville. In 1826 she presented to the Royal Society a paper onThe Magnetic Properties of the Violet Rays of the Solar Spectrum, which attracted much attention. It was for herMechanism of the Heavens(1831), a popular translation of Laplace'sMécanique Céleste, that she was pensioned.[561]Dominique François Jean Arago (1786-1853) the celebrated French astronomer and physicist.[562]For there is a well-known series1 + 1/22+ 1/32+ ... =π2/6.If, therefore, the given series equals 1, we have2 = 1/6π2orπ2= 12,whenceπ= 2 √3.But c =πd, and twice the diagonal of a cube on the diameter is 2d √3.[563]There was a second edition in 1821.[564]London, 1830.[565]He was a resident of Chatham, and seems to have published no other works.[566]Richard Whately (1787-1863) was, as a child, a calculating prodigy (see note132, page86), but lost the power as is usually the case with well-balanced minds. He was a fellow of Oriel College, Oxford, and in 1825 became principal of St. Alban Hall. He was a friend of Newman, Keble, and others who were interested in the religious questions of the day. He became archbishop of Dublin in 1831. He was for a long time known to students through hisLogic(1826) andRhetoric(1828).[567]William King, D.C.L. (1663-1712), student at Christ Church, Oxford, and celebrated as a wit and scholar. HisDialogues of the Dead(1699) is a satirical attack on Bentley.[568]Thomas Ebrington (1760-1835) was a fellow of Trinity College, Dublin, and taught divinity, mathematics, and natural philosophy there. He became provost of the college in 1811, bishop of Limerick in 1820, and bishop of Leighlin and Ferns in 1822. His edition of Euclid was reprinted a dozen times. TheReply to John Search's Considerations on the Law of Libelappeared at Dublin in 1834.[569]Joseph Blanco White (1775-1841) was the son of an Irishman living in Spain. He was born at Seville and studied for orders there, being ordained priest in 1800. He lost his faith in the Roman Catholic Church, and gave up the ministry, escaping to England at the time of the French invasion. At London he editedEspañol, a patriotic journal extensively circulated in Spain, and for this service he was pensioned after the expulsion of the French. He then studied at Oriel College, Oxford, and became intimate with men like Whately, Newman, and Keble. In 1835 he became a Unitarian. Among his theological writings is hisEvidences against Catholicism(1825). The "rejoinder" to which De Morgan refers consisted of two letters:The law of anti-religious Libel reconsidered(Dublin, 1834) andAn Answer to some Friendly Remarks on "The Law of Anti-Religious Libel Reconsidered"(Dublin, 1834).[570]The work was translated from the French.[571]J. Hoëné Wronski (1778-1853) served, while yet a mere boy, as an artillery officer in Kosciusko's army (1791-1794). He was imprisoned after the battle of Maciejowice. He afterwards lived in Germany, and (after 1810) in Paris. For the bibliography of his works see S. Dickstein's article in theBibliotheca Mathematica, vol. VI (2), page 48.[572]Perhaps referring to hisIntroduction à la philosophie des mathématiques(1811).[573]Read "equation of the."[574]Thomas Young (1773-1829), physician and physicist, sometimes called the founder of physiological optics. He seems to have initiated the theory of color blindness that was later developed by Helmholtz. The attack referred to was because of his connection with the Board of Longitude, he having been made (1818) superintendent of the Nautical Almanac and secretary of the Board. He opposed introducing into the Nautical Almanac anything not immediately useful to navigation, and this antagonized many scientists.[575]Isaac Milner (1750-1820) was professor of natural philosophy at Cambridge (1783) and later became, as De Morgan states, president of Queens' College (1788). In 1791 he became dean of Carlisle, and in 1798 Lucasian professor of mathematics. His chief interest was in chemistry and physics, but he contributed nothing of importance to these sciences or to mathematics.[576]Thomas Perronet Thompson (1783-1869), fellow of Queens' College, Cambridge, saw service in Spain and India, but after 1822 lived in England. He became major general in 1854, and general in 1868. Besides some works on economics and politics he wrote aGeometry without Axioms(1830) that De Morgan includes later on in hisBudget. In it Thompson endeavored to prove the parallel postulate.[577]De Morgan's father-in-law. See note441, page196.[578]Johann Friedrich Herbart (1776-1841), successor of Kant as professor of philosophy at Königsberg (1809-1833), where he established a school of pedagogy. From 1833 until his death he was professor of philosophy at Göttingen. The title of the pamphlet is:De Attentionis mensura causisque primariis. Psychologiae principia statica et mechanica exemplo illustraturus.... Regiomonti,... 1822. The formulas in question are given on pages 15 and 17, and De Morgan has omitted the preliminary steps, which are, for the first one:β(φ-z)δt=δzundeβt= Const / (φ-z).Prot= 0 etiamz= 0; hincβt= logφ/(φ-z).z=φ(1 -ε-βt);etδz/δt=βφε-βtThese are, however, quite elementary as compared with other portions of the theory.[579]See note371, page168.[580]William Law (1686-1761) was a clergyman, a fellow of Emanuel College, Cambridge, and in later life a convert to Behmen's philosophy. He was so free in his charities that the village in which he lived became so infested by beggars that he was urged by the citizens to leave. He wroteA serious call to a devout and holy life(1728).[581]He was a curate at Cheshunt, and wrote theSpiritual voice to the Christian Church and to the Jews(London, 1760),A second warning to the world by the Spirit of Prophecy(London, 1760), andSigns of the Times; or a Voice to Babylon(London, 1773).[582]His real name was Thomas Vaughan (1622-1666). He was a fellow of Jesus College, Oxford, taking orders, but was deprived of his living on account of drunkenness. He became a mystic philosopher and gave attention to alchemy. His works had a large circulation, particularly on the continent. He wroteMagia Adamica(London, 1650),Euphrates; or the Waters of the East(London, 1655), andThe Chymist's key to shut, and to open; or the True Doctrine of Corruption and Generation(London, 1657).[583]Emanuel Swedenborg, or Svedberg (1688-1772) the mystic. It is not commonly known to mathematicians that he was one of their guild, but he wrote on both mathematics and chemistry. Among his works are theRegelkonst eller algebra(Upsala, 1718) and theMethodus nova inveniendi longitudines locorum, terra marique, ope lunae(Amsterdam, 1721, 1727, and 1766). After 1747 he devoted his attention to mystic philosophy.[584]Pierre Simon Laplace (1749-1827), whoseExposition du système du monde(1796) andTraité de mécanique celeste(1799) are well known.[585]See note117, page76.[586]John Dalton (1766-1844), who taught mathematics and physics at New College, Manchester (1793-1799) and was the first to state the law of the expansion of gases known by his name and that of Gay-Lussac. HisNew system of Chemical Philosophy(Vol. I, pt. i, 1808; pt. ii, 1810; vol. II, 1827) sets forth his atomic theory.[587]Howison was a poet and philosopher. He lived in Edinburgh and was a friend of Sir Walter Scott. This work appeared in 1822.[588]He was a shoemaker, born about 1765 at Haddiscoe, and his "astro-historical" lectures at Norwich attracted a good deal of attention at one time. He traced all geologic changes to differences in the inclination of the earth's axis to the plane of its orbit. Of the works mentioned by De Morgan the first appeared at Norwich in 1822-1823, and there was a second edition in 1824. The second appeared in 1824-1825. The fourth wasUrania's Key to the Revelation; or the analyzation of the writings of the Jews..., and was first published at Norwich in 1823, there being a second edition at London in 1833. His books were evidently not a financial success, for Mackey died in an almshouse at Norwich.[589]Godfrey Higgins (1773-1833), the archeologist, was interested in the history of religious beliefs and in practical sociology. He wroteHorae Sabbaticae(1826),The Celtic Druids(1827 and 1829), andAnacalypsis, an attempt to draw aside the veil of the Saitic Isis; or an Inquiry into the Origin of Languages, Nations, and Religions(posthumously published, 1836), and other works. See also page274,infra.[590]The work also appeared in French. Wirgman wrote, or at least began, two other works:Divarication of the New Testament into Doctrine and History; part I, The Four Gospels(London, 1830), andMental Philosophy; part I, Grammar of the five senses; being the first step to infant education(London, 1838).[591]He was born at Shandrum, County Limerick, and supported himself by teaching writing and arithmetic. He died in an almshouse at Cork.