[328] See Vol. I, page 309, note 2 {670}.

[329] This was his Practical short and direct Method of Calculating the Logarithm of any given Number, and the Number corresponding to any given Logarithm (1849).

[330] This is William Neile (1637-1670), grandson of Richard Neile (not Neal), Archbishop of York. At the age of 19, in 1657, he gave the first rectification of the semicubical parabola. Although he communicated it to Brouncker, Wren, and others, it was not published until 1639, when it appeared in John Wallis's De Cycloide.

[331] I myself "was a considerable part."

[332] He also wrote A Glance at the Universe ("2d thousand" in 1862), and The Resurrection Body (1869).

[333] See Vol. I, page 63, note 1 {74}.

[334] As Swift gave it in his Poetry. A Rhapsody, it is as follows:

"So, naturalists observe, a flea Has smaller fleas that on him prey; And these have smaller still to bite 'em. And so proceed ad infinitum."

[335] Perhaps 1,600,000,000 years, if Boltwood's recent computations based on radium disintegration stand the test. This would mean, according to MacCurdy's estimate, 60,000,000 years since life first appeared on the earth.

[336] De Morgan wrote better than he knew, for this work, the Allgemeine Encyclopaedie der Wissenschaften und Kuenste, begun at Leipsic in 1818, is still (1913) unfinished. Section I, A-G, consists of 99 parts in 56 volumes; Section II, H-N, consists of 43 volumes and is not yet completed; and Section III, O-Z, consists of 25 volumes thus far, with most of the work still to be done. Johann Samuel Ersch (1766-1828), the founder, was head librarian at Halle. Johann Gottfried Gruber (1774-1851), his associate, was professor of philosophy at the same university.

[337] William Howitt (1792-1879) was a poet, a spiritualist, and a miscellaneous writer. He and his wife became spiritualists about 1850. He wrote numerous popular works on travel, nature and history.

[338] See Vol. II, page 55, note 108.

[339] As will be inferred from the text, C. D. was Mrs. De Morgan, and A. B. was De Morgan.

[340] Jean Meslier (1678-1733), cure of Estrepigny, in Champagne, was a skeptic, but preached only strict orthodoxy to his people. It was only in his manuscript, Mon Testament, that was published after his death, and that caused a great sensation in France, that his antagonism to Christianity became known.

[341] Baron Zach relates that a friend of his, in a writing intended for publication, said Un esprit doit se frotter contre un autre. The censors struck it out. The Austrian police have a keen eye for consequences.—A. De M.

"One mind must rub against another." On Baron Zach, see Vol. II, page 45, note 4.

[342] Referring to the first Lord Eldon (1751-1838), who was Lord Chancellor from 1799 to 1827, with the exception of one year.

[343] "Sleeping power."

[344] "Causes sleep."

[345] Richard Hooker (c. 1554-1600), a theologian, "the ablest living advocate of the Church of England as by law established."

[346] See Vol. I, page 76, note 3 {112}.

[347] "Other I,"—other self.

[348] This "utter rejection" has been repeated (1872) by the same writer.—S. E. De M.

[349] Edward Jenner (1749-1823) was a physician and biologist. His first experiments in vaccination were made in 1796, and his discovery was published in 1798.

[350] See Vol. II, page 38, note 80.

[351] "You will go most safely in the middle (way)."

[352] Pierre Joseph Arson was known early in the 19th century for his controversy with Hoene Wronski the mathematician, whom he attacked in his Document pour l'histoire des grands fourbes qui ont figure sur la terre (1817-1818).

[353] "We enter the course by night and are consumed by fire."

[354] See Vol. I, page 51, note 3 {51}.

[355] See Vol. I, page 336, note 8 {713}.

[356] See Vol. I, page 137, note 8 {286}.

[357] See Vol. I, page 229, note 2 {515}.

[358] Richard Cobden (1804-1865), the cotton manufacturer and statesman who was prominent in his advocacy of the repeal of the Corn Laws.

[359] James Smith (1775-1839), solicitor to the Board of Ordnance. With his brother Horatio he wrote numerous satires. His Horace in London (1813) imitated the Roman poet. His works were collected and published in 1840.

[360] Samuel Butler (1612-1680), the poet and satirist, author of Hudibras (1663-1678).

[361] "Is it not fine to be sure of one's action when entering in a combat with another? There, push me a little in order to see. NICOLE. Well! what's the matter? M. JOURDAIN. Slowly. Ho there! Ho! gently. Deuce take the rascal! NICOLE. You told me to push. M. JOURDAIN. Yes, but you pushed me en tierce, before you pushed en quarte, and you did not give me time to parry."

[362] John Abernethy (1764-1831), the famous physician and surgeon.

[363] See Vol. I, page 102, note 5 {175}.

[364] "With what measure ye mete, it shall be measured to you again."

[365] Eusebius of Caesarea (c. 260-340), leader of the moderate party at the Council of Nicaea, and author of a History of the Christian Church in ten books (c. 324 A. D.).

[366] Nathaniel Lardner (1684-1768), a non-conformist minister and one of the first to advocate the scientific study of early Christian literature.

[367] Henry Alford (1810-1871) Dean of Canterbury (1857-1871) and editor of the Greek Testament (1849-1861).

[368] The work was The Number and Names of the Apocalyptic Beasts: with an explanation and application. Part I. London, 1848, as mentioned below. Thom also wrote The Assurance of Faith, or Calvinism identified with Universalism (London, 1833), and various other religious works.

[369] See Vol. I, page 222, note 14 {490}.

[370] John Hamilton Thom (1808-1894) was converted to Unitarianism and was long a minister in that church, preaching in the Renshaw Street Chapel from 1831 to 1866. De Morgan refers to the Liverpool Unitarian controversy conducted by James Martineau and Henry Giles in response to a challenge by thirteen Anglican Clergy. In 1839 Thom contributed four lectures and a letter to this controversy. Among his religious works were a Life of Blanco White (1845) and Hymns, Chants, and Anthems (1854).

[371] The spelling of these names is occasionally changed to meet the condition that the numerical value of the letters shall be 666, "the number of the beast" of Revelations. The names include Julius Caesar; Valerius Jovius Diocletianus (249-313), emperor from 287 to 305, persecutor of the Christians; Louis, presumably Louis XIV; Gerbert (940-1003), who reigned as Pope Sylvester II from 999 to 1003, known to mathematicians for his abacus and his interest in geometry, and accused by his opponents as being in league with the devil; Linus, the second Bishop of Rome, the successor of Peter; Camillo Borghese (1552-1621), who reigned as Pope Paul V from 1605 to 1621, and who excommunicated all Venice in 1606 for its claim to try ecclesiastics before lay tribunals, thus taking a position which he was forced to abandon; Luther, Calvin; Laud (see Vol. I, page 145, note 7 {307}); Genseric (c. 406-477), king of the Vandals, who sacked Rome in 455 and persecuted the orthodox Christians in Africa; Boniface III, who was pope for nine months in 606; Beza (see Vol. I, page 66, note 6 {83}); Mohammed; [Greek: braski], who was Giovanni Angelo Braschi (1717-1799), and who reigned as Pope Pius VI from 1775 to 1799, dying in captivity because he declined to resign his temporal power to Napoleon; Bonaparte; and, under [Greek: Ion Paune], possibly Pope John XIV, who reigned in 983 and 984 during the absence of Boniface VII in Constantinople.