[592]George Boole (1815-1864), professor of mathematics at Queens' College, Cork. HisLaws of Thought(1854) was the first work on the algebra of logic.[593]Oratio Grassi (1582-1654), the Jesuit who became famous for his controversy with Galileo over the theory of comets. Galileo ridiculed him inIl Saggiatore, although according to the modern view Grassi was the more nearly right. It is said that the latter's resentment led to the persecution of Galileo.[594]De Morgan might have found much else for his satire in the letters of Walsh. He sought, in hisTheory of Partial Functions, to substitute "partial equations" for the differential calculus. In his diary there is an entry: "Discovered the general solution of numerical equations of the fifth degree at 114 Evergreen Street, at the Cross of Evergreen, Cork, at nine o'clock in the forenoon of July 7th, 1844; exactly twenty-two years after the invention of the Geometry of Partial Equations, and the expulsion of the differential calculus from Mathematical Science."[595]"It has been ordered, sir, it has been ordered."[596]Bartholomew Prescot was a Liverpool accountant. De Morgan gives this correct spelling on page278. He died after 1849. HisInverted Scheme of Copernicusappeared in Liverpool in 1822.[597]Robert Taylor (1784-1844) had many more ups and downs than De Morgan mentions. He was a priest of the Church of England, but resigned his parish in 1818 after preaching against Christianity. He soon recanted and took another parish, but was dismissed by the Bishop almost immediately on the ground of heresy. As stated in the text, he was convicted of blasphemy in 1827 and was sentenced to a year's imprisonment, and again for two years on the same charge in 1831. He then married a woman who was rich in money and in years, and was thereupon sued for breach of promise by another woman. To escape paying the judgment that was rendered against him he fled to Tours where he took up surgery.[598]Herbert Marsh, Bishop of Peterborough. See note449on page199.[599]"Argument from the prison."[600]Richard Carlile (1790-1843), one of the leading radicals of his time. He published Hone's parodies (see note250, page124) after they had been suppressed, and an edition of Thomas Paine (1818). He was repeatedly imprisoned, serving nine years in all. His continued conflict with the authorities proved a good advertisement for his bookshop.[601]Wilhelm Ludwig Christmann (1780-1835) was a protestant clergyman and teacher of mathematics. For a while he taught under Pestalozzi. Disappointed in his ambition to be professor of mathematics at Tubingen, he became a confirmed misanthrope and is said never to have left his house during the last ten years of his life. He wrote several works:Ein Wort über Pestalozzi und Pestalozzismus(1812);Ars cossae promota(1814);Philosophia cossica(1815);Aetas argentea cossae(1819);Ueber Tradition und Schrift, Logos und Kabbala(1829), besides the one mentioned above. The wordcossin the above titles was a German name for algebra, from the Italiancosa(thing), the name for the unknown quantity. It appears in English in the early name for algebra, "the cossic art."[602]See note174, page101.[603]See note589, page257.[604]He seems to have written nothing else.[605]See note596on page270. The name is here spelled correctly.[606]Joseph Jacotot (1770-1840), the father of this Fortuné Jacotot, was an infant prodigy. At nineteen he was made professor of the humanities at Dijon. He served in the army, and then became professor of mathematics at Dijon. He continued in his chair until the restoration of the Bourbons, and then fled to Louvain. It was here that he developed the method with which his name is usually connected. He wrote aMathématiquesin 1827, which went through four editions. TheEpitoméis by his son, Fortuné.[607]He wrote on educational topics and aSacred Historythat went through several editions.[608]"All is in all."[609]"Know one thing and refer everything else to it," as it is often translated.[610]A writer of no reputation.[611]Sir John Lubbock (1803-1865), banker, scientist, publicist, astronomer, one of the versatile men of his time.[612]See note165, page99.[613]"Those about to die salute you."[614]Georges Louis Leclerc Buffon (1707-1788), the well-known biologist. He also experimented with burning mirrors, his results appearing in hisInvention des miroirs ardens pour brûler à une grande distance(1747). The reference here may be to hisResolution des problèmes qui regardent le jeu du franc carreau(1733). The prominence of hisHistoire naturelle(36 volumes, 1749-1788) has overshadowed the credit due to him for his translation of Newton's work on Fluxions.[615]See page285. This article was a supplement to No. 14 in theAthenæumBudget.—A. De M.[616]There are many similar series and products. Among the more interesting are the following:π/2=2·2·4·4·6·6·8.../1·3·3·5·5·7·7...,π-3/4=1/2·3·4-1/4·5·6+1/6·7·8-...,π/6=square root1/3·left bracket1 -1/3·3+1/32·5-1/33·7+1/34·9- ...right bracket,π/4= 4left bracket1/5-1/3·53+1/5·55-1/7·57+ ...right bracket-left bracket1/239-1/3·2393+1/5·2395- ...right bracket.[617]"To a privateer, a privateer and a half."[618]Joshua Milne (1776-1851) was actuary of the Sun Life Assurance Society. He wroteA Treatise on the Valuation of Annuities and Assurances on Lives and Survivorships; on the Construction of tables of mortality; and on the Probabilities and Expectations of Life, London, 1815. Upon the basis of the Carlisle bills of mortality of Dr. Heysham he reconstructed the mortality tables then in use and which were based upon the Northampton table of Dr. Price. His work revolutionized the actuarial science of the time. In later years he devoted his attention to natural history.[619]See note576, page252. He also wrote theTheory of Parallels. The proof of Euclid's axiom looked for in the properties of the equiangular spiral(London, 1840), which went through four editions, and theTheory of Parallels. The proof that the three angles of a triangle are equal to two right angles looked for in the inflation of the sphere(London, 1853), of which there were three editions.[620]For the latest summary, see W. B. Frankland,Theories of Parallelism, an historical critique, Cambridge, 1910.[621]Joseph Louis Lagrange (1736-1813), author of theMécanique analytique(1788),Théorie des functions analytiques(1797),Traité de la résolution des équations numériques de tous degrés(1798),Leçons sur le calcul des fonctions(1806), and many memoirs. Although born in Turin and spending twenty of his best years in Germany, he is commonly looked upon as the great leader of French mathematicians. The last twenty-seven years of his life were spent in Paris, and his remarkable productivity continued to the time of his death. His genius in the theory of numbers was probably never excelled except by Fermat. He received very high honors at the hands of Napoleon and was on the first staff of the Ecole polytechnique (1797).[622]"I shall have to think it over again."[623]Henry Goulburn (1784-1856) held various government posts. He was under-secretary for war and the colonies (1813), commissioner to negotiate peace with America (1814), chief secretary to the Lord Lieutenant of Ireland (1821), and several times Chancellor of the Exchequer. On the occasion mentioned by De Morgan he was standing for parliament, and was successful.[624]On Drinkwater Bethune see note165, page99.[625]Charles Henry Cooper (1808-1866) was a biographer and antiquary. He was town clerk of Cambridge (1849-1866) and wrote theAnnals of Cambridge(1842-1853). HisMemorials of Cambridge(1874) appeared after his death. Thompson Cooper was his son, and the two collaborated in theAthenae Cantabrigiensis(1858).[626]William Yates Peel (1789-1858) was a brother of Sir Robert Peel, he whose name degenerated into the familiar title of the London "Bobby" or "Peeler." Yates Peel was a member of parliament almost continuously from 1817 to 1852. He represented Cambridge at Westminster from 1831 to 1835.[627]Henry John Temple, third Viscount of Palmerston (1784-1865), was member for Cambridge in 1811, 1818, 1820, 1826 (defeating Goulburn), and 1830. He failed of reelection in 1831 because of his advocacy of reform. This must have been the time when Goulburn defeated him. He was Foreign Secretary (1827) and Secretary of State for Foreign Affairs (1830-1841, and 1846-1851). It is said of him that he "created Belgium, saved Portugal and Spain from absolutism, rescued Turkey from Russia and the highway to India from France." He was Prime Minister almost continuously from 1855 to 1865, a period covering the Indian Mutiny and the American Civil War.[628]William Cavendish, seventh Duke of Devonshire (1808-1891). He was member for Cambridge from 1829 to 1831, but was defeated in 1831 because he had favored parliamentary reform. He became Earl of Burlington in 1834, and Duke of Devonshire in 1858. He was much interested in the promotion of railroads and in the iron and steel industries.[629]Richard Sheepshanks (1794-1855) was a brother of John Sheepshanks the benefactor of art. (See note314, p.147.) He was a fellow of Trinity College, Cambridge, a fellow of the Royal Society and secretary of the Astronomical Society. Babbage (See note469, p.207) suspected him of advising against the government support of his calculating machine and attacked him severely in hisExposition of 1851, in the chapter onThe Intrigues of Science. Babbage also showed that Sheepshanks got an astronomical instrument of French make through the custom house by having Troughton's (See note332, page152) name engraved on it. Sheepshanks admitted this second charge, but wrote aLetter in Reply to the Calumnies of Mr. Babbage, which was published in 1854. He had a highly controversial nature.[630]See note469, page207. The work referred to isPassages from the Life of a Philosopher, London, 1864.[631]Drinkwater Bethune. See note165, page99.[632]Siméon-Denis Poisson (1781-1840) was professor of calculus and mechanics at the Ecole polytechnique. He was made a baron by Napoleon, and was raised to the peerage in 1837. His chief works are theTraité de mécanìque(1811) and theTraité mathématique de la chaleur(1835).[633]"As to M. Poisson, I really wish I had a thousandth part of his mathematical knowledge that I might prove my system to the incredulous."[634]This list includes most of the works of Antoine-Louis-Guénard Demonville. There was also theNouveau système du monde ... et hypothèses conformes aux expériences sur les vents, sur la lumière et sur le fluide électro-magnétique, Paris, 1830.[635]Paris, 1835.[636]Paris, 1833.[637]The second part appeared in 1837. There were also editions in 1850 and 1852, and one edition appeared without date.[638]Paris, 1842.[639]Parsey also wroteThe Art of Miniature Painting on Ivory(1831),Perspective Rectified(1836), andThe Science of Vision(1840), the third being a revision of the second.[640]William Ritchie (1790-1837) was a physicist who had studied at Paris under Biot and Gay-Lussac. He contributed several papers on electricity, heat, and elasticity, and was looked upon as a good experimenter. Besides the geometry he wrote thePrinciples of the Differential and Integral Calculus(1836).[641]Alfred Day (1810-1849) was a man who was about fifty years ahead of his time in his attempt to get at the logical foundations of geometry. It is true that he laid himself open to criticism, but his work was by no means bad. He also wroteA Treatise on Harmony(1849, second edition 1885),The Rotation of the Pendulum(1851), and several works on Greek and Latin Grammar.[642]Walter Forman wrote a number of controversial tracts. His first seems to have beenA plan for improving the Revenue without adding to the burdens of the people, a letter to Canning in 1813. He also wroteA New Theory of the Tides(1822). HisLetter to Lord John Russell, on Lord Brougham's most extraordinary conduct; and another to Sir J. Herschel, on the application of Kepler's third lawappeared in 1832.[643]Lord John Russell (1792-1878) first Earl Russell, was one of the strongest supporters of the reform measures of the early Victorian period. He became prime minister in 1847, and again in 1865.[644]Lauder seems never to have written anything else.[645]See note22, page40.[646]The names of Alphonso Cano de Molina, Yvon, and Robert Sara have no standing in the history of the subject beyond what would be inferred from De Morgan's remark.[647]Claude Mydorge (1585-1647), an intimate friend of Descartes, was a dilletante in mathematics who read much but accomplished little. HisRécréations mathématiquesis his chief work. Boncompagni published the "Problèmes de Mydorge" in hisBulletino.[648]Claude Hardy was born towards the end of the 16th century and died at Paris in 1678. In 1625 he edited theData Euclidis, publishing the Greek text with a Latin translation. He was a friend of Mydorge and Descartes, but an opponent of Fermat.[649]That is, in theBibliotheca Realisof Martin Lipen, or Lipenius (1630-1692), which appeared in six folio volumes, at Frankfort, 1675-1685.[650]See note29, page43.[651]Baldassare Boncompagni (1821-1894) was the greatest general collector of mathematical works that ever lived, possibly excepting Libri. His magnificent library was dispersed at his death. HisBulletino(1868-1887) is one of the greatest source books on the history of mathematics that we have. He also edited the works of Leonardo of Pisa.[652]He seems to have attracted no attention since De Morgan's search, for he is not mentioned in recent bibliographies.[653]Joseph-Louis Vincens de Mouléon de Causans was born about the beginning of the l8th century. He was a Knight of Malta, colonel in the infantry, prince of Conti, and governor of the principality of Orange. His works on geometry are theProspectus apologétique pour la quadrature du cercle(1753), andLa vraie géométrie transcendante(1754).[654]See note119, page80.[655]See note120, page81.[656]Lieut. William Samuel Stratford (1791-1853), was in active service during the Napoleonic wars but retired from the army in 1815. He was first secretary of the Astronomical Society (1820) and became superintendent of the Nautical Almanac in 1831. With Francis Baily he compiled a star catalogue, and wrote on Halley's (1835-1836) and Encke's (1838) comets.[657]See Sir J. Herschel'sAstronomy, p. 369.—A. De M.[658]Captain Ross had just stuck a bit of brass there.—A. De M.Sir James Clark Ross (1800-1862) was a rear admiral in the British navy and an arctic and antarctic explorer of prominence. De Morgan's reference is to Ross's discovery of the magnetic pole on June 1, 1831. In 1838 he was employed by the Admiralty on a magnetic survey of the United Kingdom. He was awarded the gold medal of the geographical societies of London and Paris in 1842.[659]John Partridge (1644-1715), the well-known astrologer and almanac maker. Although bound to a shoemaker in his early boyhood, he had acquired enough Latin at the age of eighteen to read the works of the astrologers. He then mastered Greek and Hebrew and studied medicine. In 1680 he began the publication of his almanac, theMerlinus Liberatus, a book that acquired literary celebrity largely through the witty comments upon it by such writers as Swift and Steele.[660]See note642on page296.[661]William Woodley also published several almanacs (1838, 1839, 1840) after his rejection by the Astronomical Society in 1834.[662]It appeared at London.[663]The first edition appeared in 1830, also at London.[664]See note441, page196.[665]Thomas Kerigan wroteThe Young Navigator's Guide to the siderial and planetary parts of Nautical Astronomy(London, 1821, second edition 1828), a work on eclipses (London, 1844), and the work on tides (London, 1847) to which De Morgan refers.[666]Jean Sylvain Bailly, who was guillotined. See note365, page166.[667]See note670, page309.[668]Laurent seems to have had faint glimpses of the modern theory of matter. He is, however, unknown.[669]See note133, page87.[670]Francis Baily (1774-1844) was a London stockbroker. His interest in science in general and in astronomy in particular led to his membership in the Royal Society and to his presidency of the Astronomical Society. He wrote on interest and annuities (1808), but his chief works were on astronomy.[671]If the story is correctly told Baily must have enjoyed his statement that Gauss was "the oldest mathematician now living." As a matter of fact he was then only 58, three years the junior of Baily himself. Gauss was born in 1777 and died in 1855, and Baily was quite right in saying that he was "generally thought to be the greatest" mathematician then living.[672]Margaret Cooke, who married Flamsteed in 1692.[673]John Brinkley (1763-1835), senior wrangler, first Smith's prize-man (1788), Andrews professor of astronomy at Dublin, first Astronomer Royal for Ireland (1792), F.R.S. (1803), Copley medallist, president of the Royal Society and Bishop of Cloyne. HisElements of Astronomyappeared in 1808.[674]See note248, page124.[675]See note276, page133.[676]See note352, page161.[677]"It becomes the doctors of the Sorbonne to dispute, the Pope to decree, and the mathematician to go to Paradise on a perpendicular line."[678]See note124, page83.[679]See note621, page288.[680]Sylvain van de Weyer, who was born at Louvain in 1802. He was a jurist and statesman, holding the portfolio for foreign affairs (1831-1833), and being at one time ambassador to England.[681]Henry Crabb Robinson (1775-1867), correspondent of theTimesat Altona and in the Peninsula, and later foreign editor. He was one of the founders of the Athenæum Club and of University College, London. He seems to have known pretty much every one of his day, and his posthumousDiaryattracted attention when it appeared.