[372] The Greek words and names are also occasionally misspelled so as to fit them to the number 666. They are [Greek: Lateinos] (Latin), [Greek: he latine basileia] (the Latin kingdom), [Greek: ekklesia italika] (the Italian Church), [Greek: euanthas] (blooming), [Greek: teitan] (Titan), [Greek: arnoume] (renounce), [Greek: lampetis] (the lustrous), [Greek: ho niketes] (conqueror), [Greek: kakos hodegos] (bad guide), [Greek: alethes blaberos] (truthful harmful one), [Greek: palai baskanos] (a slanderer of old), [Greek: amnos adikos] (unmanageable lamb), [Greek: antemos] (Antemos), [Greek: genserikos] (Genseric), [Greek: euinas] (with stout fibers), [Greek: Benediktos] (Benedict), [Greek: Bonibazios g. papa x. e. e. e. a.] (Boniface III, pope 68, bishop of bishops I), [Greek: oulpios] (baneful), [Greek: dios eimi he heras] (I, a god, am the), [Greek: he missa he papike] (the papal brief), [Greek: loutherana] (Lutheran), [Greek: saxoneios] (Saxon), [Greek: Bezza antitheos] (Beza antigod), [Greek: he alazoneia biou] (the illusion of life), [Greek: Maometis] (Mahomet); [Greek: Maometes b.] (Mahomet II), [Greek: theos eimi epi gaies] (I am lord over the earth), [Greek: iapetos] (Iapetos, father of Atlas), [Greek: papeiskos] (Papeiskos), [Greek: dioklasianos] (Diocletian), [Greek: cheina] (Cheina = Cain? China?), [Greek: braski] (Braschi, as explained in note 10), [Greek: Ion Paune] (Paunian violet, but see note 10), [Greek: koupoks] (cowpox), [Greek: Bonneparte] (Bonneparte), [Greek: N. Boneparte] (N. Boneparte), [Greek: euporia] (facility), [Greek: paradosis] (surrender), [Greek: to megatherion] (the megathereum, the beast).

[373] James Wapshare, whose Harmony of the Word of God in Spirit and in Truth appeared in 1849.

[374] The literature relating to the Swastika is too extended to permit of any adequate summary in these notes.

[375] Henry Edward Manning (1808-1892), at first an Anglican clergyman, he became a Roman Catholic priest in 1851, and became Cardinal in 1875. He succeeded Cardinal Wiseman as Archbishop of Westminster in 1865. He wrote a number of religious works.

[376] John Bright (1811-1889), Quaker, cotton manufacturer, and statesman. He worked with Cobden for free trade, peace, and reform of the electorate.

[377] "The fallacy of many questions."

[378] William Wilberforce (1759-1833), best known for his long fight for the abolition of the slave trade.

[379] Richard Martin (1754-1834), high sheriff of County Galway and owner of a large estate in Connemara. Curiously enough, he was known both for his readiness in duelling and for his love for animals. He was known as "Humanity Martin," and in 1822 secured the passage of an act "to prevent the cruel and improper treatment of cattle." He was one of the founders (1824) of the Royal Society for the Prevention of Cruelty to Animals. He is usually considered the original of Godfrey O'Malley in Lever's novel, Charles O'Malley.

[380] See Vol. I, page 149, note 1 {323}, also text on same page.

[381] See Vol. I, page 44, note 9 {34}, also text, Vol. I, page 110.

[382] "Penitential seat."

[383] "Well placed upon the cushion."

[384] See Vol. II, page 58, note 109.

[385] "He has lost the right of being influenced by evidence."

[386] "Hung up."

[387] "A few things to the wise, nothing to the unlettered."

[388] The fallacy results from dividing both members of an equation by 0, x - 1 being the same as 1 - 1, and calling the quotients finite.

[389] "If you order him to the sky he will go."

[390] Similia similibus curanter, "Like cures like," the homeopathic motto.

[391] "Without harm to the proprieties."

[392] "What are you doing? I am standing here."

[393] Lors feist l'Anglois tel signe. La main gausche toute ouverte il leva hault en l'aer, puis ferma au poing les quatres doigtz d'icelle et le poulce estendu assit sus la pinne du nez. Soubdain apres leva la dextre toute ouverte, et toute ouverte la baissa, joignant la poulce au lieu que fermait le petit doigt de la gausche, et les quatre doigtz d'icelle mouvoit lentement en l'aer. Puis au rebours feit de la dextre ce qu'il avoit faict de la gausche, et de la gausche ce que avoit faict de la dextre.—A. De M.

[394] Suaviter in modo, fortiter in re, "Gentle in manners, firm in action."

[395] See Vol. I, page 101, note 4 {174}.

[396] See Vol. I, page 315, note 3 {686}.

[397] Henry Fawcett (1833-1884) became totally blind in 1858, but in spite of this handicap he became professor of political economy at Cambridge and sat in parliament for a number of years. He championed the cause of reform and in particular he was prominent in the protection of the native interests of India. The establishing of the parcels post (1882) took place while he was postmaster general (1880-1884).

[398] Of course the whole thing depends upon what definition of division is taken. We can multiply 2 ft. by 3 ft. if we define multiplication so as to allow it, or 2 ft. by 3 lb, getting foot-pounds, as is done in physics.

[399] Richard Milward (1609-1680), for so the name is usually given, was rector of Great Braxted (Essex) and canon of Windsor. He was long the amanuensis of John Selden, and the Table Talk was published nine years after Milward's death, from notes that he left. Some doubt has been cast upon the authenticity of the work owing to many of the opinions that it ascribes to Selden.

[400] John Selden (1584-1654) was a jurist, legal antiquary, and Oriental scholar. He sat in the Long Parliament, and while an advocate of reform he was not an extremist. He was sent to the Tower for his support of the resolution against "tonnage and poundage," in 1629. His History of Tythes (1618) was suppressed at the demand of the bishops. His De Diis Syriis (1617) is still esteemed a classic on Semitic mythology.

[401] See Vol. I, page 42, note 4 {24}.

[402] See Vol. II, page 249, note 398.

[403] John Palmer (1742-1818) was a theatrical manager. In 1782 he set forth a plan for forwarding the mails by stage coaches instead of by postmen. Pitt adopted the plan in 1784. Palmer was made comptroller-general of the post office in 1786 and was dismissed six years later for arbitrarily suspending a deputy. He had been verbally promised 2-1/2% on the increased revenue, but Pitt gave him only a pension of L3000. In 1813 he was awarded L50,000 in addition to his pension.

[404] Dionysius Lardner (1793-1859), professor of natural philosophy in London University (now University College). His Cabinet Cyclopaedia (1829-1849) contained 133 volumes. De Morgan wrote on probabilities, and Lardner on various branches of mathematics, and there were many other well-known contributors. Lardner is said to have made $200,000 on a lecture tour in America.