[516]Johann Joseph Ignatz von Hoffmann (1777-1866), professor of mathematics at Aschaffenburg, published hisTheorie der Parallellinienin 1801. He supplemented this by hisKritik der Parallelen-Theoriein 1807, and hisDas eilfte Axiom der Elemente des Euclidis neu bewiesenin 1859. He wrote other works on mathematics, but none of his contributions was of any importance.
[517]Johann Karl Friedrich Hauff (1766-1846) was successively professor of mathematics at Marburg, director of the polytechnic school at Augsburg, professor at the Gymnasium at Cologne, and professor of mathematics and physics at Ghent. The work to which Kircher refers is his memoirs on the EuclideanTheorie der Parallelenin Hindenburg'sArchiv, vol. III (1799), an article of no merit in the general theory.
[518]Wenceslaus Johann Gustav Karsten (1732-1787) was professor of logic at Rostock (1758) and Butzow (1760), and later became professor of mathematics and physics at Halle. His work on parallels is theVersuch einer völlig berichtigten Theorie der Parallellinien(1779). He also wrote a work entitledAnfangsgründe der mathematischen Wissenschaften(1780), but neither of these works was more than mediocre.
[519]Johann Christoph Schwab (not Schwal) was born in 1743 and died in 1821. He was professor at the Karlsschule at Stuttgart. De Morgan's wish was met, for the catalogues give "c. fig. 8," so that it evidently had eight illustrations instead of eight volumes. He wrote several other works on the principles of geometry, none of any importance.
[520]Gaetano Rossi of Catanzaro. This was the libretto writer (1772-1855), and hence the imperfections of the work can better be condoned. De Morgan should have given a little more of the title:Solusione esatta e regolare ... del ... problema della quadratura del circolo. There was a second edition, London, 1805.
[521]This identifies Rossi, for Joséphine Grassini (1773-1850) was a well-known contralto,prima donnaat Napoleon's court opera.
[522]William Spence (1783-1860) was an entomologist and economist of some standing, a fellow of the Royal Society, and one of the founders of the Entomological Society of London. The work here mentioned was a popular one, the first edition appearing in 1807, and four editions being justified in a single year. He also wroteAgriculture the Source of Britain's Wealth(1808) andObjections against the Corn Bill refuted(1815), besides a work in four volumes on entomology (1815-1826) in collaboration with William Kirby.
[523]"That used to be so, but we have changed all that."
[524]"Meet the coming disease."
[525]George Douglas (or Douglass) was a Scotch writer. He got out an edition of theElements of Euclidin 1776, with an appendix on trigonometry and a set of tables. His work onMathematical Tablesappeared in 1809, and hisArt of Drawing in Perspective, from mathematical principles, in 1810.
[526]See note443, on page197.
[527]John Playfair (1748-1848) was professor of mathematics (1785) and natural philosophy (1805) at the University of Edinburgh. HisElements of Geometrywent through many editions.
[528]"Tell Apella" was an expression current in classical Rome to indicate incredulity and to show the contempt in which the Jew was held. Horace says:Credat Judæus Apella, "Let Apella the Jew believe it." Our "Tell it to the marines," is a similar phrase.
[529]As De Morgan says two lines later, "No mistake is more common than the natural one of imagining that the"—University of Virginia is at Richmond. The fact is that it is not there, and that it did not exist in 1810. It was not chartered until 1819, and was not opened until 1825, and then at Charlottesville. The act establishing the Central College, from which the University of Virginia developed, was passed in 1816. The Jean Wood to whom De Morgan refers was one John Wood who was born about 1775 in Scotland and who emigrated to the United States in 1800. He published aHistory of the Administration of J. Adams(New York, 1802) that was suppressed by Aaron Burr. This act called forth two works, aNarrative of the Suppression, by Col. Burr, of the 'History of the Administration of John Adams'(1802), in which Wood was sustained; and theAntidote to John Wood's Poison(1802), in which he was attacked. The work referred to in the "printed circular" may have been theNew theory of the diurnal rotation of the earth(Richmond, Va., 1809). Wood spent the last years of his life in Richmond, Va., making county maps. He died there in 1822. A careful search through works relating to the University of Virginia fails to show that Wood had any connection with it.
[530]There seems to be nothing to add to Dobson's biography beyond what De Morgan has so deliciously set forth.
[531]"Give to each man his due."
[532]Hester Lynch Salusbury (1741-1821), the friend of Dr. Johnson, married Henry Thrale (1763), a brewer, who died in 1781. She then married Gabriel Piozzi (1784), an Italian musician. HerAnecdotes of the late Samuel Johnson(1786) andLetters to and from Samuel Johnson(1788) are well known. She also wrote numerous essays and poems.
[533]Samuel Pike (c. 1717-1773) was an independent minister, with a chapel in London and a theological school in his house. He later became a disciple of Robert Sandeman and left the Independents for the Sandemanian church (1765). ThePhilosophia Sacrawas first published at London in 1753. De Morgan here cites the second edition.
[534]Pike had been dead over forty years when Kittle published this second edition. Kittle had already published a couple of works:King Solomon's portraiture of Old Age(Edinburgh, 1813), andCritical and Practical Lectures on the Apocalyptical Epistles to the Seven Churches of Asia Minor(London, 1814).
[535]See note334, on page152.
[536]William Stukely (1687-1765) was a fellow of the Royal Society and of the College of Physicians and Surgeons. He afterwards (1729) entered the Church. He was prominent as an antiquary, especially in the study of the Roman and Druidic remains of Great Britain. He was the author of numerous works, chiefly on paleography.