[405] Thomas Fysche Palmer (1747-1802) joined the Unitarians in 1783, and in 1785 took a charge in Dundee. He was arrested for sedition because of an address that it was falsely alleged that he gave before a society known as the "Friends of Liberty." As a matter of fact the address was given by an uneducated weaver, and Palmer was merely asked to revise it, declining to do even this. Nevertheless he was sentenced to Botany Bay (1794) for seven years. The trial aroused great indignation.

[406] See Vol. I, page 80, note 5 {119}.

[407] See Vol. II, page 244, note 394.

[408] See Vol. I, page 352, note 1 {731}.

[409] See Vol. I, page 332, note 4 {709}.

[410] "The lawyers are brought into court; let them accuse each other."

[411] Samuel Rogers (1763-1855), the poet and art connoisseur. He declined the laureateship on the death of Wordsworth (1850). Byron, his pretended friend, wrote a lampoon (1818) ridiculing his cadaverous appearance.

[412] Theodore Edward Hook (1788-1841), the well-known wit. He is satirized as Mr. Wagg in Vanity Fair. The John Bull was founded in 1820 and Hook was made editor.

[413] "On pitying the heretic."

[414] A term of medieval logic. Barbara: All M is P, all S is M, hence all S is P. Celarent: No M is P, all S is M, hence no S is P.

[415] "Simply," "According to which," "It does not follow."

[416]

"O sweet soul, what good shall I declare That heretofore was thine, since such are thy remains!"

[417] "Stupid fellow!"

[418] Christopher Barker (c. 1529-1599), also called Barkar, was the Queen's printer. He began to publish books in 1569, but did no actual printing until 1576. In 1575 the Geneva Bible was first printed in England, the work being done for Barker. He published 38 partial or complete editions of the Bible from 1575 to 1588, and 34 were published by his deputies (1588-1599).

[419] James Franklin (1697-1735) was born in Boston, Mass., and was sent to London to learn the printer's trade. He returned in 1717 and started a printing house. Benjamin, his brother, was apprenticed to him but ran away (1723). James published the New England Courant (1721-1727), and Benjamin is said to have begun his literary career by writing for it.

[420] James Hodder was a writing master in Tokenhouse Yard, Lothbury, in 1661, and later kept a boarding school in Bromley-by-Bow. His famous arithmetic appeared at London in 1661 and went through many editions. It was the basis of Cocker's work. (See Vol. I, page 42, note 4 {24}.) It was long thought to have been the first arithmetic published in America, and it was the first English one. There was, however, an arithmetic published much earlier than this, in Mexico, the Sumario compendioso ... con algunas reglas tocantes al Aritmetica, by "Juan Diaz Freyle," in 1556.

[421] Henry Mose, Hodder's successor, kept a school in Sherborne Lane, London.

[422] Rear Admiral Sir Francis Beaufort (1774-1857), F.R.S., was hydrographer to the Navy from 1829 to 1855. He prepared an atlas that was printed by the Society for the Diffusion of Useful Knowledge.

[423] Antoine Sabatier (1742-1817), born at Castres, was known as the Abbe but was really nothing more than a "clerc tonsure." He lived at Court and was pensioned to write against the philosophers of the Voltaire group. He posed as the defender of morality, a commodity of which he seems to have possessed not the slightest trace.

[424] Maffeo Barberini was pope, as Urban VIII, from 1623 to 1644. It was during his ambitious reign that Galileo was summoned to Rome to make his recantation (1633), the exact nature of which is still a matter of dispute.

[425] This Baden Powell (1796-1860) was the Savilian professor of geometry (1827-1860) at Oxford.

[426] "Memoirs of the famous bishop of Chiapa, by which it appears that he had butchered or burned or drowned ten million infidels in America in order to convert them. I believe that this bishop exaggerated; but if we should reduce these sacrifices to five million victims, this would still be admirable."

[427] Alfonso X (1221-1284), known as El Sabio (the Wise), was interested in astronomy and caused the Alphonsine Tables to be prepared. These table were used by astronomers for a long time. It is said that when the Ptolemaic system of the universe was explained to him he remarked that if he had been present at the Creation he could have shown how to arrange things in a much simpler fashion.

[428] George Richards (c. 1767-1837), fellow of Oriel (1790-1796), Bampton lecturer (1800), Vicar of St. Martin's-in-the-Fields, Westminster (1824), and a poet of no mean ability.

[429] The "Aboriginal Britons," an excellent poem, by Richards. (Note by Byron.)—A. De M.

[430] John Watkins (d. after 1831), a teacher and miscellaneous writer.

[431] Frederic Shoberl (1775-1853), a miscellaneous writer.

[432] He wrote, besides the Aboriginal Britons, Songs of the Aboriginal Bards (1792), Modern France: a Poem (1793), Odin, a drama (1804), Emma, a drama on the model of the Greek theatre (1804), Poems (2 volumes, 1804), and a Monody on the Death of Lord Nelson (1806).

[433] Henry Kirke White (1785-1806), published his first volume of poems at the age of 18. Southey and William Wilberforce became interested in him and procured for him a sizarship at St. John's College, Cambridge. He at once showed great brilliancy, but he died of tuberculosis at the age of 21.

[434] John Wolcot, known as Peter Pindar (1738-1819), was a London physician. He wrote numerous satirical poems. His Bozzy and Piozzi, or the British Biographers, appeared in 1786, and reached the 9th edition in 1788.

[435] See Vol. I, page 235, note 8 {532}.

[436] Richard Payne Knight (1750-1824) was a collector of bronzes, gems, and coins, many of his pieces being now in the British Museum. He sat in parliament for twenty-six years (1780-1806), but took no active part in legislation. He opposed the acquisition of the Elgin Marbles, holding them to be of little importance. His Analytical Inquiry into the Principles of Taste appeared in 1808.

[437] Mario Nizzoli (1498-1566), a well-known student of Cicero, was for a time professor at the University of Parma. His Observationes in M. Tullium Ciceronem appeared at Pratalboino in 1535. It was revised by his nephew under the title Thesaurus Ciceronianus (Venice, 1570).

[438] See Vol. I, page 314, note 4 {681}.

[439]

"Like the geometer, who bends all his powers To measure the circle, and does not succeed, Thinking what principle he needs."

[440] Francis Quarles (1592-1644), a religious poet. He wrote paraphrases of the Bible and numerous elegies. In the early days of the revolutionary struggle he sided with the Royalists. One of his most popular works was the Emblems (1635), with illustrations by William Marshall.

[441] Regnault de Becourt wrote La Creation du monde, ou Systeme d'organisation primitive suivi de l'interpretation des principaux phenomenes et accidents que se sont operes dans la nature depuis l'origine de univers jusqu'a nos jours (1816). This may be the work translated by Dalmas.

[442] "Because it lacks a holy prophet."

[443] Anghera. See Vol. II, page 60, note 127.

[444] Edmund Curll (1675-1747), a well-known bookseller, publisher, and pamphleteer. He was for a time at "The Peacock without Temple Bar," and later at "The Dial and Bible against St. Dunstan's Church." He was fined repeatedly for publishing immoral works, and once stood in the pillory for it. He is ridiculed in the Dunciad for having been tossed in a blanket by the boys of Westminster School because of an oration that displeased them.

[445] See Vol. II, page 109, note 206.