[537]William Jones (1726-1800), who should not be confused with his namesake who is mentioned in note281on page135. He was a lifelong friend of Bishop Horne, and his vicarage at Nayland was a meeting place of an influential group of High Churchmen. Besides thePhysiological Disquisitions(1781) he wroteThe Catholic Doctrine of the Trinity(1756) andThe Grand Analogy(1793).
[538]Robert Spearman (1703-1761) was a pupil of John Hutchinson, and not only edited his works but wrote his life. He wrote a work against the Newtonian physics, entitledAn Enquiry after Philosophy and Theology(Edinburgh, 1755), besides theLetters to a Friend concerning the Septuagint Translation(Edinburgh, 1759) to which De Morgan refers.
[539]A writer of no importance, at least in the minds of British biographers.
[540]Alexander Catcott (1725-1779), a theologian and geologist, wrote not only a work on the creation (1756) but aTreatise on the Deluge(1761, with a second edition in 1768). Sir Charles Lyell considered the latter work a valuable contribution to geology.
[541]James Robertson (1714-1795), professor of Hebrew at the University of Edinburgh. Probably De Morgan refers to hisGrammatica Linguae Hebrææ(Edinburgh, 1758; with a second edition in 1783). He also wroteClavis Pentateuchi(1770).
[542]Benjamin Holloway (c. 1691-1759), a geologist and theologian. He translated Woodward'sNaturalis Historia Telluris, and was introduced by Woodward to Hutchinson. The work referred to by De Morgan appeared at Oxford in two volumes in 1754.
[543]His work wasThe Christian plan exhibited in the interpretation of Elohim: with observations upon a few other matters relative to the same subject, Oxford, 1752, with a second edition in 1755.
[544]Duncan Forbes (1685-1747) studied Oriental languages and Civil law at Leyden. He was Lord President of the Court of Sessions (1737). He wrote a number of theological works.
[545]Should be 1756.
[546]Edward Henry Bickersteth (1825-1906), bishop of Exeter (1885-1900); publishedThe Rock of Ages; or scripture testimony to the one Eternal Godhead of the Father, and of the Son, and of the Holy Ghostat Hampstead in 1859. A second edition appeared at London in 1860.
[547]Thomas Sadler (1822-1891) took his Ph.D. at Erlangen in 1844, and became a Unitarian minister at Hampstead, where Bickersteth's work was published. Besides writing theGloria Patri(1859), he edited Crabb Robinson's Diaries.
[548]This was hisVirgil's Bucolics and the two first Satyrs of Juvenal, 1634.
[549]Possibly in hisTwelve Questions or Arguments drawn out of Scripture, wherein the commonly received Opinion touching the Deity of the Holy Spirit is clearly and fully refuted, 1647. This was his first heretical work, and it was followed by a number of others that were written during the intervals in which the Puritan parliament allowed him out of prison. It was burned by the hangman as blasphemous. Biddle finally died in prison, unrepentant to the last.
[550]The first edition of theanonymousἉιρεσεων ἀναστασις(by Vicars?) appeared in 1805.
[551]Possibly by Thomas Pearne (c. 1753-1827), a fellow of St. Peter's College, Cambridge, and a Unitarian minister.
[552]Thomas Wentworth, Earl of Strafford, was borne in London in 1593, and was executed there in 1641. He was privy councilor to Charles I, and was Lord Deputy of Ireland. On account of his repressive measures to uphold the absolute power of the king he was impeached by the Long Parliament and was executed for treason. The essence of his defence is in the sentence quoted by De Morgan, to which Pym replied that taken as a whole, the acts tended to show an intention to change the government, and this was in itself treason.
[553]The name assumed by a writer who professed to give a mathematical explanation of the Trinity, see farther on.—S. E. De M.
[554]Sabellius (fl. 230 A.D.) was an early Christian of Libyan origin. He taught that Father, Son, and Holy Spirit were different names for the same person.
[555]Sir Richard Phillips was born in London in 1767 (not 1768 as stated above), and died there in 1840. He was a bookseller and printer in Leicester, where he also edited a radical newspaper. He went to London to live in 1795 and started theMonthly Magazinethere in 1796. Besides the works mentioned by De Morgan he wrote on law and economics.
[556]It was really eighteen months.
[557]While he was made sheriff in 1807 he was not knighted until the following year.
[558]James Mitchell (c. 1786-1844) was a London actuary, or rather a Scotch actuary living a good part of his life in London. Besides the work mentioned he compiled aDictionary of Chemistry, Mineralogy, and Geology(1823), and wroteOn the Plurality of Worlds(1813) andThe Elements of Astronomy(1820).
[559]Richarda Smith, wife of Sir George Biddell Airy (see note129, page85) the astronomer. In 1835 Sir Robert Peel offered a pension of £300 a year to Airy, who requested that it be settled on his wife.
[560]Mary Fairfax (1780-1872) married as her second husband Dr. William Somerville. In 1826 she presented to the Royal Society a paper onThe Magnetic Properties of the Violet Rays of the Solar Spectrum, which attracted much attention. It was for herMechanism of the Heavens(1831), a popular translation of Laplace'sMécanique Céleste, that she was pensioned.
[561]Dominique François Jean Arago (1786-1853) the celebrated French astronomer and physicist.
[562]For there is a well-known series
1 + 1/22+ 1/32+ ... =π2/6.
1 + 1/22+ 1/32+ ... =π2/6.
1 + 1/22+ 1/32+ ... =π2/6.
If, therefore, the given series equals 1, we have
2 = 1/6π2orπ2= 12,whenceπ= 2 √3.
2 = 1/6π2
2 = 1/6π2
orπ2= 12,
orπ2= 12,
whenceπ= 2 √3.
whenceπ= 2 √3.
But c =πd, and twice the diagonal of a cube on the diameter is 2d √3.
[563]There was a second edition in 1821.
[564]London, 1830.
[565]He was a resident of Chatham, and seems to have published no other works.
[566]Richard Whately (1787-1863) was, as a child, a calculating prodigy (see note132, page86), but lost the power as is usually the case with well-balanced minds. He was a fellow of Oriel College, Oxford, and in 1825 became principal of St. Alban Hall. He was a friend of Newman, Keble, and others who were interested in the religious questions of the day. He became archbishop of Dublin in 1831. He was for a long time known to students through hisLogic(1826) andRhetoric(1828).
[567]William King, D.C.L. (1663-1712), student at Christ Church, Oxford, and celebrated as a wit and scholar. HisDialogues of the Dead(1699) is a satirical attack on Bentley.
[568]Thomas Ebrington (1760-1835) was a fellow of Trinity College, Dublin, and taught divinity, mathematics, and natural philosophy there. He became provost of the college in 1811, bishop of Limerick in 1820, and bishop of Leighlin and Ferns in 1822. His edition of Euclid was reprinted a dozen times. TheReply to John Search's Considerations on the Law of Libelappeared at Dublin in 1834.
[569]Joseph Blanco White (1775-1841) was the son of an Irishman living in Spain. He was born at Seville and studied for orders there, being ordained priest in 1800. He lost his faith in the Roman Catholic Church, and gave up the ministry, escaping to England at the time of the French invasion. At London he editedEspañol, a patriotic journal extensively circulated in Spain, and for this service he was pensioned after the expulsion of the French. He then studied at Oriel College, Oxford, and became intimate with men like Whately, Newman, and Keble. In 1835 he became a Unitarian. Among his theological writings is hisEvidences against Catholicism(1825). The "rejoinder" to which De Morgan refers consisted of two letters:The law of anti-religious Libel reconsidered(Dublin, 1834) andAn Answer to some Friendly Remarks on "The Law of Anti-Religious Libel Reconsidered"(Dublin, 1834).
[570]The work was translated from the French.
[571]J. Hoëné Wronski (1778-1853) served, while yet a mere boy, as an artillery officer in Kosciusko's army (1791-1794). He was imprisoned after the battle of Maciejowice. He afterwards lived in Germany, and (after 1810) in Paris. For the bibliography of his works see S. Dickstein's article in theBibliotheca Mathematica, vol. VI (2), page 48.
[572]Perhaps referring to hisIntroduction à la philosophie des mathématiques(1811).
[573]Read "equation of the."
[574]Thomas Young (1773-1829), physician and physicist, sometimes called the founder of physiological optics. He seems to have initiated the theory of color blindness that was later developed by Helmholtz. The attack referred to was because of his connection with the Board of Longitude, he having been made (1818) superintendent of the Nautical Almanac and secretary of the Board. He opposed introducing into the Nautical Almanac anything not immediately useful to navigation, and this antagonized many scientists.
[575]Isaac Milner (1750-1820) was professor of natural philosophy at Cambridge (1783) and later became, as De Morgan states, president of Queens' College (1788). In 1791 he became dean of Carlisle, and in 1798 Lucasian professor of mathematics. His chief interest was in chemistry and physics, but he contributed nothing of importance to these sciences or to mathematics.
[576]Thomas Perronet Thompson (1783-1869), fellow of Queens' College, Cambridge, saw service in Spain and India, but after 1822 lived in England. He became major general in 1854, and general in 1868. Besides some works on economics and politics he wrote aGeometry without Axioms(1830) that De Morgan includes later on in hisBudget. In it Thompson endeavored to prove the parallel postulate.
[577]De Morgan's father-in-law. See note441, page196.
[578]Johann Friedrich Herbart (1776-1841), successor of Kant as professor of philosophy at Königsberg (1809-1833), where he established a school of pedagogy. From 1833 until his death he was professor of philosophy at Göttingen. The title of the pamphlet is:De Attentionis mensura causisque primariis. Psychologiae principia statica et mechanica exemplo illustraturus.... Regiomonti,... 1822. The formulas in question are given on pages 15 and 17, and De Morgan has omitted the preliminary steps, which are, for the first one:
β(φ-z)δt=δzundeβt= Const / (φ-z).Prot= 0 etiamz= 0; hincβt= logφ/(φ-z).z=φ(1 -ε-βt);etδz/δt=βφε-βt
β(φ-z)δt=δz
β(φ-z)δt=δz
undeβt= Const / (φ-z).
undeβt= Const / (φ-z).
Prot= 0 etiamz= 0; hincβt= logφ/(φ-z).
Prot= 0 etiamz= 0; hincβt= logφ/(φ-z).
z=φ(1 -ε-βt);
z=φ(1 -ε-βt);
etδz/δt=βφε-βt
etδz/δt=βφε-βt
These are, however, quite elementary as compared with other portions of the theory.
[579]See note371, page168.
[580]William Law (1686-1761) was a clergyman, a fellow of Emanuel College, Cambridge, and in later life a convert to Behmen's philosophy. He was so free in his charities that the village in which he lived became so infested by beggars that he was urged by the citizens to leave. He wroteA serious call to a devout and holy life(1728).
[581]He was a curate at Cheshunt, and wrote theSpiritual voice to the Christian Church and to the Jews(London, 1760),A second warning to the world by the Spirit of Prophecy(London, 1760), andSigns of the Times; or a Voice to Babylon(London, 1773).
[582]His real name was Thomas Vaughan (1622-1666). He was a fellow of Jesus College, Oxford, taking orders, but was deprived of his living on account of drunkenness. He became a mystic philosopher and gave attention to alchemy. His works had a large circulation, particularly on the continent. He wroteMagia Adamica(London, 1650),Euphrates; or the Waters of the East(London, 1655), andThe Chymist's key to shut, and to open; or the True Doctrine of Corruption and Generation(London, 1657).
[583]Emanuel Swedenborg, or Svedberg (1688-1772) the mystic. It is not commonly known to mathematicians that he was one of their guild, but he wrote on both mathematics and chemistry. Among his works are theRegelkonst eller algebra(Upsala, 1718) and theMethodus nova inveniendi longitudines locorum, terra marique, ope lunae(Amsterdam, 1721, 1727, and 1766). After 1747 he devoted his attention to mystic philosophy.
[584]Pierre Simon Laplace (1749-1827), whoseExposition du système du monde(1796) andTraité de mécanique celeste(1799) are well known.
[585]See note117, page76.
[586]John Dalton (1766-1844), who taught mathematics and physics at New College, Manchester (1793-1799) and was the first to state the law of the expansion of gases known by his name and that of Gay-Lussac. HisNew system of Chemical Philosophy(Vol. I, pt. i, 1808; pt. ii, 1810; vol. II, 1827) sets forth his atomic theory.
[587]Howison was a poet and philosopher. He lived in Edinburgh and was a friend of Sir Walter Scott. This work appeared in 1822.
[588]He was a shoemaker, born about 1765 at Haddiscoe, and his "astro-historical" lectures at Norwich attracted a good deal of attention at one time. He traced all geologic changes to differences in the inclination of the earth's axis to the plane of its orbit. Of the works mentioned by De Morgan the first appeared at Norwich in 1822-1823, and there was a second edition in 1824. The second appeared in 1824-1825. The fourth wasUrania's Key to the Revelation; or the analyzation of the writings of the Jews..., and was first published at Norwich in 1823, there being a second edition at London in 1833. His books were evidently not a financial success, for Mackey died in an almshouse at Norwich.
[589]Godfrey Higgins (1773-1833), the archeologist, was interested in the history of religious beliefs and in practical sociology. He wroteHorae Sabbaticae(1826),The Celtic Druids(1827 and 1829), andAnacalypsis, an attempt to draw aside the veil of the Saitic Isis; or an Inquiry into the Origin of Languages, Nations, and Religions(posthumously published, 1836), and other works. See also page274,infra.
[590]The work also appeared in French. Wirgman wrote, or at least began, two other works:Divarication of the New Testament into Doctrine and History; part I, The Four Gospels(London, 1830), andMental Philosophy; part I, Grammar of the five senses; being the first step to infant education(London, 1838).
[591]He was born at Shandrum, County Limerick, and supported himself by teaching writing and arithmetic. He died in an almshouse at Cork.
[592]George Boole (1815-1864), professor of mathematics at Queens' College, Cork. HisLaws of Thought(1854) was the first work on the algebra of logic.
[593]Oratio Grassi (1582-1654), the Jesuit who became famous for his controversy with Galileo over the theory of comets. Galileo ridiculed him inIl Saggiatore, although according to the modern view Grassi was the more nearly right. It is said that the latter's resentment led to the persecution of Galileo.
[594]De Morgan might have found much else for his satire in the letters of Walsh. He sought, in hisTheory of Partial Functions, to substitute "partial equations" for the differential calculus. In his diary there is an entry: "Discovered the general solution of numerical equations of the fifth degree at 114 Evergreen Street, at the Cross of Evergreen, Cork, at nine o'clock in the forenoon of July 7th, 1844; exactly twenty-two years after the invention of the Geometry of Partial Equations, and the expulsion of the differential calculus from Mathematical Science."
[595]"It has been ordered, sir, it has been ordered."
[596]Bartholomew Prescot was a Liverpool accountant. De Morgan gives this correct spelling on page278. He died after 1849. HisInverted Scheme of Copernicusappeared in Liverpool in 1822.