[446] Encyclopaedia.

[447] Author of the Historia Naturalis (77 A.D.)

[448] Author of the De Institutione Oratorio Libri XII (c. 91 A.D.)

[449] His De Architectures Libri X was not merely a work on architecture and building, but on the education of the architect.

[450] Cyclophoria.

[451] William Caxton (c. 1422-c.1492), sometime Governor of the Company of Merchant Adventurers in Bruges (between 1449 and 1470). He learned the art of printing either at Bruges or Cologne, and between 1471 and 1477 set up a press at Westminster. Tradition says that the first book printed in England was his Game and Playe of Chesse (1474). The Myrrour of the Worlde and th'ymage of the same appeared in 1480. It contains a brief statement on arithmetic, the first mathematics to appear in print in England.

[452] See Vol. I, page 45, note 6 {40}. De Morgan is wrong as to the date of the Margarita Philosophica. The first edition appeared at Freiburg in 1503.

[453] Reisch was confessor to Maximilian I (1459-1519), King of the Romans (1486) and Emperor (1493-1519).

[454] Joachim Sterck Ringelbergh (c. 1499-c. 1536), teacher of philosophy and mathematics in various cities of France and Germany. His Institutionum astronomicarum libri III appeared at Basel in 1528, his Cosmographia at Paris in 1529, and his Opera at Leyden in 1531.

[455] Johannes Heinrich Alsted (1588-1638) was professor of philosophy and theology at his birthplace, Herborn, in Nassau, and later at Weissenberg. He published several works, including the Elementale mathematicum (1611), Systema physicae harmonicae (1612), Methodus admirandorum mathematicorum (1613), Encyclopaedia septem tomis distincta (1630), and the work mentioned above.

[456] Johann Jakob Hoffmann (1635-1706), professor of Greek and history at his birthplace, Basel. He also wrote the Epitome metrica historiae universalis civilis et sacrae ab orbe condito (1686).

[457] Ephraim Chambers (c. 1680-1740), a crotchety, penurious, but kind-hearted freethinker. His Cyclopaedia, or an Universal Dictionary was translated into French and is said to have suggested the great Encyclopedie.

[458] Encyclopedie, ou Dictionnaire raisonne des sciences, des arts et des metiers, par un societe de gens de lettres. Mis en ordre et publie par M. Diderot, et quant a la partie mathematique, par M. d'Alembert. Paris, 1751-1780, 35 volumes.

[459] "From the egg" (state).

[460] See Vol. I, page 382, note 12 {785}.

[461] See Vol. II, page 4, note 15.

[462] "In morals nothing should serve man as a model but God; in the arts, nothing but nature."

[463] Encyclopedie Methodique, ou par ordre de matieres. Paris, 1782-1832, 166-1/2 volumes.

[464] See Vol. II, page 193, note 336.

[465] Encyclopaedia Metropolitana; or, Universal Dictionary of Knowledge. London, 1845, 29 volumes. A second edition came out in 1848-1858 in 40 volumes.

[466] See Vol. I, page 137, note 8 {286}.

[467] See Vol. I, page 80, note 5 {119}.

[468] De Morgan should be alive to satirize some of the statements on the history of mathematics in the eleventh edition.

[469] John Pringle Nichol (1804-1859), Regius professor of astronomy at Glasgow and a popular lecturer on the subject. He lectured in the United States in 1848-1849. His Views of the Architecture of the Heavens (1838) was a very popular work, and his Planetary System (1848, 1850) contains the first suggestion for the study of sun spots by the aid of photography.

[470] See Vol. II, page 109, note 206.

[471] George Long (1800-1879), a native of Poulton, in Lancashire, was called to the University of Virginia when he was only twenty-four years old as professor of ancient languages. He returned to England in 1828 to become professor of Greek at London University. From 1833 to 1849 he edited the twenty-nine volumes of the Penny Cyclopaedia. He was an authority on Roman law.

[472] A legal phrase, "Qui tam pro domina regina, quam pro se ipso sequitur,"—"Who sues as much on the Queen's account as on his own."

[473] Arthur Cayley (1821-1895) was a fellow of Trinity College, Cambridge (1842-1846) and was afterwards a lawyer (1849-1863). During his fourteen years at the bar he published some two hundred mathematical papers. In 1863 he became professor of mathematics at Cambridge, and so remained until his death. His collected papers, nine hundred in number, were published by the Cambridge Press in 13 volumes (1889-1898). He contributed extensively to the theory of invariants and covariants. De Morgan's reference to his coining of new names is justified, although his contemporary, Professor Sylvester, so far surpassed him in this respect as to have been dubbed "the mathematical Adam."

[474] See Vol. II, page 26, note 56.

[475] See Vol. I, page 111, note 3 {207}.

[476] See Vol. I, page 87, note 6 {135}.

[477] Pierre Dupuy (1582-1651) was a friend and relative of De Thou. With the collaboration of his brother and Nicolas Rigault he published the 1620 and 1626 editions of De Thou's History. He also wrote on law and history. His younger brother, Jacques (died in 1656), edited his works. The two had a valuable collection of books and manuscripts which they bequeathed to the Royal Library at Paris.

[478] See Vol. I, page 51, note 3 {51}.

[479] It was Cosmo de' Medici (1590-1621) who was the patron of Galileo.

[480] See Vol. I, page 40, note 4 {20}.

[481] See Vol. I, page 106, note 4 {188}.

[482] Sir Edward Sherburne (1618-1702), a scholar of considerable reputation. The reference by De Morgan is to The Sphere of Marcus Manilius, in the appendix to which is a Catalogue of Astronomers, ancient and modern.

[483] George Parker, second Earl of Macclesfield (1697-1764). He erected an observatory at Shirburn Castle, Oxfordshire, in 1739, and fitted it out with the best equipment then available. He was President of the Royal Society in 1752.

[484] See Vol. II, page 148, note 263.

[485] See Vol. I, page 140, note 7 {296}.

[486] See Vol. I, page 106, note 4 {188}.

[487] Edward Bernard (1638-1696), although Savilian professor of astronomy at Oxford, was chiefly interested in archeology.

[488] See Vol. I, page 107, note 1 {190}.

[489] See Vol. I, page 107, note 1 {190}.

[490] See Vol. I, page 135, note 3 {281}.

[491] Philip Dormer Stanhope, fourth Earl of Chesterfield (1694-1773), well known for the letters written to his son which were published posthumously (1774).

[492] Peter Daval (died in 1763), Vice-President of the Royal Society, and an astronomer of some ability.

[493] See Vol. I, page 376, note 1 {766}.

[494] William Oughtred (c. 1573-1660), a fellow of King's College, Cambridge, and afterwards vicar of Aldbury, Surrey, wrote the best-known arithmetic and trigonometry of his time. His Arithmeticae in Numero & Speciebus Institutio ... quasi Clavis Mathematicae est (1631) went through many editions and appeared in English as The Key to the Mathematicks new forged and filed in 1647.

[495] See Vol. I, page 140, note 5 {294}.

[496] Stephen Jordan Rigaud (1816-1859) was senior assistant master of Westminster School (1846) and head master of Queen Elizabeth's School at Ipswich (1850). He was made Bishop of Antigua in 1858 and died of yellow fever the following year.