[597]Robert Taylor (1784-1844) had many more ups and downs than De Morgan mentions. He was a priest of the Church of England, but resigned his parish in 1818 after preaching against Christianity. He soon recanted and took another parish, but was dismissed by the Bishop almost immediately on the ground of heresy. As stated in the text, he was convicted of blasphemy in 1827 and was sentenced to a year's imprisonment, and again for two years on the same charge in 1831. He then married a woman who was rich in money and in years, and was thereupon sued for breach of promise by another woman. To escape paying the judgment that was rendered against him he fled to Tours where he took up surgery.
[598]Herbert Marsh, Bishop of Peterborough. See note449on page199.
[599]"Argument from the prison."
[600]Richard Carlile (1790-1843), one of the leading radicals of his time. He published Hone's parodies (see note250, page124) after they had been suppressed, and an edition of Thomas Paine (1818). He was repeatedly imprisoned, serving nine years in all. His continued conflict with the authorities proved a good advertisement for his bookshop.
[601]Wilhelm Ludwig Christmann (1780-1835) was a protestant clergyman and teacher of mathematics. For a while he taught under Pestalozzi. Disappointed in his ambition to be professor of mathematics at Tubingen, he became a confirmed misanthrope and is said never to have left his house during the last ten years of his life. He wrote several works:Ein Wort über Pestalozzi und Pestalozzismus(1812);Ars cossae promota(1814);Philosophia cossica(1815);Aetas argentea cossae(1819);Ueber Tradition und Schrift, Logos und Kabbala(1829), besides the one mentioned above. The wordcossin the above titles was a German name for algebra, from the Italiancosa(thing), the name for the unknown quantity. It appears in English in the early name for algebra, "the cossic art."
[602]See note174, page101.
[603]See note589, page257.
[604]He seems to have written nothing else.
[605]See note596on page270. The name is here spelled correctly.
[606]Joseph Jacotot (1770-1840), the father of this Fortuné Jacotot, was an infant prodigy. At nineteen he was made professor of the humanities at Dijon. He served in the army, and then became professor of mathematics at Dijon. He continued in his chair until the restoration of the Bourbons, and then fled to Louvain. It was here that he developed the method with which his name is usually connected. He wrote aMathématiquesin 1827, which went through four editions. TheEpitoméis by his son, Fortuné.
[607]He wrote on educational topics and aSacred Historythat went through several editions.
[608]"All is in all."
[609]"Know one thing and refer everything else to it," as it is often translated.
[610]A writer of no reputation.
[611]Sir John Lubbock (1803-1865), banker, scientist, publicist, astronomer, one of the versatile men of his time.
[612]See note165, page99.
[613]"Those about to die salute you."
[614]Georges Louis Leclerc Buffon (1707-1788), the well-known biologist. He also experimented with burning mirrors, his results appearing in hisInvention des miroirs ardens pour brûler à une grande distance(1747). The reference here may be to hisResolution des problèmes qui regardent le jeu du franc carreau(1733). The prominence of hisHistoire naturelle(36 volumes, 1749-1788) has overshadowed the credit due to him for his translation of Newton's work on Fluxions.
[615]See page285. This article was a supplement to No. 14 in theAthenæumBudget.—A. De M.
[616]There are many similar series and products. Among the more interesting are the following:
[617]"To a privateer, a privateer and a half."
[618]Joshua Milne (1776-1851) was actuary of the Sun Life Assurance Society. He wroteA Treatise on the Valuation of Annuities and Assurances on Lives and Survivorships; on the Construction of tables of mortality; and on the Probabilities and Expectations of Life, London, 1815. Upon the basis of the Carlisle bills of mortality of Dr. Heysham he reconstructed the mortality tables then in use and which were based upon the Northampton table of Dr. Price. His work revolutionized the actuarial science of the time. In later years he devoted his attention to natural history.
[619]See note576, page252. He also wrote theTheory of Parallels. The proof of Euclid's axiom looked for in the properties of the equiangular spiral(London, 1840), which went through four editions, and theTheory of Parallels. The proof that the three angles of a triangle are equal to two right angles looked for in the inflation of the sphere(London, 1853), of which there were three editions.
[620]For the latest summary, see W. B. Frankland,Theories of Parallelism, an historical critique, Cambridge, 1910.
[621]Joseph Louis Lagrange (1736-1813), author of theMécanique analytique(1788),Théorie des functions analytiques(1797),Traité de la résolution des équations numériques de tous degrés(1798),Leçons sur le calcul des fonctions(1806), and many memoirs. Although born in Turin and spending twenty of his best years in Germany, he is commonly looked upon as the great leader of French mathematicians. The last twenty-seven years of his life were spent in Paris, and his remarkable productivity continued to the time of his death. His genius in the theory of numbers was probably never excelled except by Fermat. He received very high honors at the hands of Napoleon and was on the first staff of the Ecole polytechnique (1797).
[622]"I shall have to think it over again."
[623]Henry Goulburn (1784-1856) held various government posts. He was under-secretary for war and the colonies (1813), commissioner to negotiate peace with America (1814), chief secretary to the Lord Lieutenant of Ireland (1821), and several times Chancellor of the Exchequer. On the occasion mentioned by De Morgan he was standing for parliament, and was successful.
[624]On Drinkwater Bethune see note165, page99.
[625]Charles Henry Cooper (1808-1866) was a biographer and antiquary. He was town clerk of Cambridge (1849-1866) and wrote theAnnals of Cambridge(1842-1853). HisMemorials of Cambridge(1874) appeared after his death. Thompson Cooper was his son, and the two collaborated in theAthenae Cantabrigiensis(1858).
[626]William Yates Peel (1789-1858) was a brother of Sir Robert Peel, he whose name degenerated into the familiar title of the London "Bobby" or "Peeler." Yates Peel was a member of parliament almost continuously from 1817 to 1852. He represented Cambridge at Westminster from 1831 to 1835.
[627]Henry John Temple, third Viscount of Palmerston (1784-1865), was member for Cambridge in 1811, 1818, 1820, 1826 (defeating Goulburn), and 1830. He failed of reelection in 1831 because of his advocacy of reform. This must have been the time when Goulburn defeated him. He was Foreign Secretary (1827) and Secretary of State for Foreign Affairs (1830-1841, and 1846-1851). It is said of him that he "created Belgium, saved Portugal and Spain from absolutism, rescued Turkey from Russia and the highway to India from France." He was Prime Minister almost continuously from 1855 to 1865, a period covering the Indian Mutiny and the American Civil War.
[628]William Cavendish, seventh Duke of Devonshire (1808-1891). He was member for Cambridge from 1829 to 1831, but was defeated in 1831 because he had favored parliamentary reform. He became Earl of Burlington in 1834, and Duke of Devonshire in 1858. He was much interested in the promotion of railroads and in the iron and steel industries.
[629]Richard Sheepshanks (1794-1855) was a brother of John Sheepshanks the benefactor of art. (See note314, p.147.) He was a fellow of Trinity College, Cambridge, a fellow of the Royal Society and secretary of the Astronomical Society. Babbage (See note469, p.207) suspected him of advising against the government support of his calculating machine and attacked him severely in hisExposition of 1851, in the chapter onThe Intrigues of Science. Babbage also showed that Sheepshanks got an astronomical instrument of French make through the custom house by having Troughton's (See note332, page152) name engraved on it. Sheepshanks admitted this second charge, but wrote aLetter in Reply to the Calumnies of Mr. Babbage, which was published in 1854. He had a highly controversial nature.