[497] He also wrote a memoir of his father, privately printed at Oxford in 1883.

[498] See Vol. I, page 69, note 3 {96}.

[499] See Vol. I, page 106, note 4 {188}.

[500] William Gascoigne was born at Middleton before 1612 and was killed in the battle of Marston Moor in 1644. He was an astronomer and invented the micrometer with movable threads (before 1639).

[501] Seth Ward (1617-1689) was deprived of his fellowship at Cambridge for refusing to sign the covenant. He became professor of astronomy at Oxford (1649), Bishop of Exeter (1662), Bishop of Salisbury (1667), and Chancellor of the Garter (1671). He is best known for his solution of Kepler's problem to approximate a planet's orbit, which appeared in his Astronomia geometrica in 1656.

[502] See Vol. I, page 110, note 2 {198}.

[503] See Vol. I, page 100, note 2 {172}.

[504] See Vol. I, page 107, note 1 {190}.

[505] See Vol. I page 114, note 6 {220}.

[506] See Vol. I, page 77, note 4 {118}.

[507] See Vol. I, page 125, note 3 {253}.

[508] See Vol. I, page 105, note 2 {186}.

[509] Heinrich Oldenburgh (1626-1678) was consul in England for the City of Bremen, his birthplace, and afterwards became a private teacher in London. He became secretary of the Royal Society and contributed on physics and astronomy to the Philosophical Transactions.

[510] Thomas Brancker, or Branker (1636-1676) wrote the Doctrinae sphaericae adumbratio et usus globorum artificialium (1662) and translated the algebra of Rhonius with the help of Pell. The latter work appeared under the title of An Introduction to Algebra (1668), and is noteworthy as having brought before English mathematicians the symbol / for division. The symbol never had any standing on the Continent for this purpose, but thereafter became so popular in England that it is still used in all the English-speaking world.

[511] See Vol. I, page 118, note 1 {230}.

[512] Pierre Bertius (1565-1629) was a native of Flanders and was educated at London and Leyden. He became a professor at Leyden, and later held the chair of mathematics at the College de France. He wrote chiefly on geography.

[513] See Vol. II, page 297, note 487.

[514] Giovanni Alphonso Borelli (1608-1679) was professor of mathematics at Messina (1646-1656) and at Pisa (1656-1657), after which he taught in Rome at the Convent of St. Panteleon. He wrote several works on geometry, astronomy, and physics.

[515] See Vol. I, page 172, note 2 {381}.

[516] Ignace Gaston Pardies (c. 1636-1673), a Jesuit, professor of ancient languages and later of mathematics and physics at the College of Pau, and afterwards professor of rhetoric at the College Louis-le-Grand at Paris. He wrote on geometry, astronomy and physics.

[517] Pierre Fermat was born in 1608 (or possibly in 1595) near Toulouse, and died in 1665. Although connected with the parliament of Toulouse, his significant work was in mathematics. He was one of the world's geniuses in the theory of numbers, and was one of the founders of the theory of probabilities and of analytic geometry. After his death his son published his edition of Diophantus (1670) and his Varia opera mathematica (1679).

[518] This may be Christopher Townley (1603-1674) the antiquary, or his nephew, Richard, who improved the micrometer already invented by Gascoigne.

[519] Adrien Auzout a native of Rouen, who died at Rome in 1691. He invented a screw micrometer with movable threads (1666) and made many improvements in astronomical instruments.

[520] See Vol. I, page 66, note 9 {86}.

[521] See Vol. I, page 124, note 7 {248}.

[522] John Machin (d. 1751) was professor of astronomy at Gresham College (1713-1751) and secretary of the Royal Society. He translated Newton's Principia into English. His computation of [pi] to 100 places is given in William Jones's Synopsis palmariorum matheseos (1706).

[523] Pierre Remond de Montmort (1678-1719) was canon of Notre Dame until his marriage. He was a gentleman of leisure and devoted himself to the study of mathematics, especially of probabilities.

[524] Roger Cotes (1682-1716), first Plumian professor of astronomy and physics at Cambridge, and editor of the second edition of Newton's Principia. His posthumous Harmonia Mensurarum (1722) contains "Cotes's Theorem" on the binomial equation. Newton said of him, "If Mr. Cotes had lived we had known something."

[525] See Vol. I, page 135, note 3 {281}.

[526] See Vol. I, page 377, note 4 {769}.

[527] Charles Rene Reyneau (1656-1728) was professor of mathematics at Angers. His Analyse demontree, ou Maniere de resoudre les problemes de mathematiques (1708) was a successful attempt to popularize the theories of men like Descartes, Newton, Leibnitz, and the Bernoullis.

[528] Brook Taylor (1685-1731), secretary of the Royal Society, and student of mathematics and physics. His Methodus incrementorum directa et inversa (1715) was the first treatise on the calculus of finite differences. It contained the well-known theorem that bears his name.

[529] Pierre Louis Moreau de Maupertuis (1698-1759) was sent with Clairaut (1735) to measure an arc of a meridian in Lapland. He was head of the physics department in the Berlin Academy from 1745 until 1753. He wrote Sur la figure de la terre (1738) and on geography and astronomy.

[530] Pierre Bouguer (1698-1758) was professor of hydrography at Paris, and was one of those sent by the Academy of Sciences to measure an arc of a meridian in Peru (1735). The object of this and the work of Maupertuis was to determine the shape of the earth and see if Newton's theory was supported.

[531] Charles Marie de la Condamine (1701-1774) was a member of the Paris Academy of Sciences and was sent with Bouguer to Peru, for the purpose mentioned in the preceding note. He wrote on the figure of the earth, but was not a scientist of high rank.

[532] See Vol. I, page 136, note 5 {283}.

[533] See Vol. II, page 296, note 483.

[534] Thomas Baker (c. 1625-1689) gave a geometric solution of the biquadratic in his Geometrical Key, or Gate of Equations unlocked (1684).

[535] See Vol. I, page 160, note 5 {350}.

[536] See Vol. I, page 87, note 4 {133}.

[537] See Vol. I, page 132, note 2 {272}.

[538] See Vol. I, page 118, second note 1 {231}.

[539] The name of Newton is so well known that no note seems necessary. He was born at Woolsthorpe, Lincolnshire, in 1642, and died at Kensington in 1727.

[540] John Keill (1671-1721), professor of astronomy at Oxford from 1710, is said to have been the first to teach the Newtonian physics by direct experiment, the apparatus being invented by him for the purpose. He wrote on astronomy and physics. His Epistola de legibus virium centripetarum, in the Philosophical Transactions for 1708, accused Leibnitz of having obtained his ideas of the calculus from Newton, thus starting the priority controversy.

[541] Thomas Digges (d. in 1595) wrote An Arithmeticall Militare Treatise, named Stratioticos (1579), and completed A geometrical practise, named Pantometria (1571) that had been begun by his father, Leonard Digges.

[542] John Dee (1527-1608), the most famous astrologer of his day, and something of a mathematician, wrote a preface to Billingsley's translation of Euclid into English (1570).

[543] See Vol. I, page 76, note 3 {112}.

[544] Thomas Harriot (1560-1621) was tutor in mathematics to Sir Walter Raleigh, who sent him to survey Virginia (1585). He was one of the best English algebraists of his time, but his Artis Analyticae Praxis ad Aequationes Algebraicas resolvendas (1631) did not appear until ten years after his death.

[545] Thomas Lydiat (1572-1626), rector of Alkerton, devoted his life chiefly to the study of chronology, writing upon the subject and taking issue with Scaliger (1601).

[546] See Vol. I, page 69, note 3 {96}.

[547] Walter Warner edited Harriot's Artis Analyticae Praxis (1631). Tarporley is not known in mathematics.

[548] See Vol. I, page 105, note 2 {186}.

[549] See Vol. I, page 115, note 3 {224}.

[550] See Vol. II, page 300, note 509.

[551] See Vol. I, page 107, note 1 {190}.

[552] Sir Samuel Morland (1625-1695) was a diplomat and inventor. For some years he was assistant to John Pell, then ambassador to Switzerland. He wrote on arithmetical instruments invented by him (1673), on hydrostatics (1697) and on church history (1658).

[553] See Vol. I, page 153, note 4 {337}.

[554] See Vol. I, page 85, note 2 {129}.

[555] See Vol. I, page 43, note 8 {33}.

[556] See Vol. I, page 43, note 7 {32}.

[557] See Vol. I, page 382, note 13 {786}. The history of the subject may be followed in Braunmuehl's Geschichte der Trigonometrie.

[558] See Vol. I, page 377, note 3 {768}.

[559] See Vol. I, page 108, note 2 {192}.

[560] Michael Dary wrote Dary's Miscellanies (1669), Gauging epitomised (1669), and The general Doctrine of Equation (1664).

[561] John Newton (1622-1678), canon of Hereford (1673), educational reformer, and writer on elementary mathematics and astronomy.

[562] See Vol. I, page 87, note 4 {133}.

[563] "The average of the two equal altitudes of the sun before and after dinner."

[564] See Vol. I, page 42, note 4 {24}.

[565] London, 1678. It went though many editions.

[566] "This I who once ..."

[567] Arthur Murphy (1727-1805) worked in a banking house until 1754. He then went on the stage and met with some success at Covent Garden. His first comedy, The Apprentice (1756) was so successful that he left the stage and took to play writing. His translation of Tacitus appeared in 1793, in four volumes.

[568] Edmund Wingate (1596-1656) went to Paris in 1624 as tutor to Princess Henrietta Maria and remained there several years. He wrote L'usage de la regle de proportion (Paris, 1624, with an English translation in 1626), Arithmetique Logarithmetique (Paris, 1626, with an English translation in 1635), and Of Natural and Artificial Arithmetick (London, 1630, revised in 1650-1652), part I of which was one of the most popular textbooks ever produced in England.

[569] John Lambert (1619-1694) was Major-General during the Revolution and helped to draw up the request for Cromwell to assume the protectorate. He was imprisoned in the Tower by the Rump Parliament. He was confined in Guernsey until the clandestine marriage of his daughter Mary to Charles Hatton, son of the governor, after which he was removed (1667) to St. Nicholas in Plymouth Sound.

[570] Samuel Foster (d. in 1652) was made professor of astronomy at Gresham College in March, 1636, but resigned in November of that year, being succeeded by Mungo Murray. Murray vacated his chair by marriage in 1641 and Foster succeeded him. He wrote on dialling and made a number of improvements in geometric instruments.

[571] "Twice of the word a minister," that is, twice a minister of the Gospel.

[572] This is The Lives of the Professors of Gresham College to which is prefixed the Life of the Founder, Sir Thomas Gresham, London, 1740. It was written by John Ward (c. 1679-1758), professor of rhetoric (1720) at Gresham College and vice-president (1752) of the Royal Society.

[573] Charles Montagu (1661-1715), first Earl of Halifax, was Lord of the Treasury in 1692, and was created Baron Halifax in 1700 and Viscount Sunbury and Earl of Halifax in 1714. He introduced the bill establishing the Bank of England, the bill becoming a law in 1694. He had troubles of his own, without considering Newton, for he was impeached in 1701, and was the subject of a damaging resolution of censure as auditor of the exchequer in 1703. Although nothing came of either of these attacks, he was out of office during much of Queen Anne's reign.

[574] See Vol. II, page 302, note 547.

[575] See Vol. I, page 105, note 2 {186}.

[576] James Dodson (d. 1757) was master of the Royal Mathematical School, Christ's Hospital. He was De Morgan's great-grandfather. The Anti-Logarithmic Canon was published in 1742.

[577] See Vol. I, page 106, note 4 {188}.

[578] See Vol. I, page 110, note 2 {198}.

[579] Richard Busby, (1606-1695), master of Westminster School (1640) had among his pupils Dryden and Locke.

[580] See Vol. I, page 107, note 1 {190}.

[581] Herbert Thorndike (1598-1672), fellow of Trinity College, Cambridge (1620-1646), and Prebend of Westminster (1661), was a well-known theological writer of the time.

[582] See Vol. I, page 140, note 5 {294}.

[583] See Vol. I, page 108, note 2 {192}.

[584] "Labor performed returns in a circle."

[585] See Vol. II, page 208.

[586] "Whatever objections one may make to the above arguments, one always falls into an absurdity."

[587] See Vol. II. page 11, note 29. The Circle Squared; and the solution of the problem adapted to explain the difference between square and superficial measurement appeared at Brighton in 1865.

[588] "And beyond that nothing."

[589] Gillott (1759-1873) was the pioneer maker of steel pens by machinery, reducing the price from 1s. each to 4d. a gross. He was a great collector of paintings and old violins.

[590] William Edward Walker wrote five works on circle squaring (1853, 1854, 1857, 1862, 1864), mostly and perhaps all published at Birmingham.

[591] Solomon M. Drach wrote An easy Rule for formulizing all Epicyclical Curves (London, 1849), On the Circle area and Heptagon-chord (London, 1864), An easy general Rule for filling up all Magic Squares (London, 1873), and Hebrew Almanack-Signs (London, 1877), besides numerous articles in journals.

[592] See Vol. I, page 168, note 3 {371}.

[593] See Vol. I, page 254, note 2 {580}.

[594] See Vol. I, page 98, note 6 {163}.

[595] Robert Fludd or Flud (1574-1637) was a physician with a large London practice. He denied the diurnal rotation of the earth, and was attacked by Kepler and Mersenne, and accused of magic by Gassendi. His Apologia Compendiania, Fraternitatem de Rosea Cruce suspicionis ... maculis aspersam, veritatis quasi Fluctibus abluens (Leyden, 1616) is one of a large number of works of the mystic type.

[596] Consult To the Christianity of the Age. Notes ... comprising an elucidation of the scope and contents of the writings ... of Dionysius Andreas Freher (1854).

[597] Sir William Robert Grove (1811-1896), although called to the bar (1835) and to the bench (1853), is best known for his work as a physicist. He was professor of experimental philosophy (1840-1847) at the London Institution, and invented a battery (1839) known by his name. His Correlation of Physical Forces (1846) went through six editions and was translated into French.