[630]See note469, page207. The work referred to isPassages from the Life of a Philosopher, London, 1864.
[631]Drinkwater Bethune. See note165, page99.
[632]Siméon-Denis Poisson (1781-1840) was professor of calculus and mechanics at the Ecole polytechnique. He was made a baron by Napoleon, and was raised to the peerage in 1837. His chief works are theTraité de mécanìque(1811) and theTraité mathématique de la chaleur(1835).
[633]"As to M. Poisson, I really wish I had a thousandth part of his mathematical knowledge that I might prove my system to the incredulous."
[634]This list includes most of the works of Antoine-Louis-Guénard Demonville. There was also theNouveau système du monde ... et hypothèses conformes aux expériences sur les vents, sur la lumière et sur le fluide électro-magnétique, Paris, 1830.
[635]Paris, 1835.
[636]Paris, 1833.
[637]The second part appeared in 1837. There were also editions in 1850 and 1852, and one edition appeared without date.
[638]Paris, 1842.
[639]Parsey also wroteThe Art of Miniature Painting on Ivory(1831),Perspective Rectified(1836), andThe Science of Vision(1840), the third being a revision of the second.
[640]William Ritchie (1790-1837) was a physicist who had studied at Paris under Biot and Gay-Lussac. He contributed several papers on electricity, heat, and elasticity, and was looked upon as a good experimenter. Besides the geometry he wrote thePrinciples of the Differential and Integral Calculus(1836).
[641]Alfred Day (1810-1849) was a man who was about fifty years ahead of his time in his attempt to get at the logical foundations of geometry. It is true that he laid himself open to criticism, but his work was by no means bad. He also wroteA Treatise on Harmony(1849, second edition 1885),The Rotation of the Pendulum(1851), and several works on Greek and Latin Grammar.
[642]Walter Forman wrote a number of controversial tracts. His first seems to have beenA plan for improving the Revenue without adding to the burdens of the people, a letter to Canning in 1813. He also wroteA New Theory of the Tides(1822). HisLetter to Lord John Russell, on Lord Brougham's most extraordinary conduct; and another to Sir J. Herschel, on the application of Kepler's third lawappeared in 1832.
[643]Lord John Russell (1792-1878) first Earl Russell, was one of the strongest supporters of the reform measures of the early Victorian period. He became prime minister in 1847, and again in 1865.
[644]Lauder seems never to have written anything else.
[645]See note22, page40.
[646]The names of Alphonso Cano de Molina, Yvon, and Robert Sara have no standing in the history of the subject beyond what would be inferred from De Morgan's remark.
[647]Claude Mydorge (1585-1647), an intimate friend of Descartes, was a dilletante in mathematics who read much but accomplished little. HisRécréations mathématiquesis his chief work. Boncompagni published the "Problèmes de Mydorge" in hisBulletino.
[648]Claude Hardy was born towards the end of the 16th century and died at Paris in 1678. In 1625 he edited theData Euclidis, publishing the Greek text with a Latin translation. He was a friend of Mydorge and Descartes, but an opponent of Fermat.
[649]That is, in theBibliotheca Realisof Martin Lipen, or Lipenius (1630-1692), which appeared in six folio volumes, at Frankfort, 1675-1685.
[650]See note29, page43.
[651]Baldassare Boncompagni (1821-1894) was the greatest general collector of mathematical works that ever lived, possibly excepting Libri. His magnificent library was dispersed at his death. HisBulletino(1868-1887) is one of the greatest source books on the history of mathematics that we have. He also edited the works of Leonardo of Pisa.
[652]He seems to have attracted no attention since De Morgan's search, for he is not mentioned in recent bibliographies.
[653]Joseph-Louis Vincens de Mouléon de Causans was born about the beginning of the l8th century. He was a Knight of Malta, colonel in the infantry, prince of Conti, and governor of the principality of Orange. His works on geometry are theProspectus apologétique pour la quadrature du cercle(1753), andLa vraie géométrie transcendante(1754).
[654]See note119, page80.
[655]See note120, page81.
[656]Lieut. William Samuel Stratford (1791-1853), was in active service during the Napoleonic wars but retired from the army in 1815. He was first secretary of the Astronomical Society (1820) and became superintendent of the Nautical Almanac in 1831. With Francis Baily he compiled a star catalogue, and wrote on Halley's (1835-1836) and Encke's (1838) comets.
[657]See Sir J. Herschel'sAstronomy, p. 369.—A. De M.
[658]Captain Ross had just stuck a bit of brass there.—A. De M.
Sir James Clark Ross (1800-1862) was a rear admiral in the British navy and an arctic and antarctic explorer of prominence. De Morgan's reference is to Ross's discovery of the magnetic pole on June 1, 1831. In 1838 he was employed by the Admiralty on a magnetic survey of the United Kingdom. He was awarded the gold medal of the geographical societies of London and Paris in 1842.
[659]John Partridge (1644-1715), the well-known astrologer and almanac maker. Although bound to a shoemaker in his early boyhood, he had acquired enough Latin at the age of eighteen to read the works of the astrologers. He then mastered Greek and Hebrew and studied medicine. In 1680 he began the publication of his almanac, theMerlinus Liberatus, a book that acquired literary celebrity largely through the witty comments upon it by such writers as Swift and Steele.
[660]See note642on page296.
[661]William Woodley also published several almanacs (1838, 1839, 1840) after his rejection by the Astronomical Society in 1834.
[662]It appeared at London.
[663]The first edition appeared in 1830, also at London.
[664]See note441, page196.
[665]Thomas Kerigan wroteThe Young Navigator's Guide to the siderial and planetary parts of Nautical Astronomy(London, 1821, second edition 1828), a work on eclipses (London, 1844), and the work on tides (London, 1847) to which De Morgan refers.
[666]Jean Sylvain Bailly, who was guillotined. See note365, page166.
[667]See note670, page309.
[668]Laurent seems to have had faint glimpses of the modern theory of matter. He is, however, unknown.
[669]See note133, page87.
[670]Francis Baily (1774-1844) was a London stockbroker. His interest in science in general and in astronomy in particular led to his membership in the Royal Society and to his presidency of the Astronomical Society. He wrote on interest and annuities (1808), but his chief works were on astronomy.
[671]If the story is correctly told Baily must have enjoyed his statement that Gauss was "the oldest mathematician now living." As a matter of fact he was then only 58, three years the junior of Baily himself. Gauss was born in 1777 and died in 1855, and Baily was quite right in saying that he was "generally thought to be the greatest" mathematician then living.
[672]Margaret Cooke, who married Flamsteed in 1692.
[673]John Brinkley (1763-1835), senior wrangler, first Smith's prize-man (1788), Andrews professor of astronomy at Dublin, first Astronomer Royal for Ireland (1792), F.R.S. (1803), Copley medallist, president of the Royal Society and Bishop of Cloyne. HisElements of Astronomyappeared in 1808.
[674]See note248, page124.
[675]See note276, page133.
[676]See note352, page161.
[677]"It becomes the doctors of the Sorbonne to dispute, the Pope to decree, and the mathematician to go to Paradise on a perpendicular line."
[678]See note124, page83.
[679]See note621, page288.
[680]Sylvain van de Weyer, who was born at Louvain in 1802. He was a jurist and statesman, holding the portfolio for foreign affairs (1831-1833), and being at one time ambassador to England.
[681]Henry Crabb Robinson (1775-1867), correspondent of theTimesat Altona and in the Peninsula, and later foreign editor. He was one of the founders of the Athenæum Club and of University College, London. He seems to have known pretty much every one of his day, and his posthumousDiaryattracted attention when it appeared.