[598] Johann Tauler (c. 1300-1361), a Dominican monk of Strassburg, a mystic, closely in touch with the Gottesfreunde of Basel. His Sermons first appeared in print at Leipsic in 1498.

[599] Paracelsus (c. 1490-1541). His real name was Theophrastes Bombast von Hohenheim, and he took the name by which he is generally known because he held himself superior to Celsus. He was a famous physician and pharmacist, but was also a mystic and neo-Platonist. He lectured in German on medicine at Basel, but lost his position through the opposition of the orthodox physicians and apothecaries.

[600] See Vol. I, page 256, note 2 {588}.

[601] Philip Schwarzerd (1497-1560) was professor of Greek at Wittenberg. He helped Luther with his translation of the Bible.

[602] Johann Reuchlin (1455-1522), the first great German humanist, was very influential in establishing the study of Greek and Hebrew in Germany. His lectures were mostly delivered privately in Heidelberg and Stuttgart. Unlike Melanchthon, he remained in the Catholic Church.

[603] Joseph Chitty (1776-1841) published his Precedents of Pleading in 1808 and his Reports of Cases on Practice and Pleading in 1820-23 (2 volumes).

[604] See Vol. I, page 44, note 1 {35}.

[605] See Vol. I, page 44, note 4 {38}.

[606] Jean Pelerin, also known as Viator, who wrote on perspective. His work appeared in 1505, with editions in 1509 and 1521.

[607] Henry Stephens. See Vol. I, page 44, note 3 {37}.

[608] The well-known grammarian (1745-1826). He was born at Swatara, in Pennsylvania, and practised law in New York until 1784, after which he resided in England. His grammar (1795) went through 50 editions, and the abridgment (1818) through 120 editions. Murray's friend Dalton, the chemist, said that "of all the contrivances invented by human ingenuity for puzzling the brains of the young, Lindley Murray's grammar was the worst."

[609] Robert Recorde (c. 1510-1558) read and probably taught mathematics and medicine at Cambridge up to 1545. After that he taught mathematics at Oxford and practised medicine in London. His Grounde of Artes, published about 1540, was the first arithmetic published in English that had any influence. It went through many editions. The Castle of Knowledge appeared in 1551. It was a textbook on astronomy and the first to set forth the Copernican theory in England. Like Recorde's other works it was written on the catechism plan. His Whetstone of Witte ... containying thextraction of Rootes: The Cosike practise, with the rule of Equation: and the woorkes of Surde Nombres appeared in 1557, and it is in this work that the modern sign of equality first appears in print. The word "Cosike" is an adjective that was used for a long time in Germany as equivalent to algebraic, being derived from the Italian cosa, which stood for the unknown quantity.

[610] Robert Cecil (c. 1563-1612), first Earl of Salisbury, Secretary of State under Elizabeth (1596-1603) and under James I (1603-1612).

[611] In America the German pronunciation is at present universal among mathematicians, as in the case of most other German names. This is due, no doubt, to the great influence that Germany has had on American education in the last fifty years.

[612] The latest transliteration is substantially K'ung-fu-tzǔ.

[613] The tendency seems to be, however, to adopt the forms used of individuals or places as rapidly as the mass of people comes to be prepared for it. Thus the spelling Leipzig, instead of Leipsic, is coming to be very common in America.

[614] Sir Edward Coke (1552-1634), the celebrated jurist.

[615] Dethlef Cluvier or Cluever (d. 1708 at Hamburg) was a nephew, not a grandson, of Philippe Cluvier, or Philipp Cluever (1580-c. 1623). Dethlef traveled in France and Italy and then taught mathematics in London. He wrote on astronomy and philosophy and also published in the Acta Eruditorum (1686) his Schediasma geometricum de nova infinitorum scientia. Quadratura circuli infinitis modis demonstrata, and his Monitum ad geometras (1687). Philippe was geographer of the Academy of Leyden. His Introductionis in universam geographiam tam veterem quam novam libri sex appeared at Leyden in 1624, about the time of his death.

[616] See Vol. I, page 124, note 7 {248}.

[617] Bernard Nieuwentijt (1654-1718), a physician and burgomaster at Purmerend. His Considerationes circa Analyseos ad quantitates infinite parvas applicatae Principia et Calculi Differentialis usum (Amsterdam, 1694) was attacked by Leibnitz. He replied in his Considerationes secundae (1694), and also wrote the Analysis Infinitorum, seu Curvilineorum Proprietates ex Polygonorum Natura deductae (1695). His most famous work was on the existence of God, Het Regt Gebruik der Werelt Beschouwingen (1718).

[618] "From a given line to construct" etc.

[619] "Pirates do not fight one another."

[620] Claude Mallemens (Mallement) de Messanges (1653-1723) was professor of philosophy at the College du Plessis, in Paris, for 34 years. The work to which De Morgan refers is probably the Fameux Probleme de la quadrature du cercle, resolu geometriquement par le cercle et a ligne droite that appeared in 1683.

[621] On Tycho Brahe see Vol. I, page 76, note 3 {112}.

[622] Wilhelm Frederik von Zytphen also published the Tidens Stroem, a chronological table, in 1840. The work to which De Morgan refers, the Solens Bevaegelse i Verdensrummet, appeared first in 1861. De Morgan seems to have missed his Nogl Ord om Cirkelens Quadratur which appeared in 1865, at Copenhagen.

[623] James Joseph Sylvester (1814-1897), professor of natural philosophy at University College, London (1837-1841), professor of mathematics at the University of Virginia (1841-1845), actuary in London (1845-1855), professor of mathematics at Woolwich (1877-1884) and at Johns Hopkins University, Baltimore (1877-1884), and Savilian professor of geometry at Oxford (1884-1894).

[624] See Vol. I, page 76, note 3 {112}.

[625] See Vol. II, page 205, note 349.

[626] See Vol. I, page 76, note 3 {112}.

[627] See Vol. I, page 46, note 1 {42}.

[628] See Vol. II, page 183, note 318.

[629] See Vol. I, page 321, note 2 {691}.

[630] James Mill, born 1773, died 1836.

[631] See Vol. II, page 3, note 11.

[632] See Vol. II, page 3, note 13.

[633] See Vol. II, page 3, note 14.

[634] This anecdote is printed at page 4 (Vol. II); but as it is used in illustration here, and is given more in detail, I have not omitted it.—S.E. De M.

[635] See Vol. II, page 4, note 15.

[636] See Vol. I, page 382, note 13 {786}.

[637] "Monsieur, (a + b^{n})/n = x, whence God exists; answer that!"

[638] "Monsieur, you know very well that your argument requires the development of x according to integral powers of n."

[639] See Vol. I, page 153, note 4 {337}.

[640] Thomas Love Peacock (1785-1866) an English novelist and poet.

[641] Perhaps Dr. Samuel Warren (1807-1877), the author of Ten Thousand a Year (serially in Blackwood's in 1839; London, 1841).

[642] See Vol. I, page 255, note 6 {584}.

[643] "From many, one; much in little; Ultima Thule (the most remote region); without which not."

[644] Spurius Maelius (fl. 440 B. C.), who distributed corn freely among the poor in the famine of 440 B. C. and was assassinated by the patricians.

[645] Spurius Cassius Viscellinus, Roman consul in 502, 493, and 486 B. C. Put to death in 485.

[646] "O what a fine bearing, he said, that has no brain."

[647] Sir William Rowan Hamilton. See Vol. I, page 332, note 4 {709}.

[648] William Allen Whitworth, the author of the well-known Choice and Chance (Cambridge, 1867), and other works.

[649] James Maurice Wilson, whose Elementary Geometry appeared in 1868 and went through several editions.

[650] See Vol. II, page 183, note 315.

[651] "Force of inertia conquered," and "Victory in the whole heavens."

[652] "With all his might."

[653] George Berkeley (1685-1753), Bishop of Cloyne, the idealistic philosopher and author of the Principles of Human Knowledge (1710), The Analyst, or a Discourse addressed to an Infidel Mathematician (1734), and A Defense of Freethinking in Mathematics (1735). He asserted that space involves the idea of movement without the sensation of resistance. Space sensation less than the "minima sensibilia" is, therefore, impossible. From this he argues that infinitesimals are impossible concepts.

[654] See Vol. I, page 85, note 2 {129}.

[655] See Vol. I, page 81, note 6 {120}.

[656] Edwin Dunkin revised Lardner's Handbook of Astronomy (1869) and Milner's The Heavens and the Earth (1873) and wrote The Midnight Sky (1869).

[657] Michael Faraday (1791-1867) the celebrated physicist and chemist. He was an assistant to Sir Humphrey Davy (1813) and became professor of chemistry at the Royal Institution, London, in 1827.

[658] "If you teach a fool he shows no joyous countenance; he cordially hates you; he wishes you buried."

[659] "Every man is an animal, Sortes is a man, therefore Sortes is an animal."

[660]

"May some choice patron bless each grey goose quill; May every Bavius have his Bufo still."—POPE, Prologue to the Satires.

Bavius has become proverbial as a bad poet from the lines in Vergil's Eclogues (III, 90):

"Qui Bavium non odit, amet tua carmina, Maevi, Atque idem jungat vulpes, et mulgeat hircos."

"He who does not hate Bavius shall love thy verses, O Maevius; and the same shall yoke foxes and shall milk he-goats."

Bavius and Maevius were the worst of Latin poets, condemned by Horace as well as Vergil.

[661] See Vol. II, page 158, note 279.

[662] "Honest," "useful," "handsome," "sweet."

[663] "Let not the fourth man attempt to speak."

[664]

"In those old times,—ah 'Twas just like this, ah!"

[665] See Vol. I, page 382, note 12 {785}.

[666] These remarks were never written.—S. E. De M.

[667]

"Fleas, flies, and friars, are masters who sadly the people abuse, And thistles and briars are sure growing grains to abuse. O Christ, who hatest strife and slayst all things in peace, Destroy where'er are rife, briars, friars, flies and fleas. Fleas, flies, and friars foul fall them these fifteen years For none that there is loveth fleas, flies, nor freres."

[668] "It is my plan to restore to an unskilled race the worthy arts of a better life."

[669] The first sentences of the first oration of Cicero against Catiline: "Quo usque tandem abutere, Catilina, patientia nostra?" (How long, O Catiline, will you abuse our patience?) "Quamdiu etiam furor iste tuus nos eludet?" (How long will this your madness baffle us?) "Nihilne te nocturnum praesidium Palati, ... nihil horum ora voltusque moverunt?" (Does the night watch of the Palatium, ... do the faces and expressions of all these men fail to move you?) "In te conferri ..." (This plague should have been inflicted upon you long ago, which you have plotted against us so long.)

[670] "Beware of the things that are marked."

[671] "Farewell, ye teachers without learning! See to it that at our next meeting we may find you strong in body and sound in mind."

[672] See Vol. I, page 336, note 8 {713}.

[673] See Vol. I, page 229, note 2 {515}.

[674] This proof, although capable of improvement, is left as in the original. Those who may be interested in the mathematics of the question, may consult F. Enriques, Fragen der Elementargeometrie (German by Fleischer), Leipsic, 1907, Part II, p. 267; F. Rudio, Archimedes, Huygens, Lambert, Legendre. Vier Abhandlungen ueber die Kreismessung, Leipsic, 1892; F. Klein, Famous Problems of Elementary Geometry (English by Beman and Smith), Boston, 1895; J. W. A. Young, Monographs on Modern Mathematics, New York, 1911, Chap. IX (by the editor of the present edition of De Morgan.)

[675] See Vol. I, page 69, note 2 {95}.

[676] See Vol. I, page 137, note 8 {286}.

[677] Joseph Allen Galbraith who, with Samuel Haughton, wrote the Galbraith and Haughton's Scientific Manuals. (Euclid, 1856; Algebra, 1860; Trigonometry, 1854; Optics, 1854, and others.)

[678] This note on Carlyle (1795-1881) is interesting. The translation of Legendre appeared in the same year (1824) as his translation of Goethe's Wilhelm Meister.

[679] Michael Stifel (1487-1567), also known as Stiefel, Styfel, and Stifelius, was an Augustine monk but became a convert to Lutheranism. He was professor of mathematics at Jena (1559-1567). His edition of the Coss appeared at Koenigsberg in 1553, the first edition having been published in 1525. The + and - signs first appeared in print in Widman's arithmetic of 1489, but for purposes of algebra this book was one of the first to make them known.

[680] Christoff Rudolff was born about 1500 and died between 1540 and 1552. Die Coss appeared in 1525 and his arithmetic in 1526.

* * * * *

Corrections made to printed original.

Page 9, "long-fostered prejudice": 'perjudice' in original.

Page 73, "Pensees, ch. 7": 'Pansees' in original.

Page 127, "and pulled out a plum": 'und' in original.

Page 147, "did not come forward": 'forword' in original.

Page 172, "come into general circulation": 'circulalation' in original.

Ibid., "the more difficult fractions which we have got": 'he have got' in original.

Page 192, "it has been stated": 'started' in original.

Page 216, "the obsolete word tetch of the same meaning": 'meaing' in original.

Page 228, "[Greek: dioklasianos]": 'dioklalasianos' in original.

Page 233. After 'Henry E. Manning' were printed two paragraphs 'Shilling versus Franc.' and 'Teutonic Long Hundred 120 versus 100 or the Decimal question.' These appear to have been set in error, there is no applicable context.

Page 316, "in a manner depending upon the difference": 'maner' in original.

Page 322, "neither what Newton did, nor what was done before him.": 'not' (for 'nor') in original.

Page 344, "Victoria toto coelo": 'tolo' in original.

Page 368, "cannot be brought up to 1": 'up to +-' in original.

Page 371, "Q2=b2 Q1+a2": 'Q2=b2 Q1-a2' in original.

Note 50, "all who were not in the road to Heaven were excommunicated": 'excomunicated' in original.

Note 372, "[Greek: he alazoneia biou]": 'alaxoneia' in original.

Ibid., "Iapetos": 'Ispetos' in original.

Ibid., "Papeiskos": 'Paspeisoks' in original.

Ibid., "[Greek: dioklasianos]": 'dioklalasianos' in original.

THE END