"O sweet soul, what good shall I declareThat 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 theNew 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, theSumario compendioso ... con algunas reglas tocantes al Aritmética, 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 Abbé but was really nothing more than a "clerc tonsuré." 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 theAboriginal 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 aMonody 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. HisBozzy 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. HisAnalytical Inquiry into the Principles of Tasteappeared in 1808.[437]Mario Nizzoli (1498-1566), a well-known student of Cicero, was for a time professor at the University of Parma. HisObservationes in M. Tullium Ciceronemappeared at Pratalboino in 1535. It was revised by his nephew under the titleThesaurus Ciceronianus(Venice, 1570).[438]See Vol. I, page 314, note 4 {681}.[439]"Like the geometer, who bends all his powersTo 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 theEmblems(1635), with illustrations by William Marshall.[441]Regnault de Bécourt wroteLa Création du monde, ou Système d'organisation primitive suivi de l'interprétation des principaux phénomènes et accidents que se sont opérés dans la nature depuis l'origine de univers jusqu'à nos jours(1816). This may be the work translated by Dalmas.[442]"Because it lacks a holy prophet."[443]Angherà. See Vol. II, page 60, note127.[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 theDunciadfor 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, note206.[446]Encyclopædia.[447]Author of theHistoria Naturalis(77 A.D.)[448]Author of theDe Institutione Oratorio LibriXII (c. 91 A.D.)[449]HisDe Architectures LibriX 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 hisGame and Playe of Chesse(1474). TheMyrrour of the Worlde and th'ymage of the sameappeared 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 theMargarita 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. HisInstitutionum astronomicarum libri IIIappeared at Basel in 1528, hisCosmographiaat Paris in 1529, and hisOperaat 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 theElementale mathematicum(1611),Systema physicae harmonicae(1612),Methodus admirandorum mathematicorum(1613),Encyclopædia 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 theEpitome metrica historiæ universalis civilis et sacræ ab orbe condito(1686).[457]Ephraim Chambers (c. 1680-1740), a crotchety, penurious, but kind-hearted freethinker. HisCyclopædia, or an Universal Dictionarywas translated into French and is said to have suggested the greatEncyclopédie.[458]Encyclopédie, ou Dictionnaire raisonné des sciences, des arts et des métiers, par un société de gens de lettres. Mis en ordre et publié par M. Diderot, et quant à la partie mathématique, 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, note15.[462]"In morals nothing should serve man as a model but God; in the arts, nothing but nature."[463]Encyclopédie Méthodique, ou par ordre de matières.Paris, 1782-1832, 166½ volumes.[464]See Vol. II, page 193, note336.[465]Encyclopædia 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. HisViews of the Architecture of the Heavens(1838) was a very popular work, and hisPlanetary System(1848, 1850) contains the first suggestion for the study of sun spots by the aid of photography.[470]See Vol. II, page 109, note206.[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 thePenny Cyclopædia. 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, note56.[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 toThe Sphere of Marcus Manilius, in the appendix to which is aCatalogue 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, note263.[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. HisArithmeticæ in Numero & Speciebus Institutio ... quasi Clavis Mathematicæ est(1631) went through many editions and appeared in English asThe Key to the Mathematicks new forged and filedin 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 hisAstronomia geometricain 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 thePhilosophical Transactions.[510]Thomas Brancker, or Branker (1636-1676) wrote theDoctrinæ sphæricæ adumbratio et usus globorum artificialium(1662) and translated the algebra of Rhonius with the help of Pell. The latter work appeared under the title ofAn 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 Collège de France. He wrote chiefly on geography.[513]See Vol. II, page 297, note487.[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 Collège of Pau, and afterwards professor of rhetoric at the Collège 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 hisVaria 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'sPrincipiainto English. His computation ofπto 100 places is given in William Jones'sSynopsis palmariorum matheseos(1706).[523]Pierre Rémond 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'sPrincipia. His posthumousHarmonia 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 Réné Reyneau (1656-1728) was professor of mathematics at Angers. HisAnalyse démontrée, ou Manière de resoudre les problèmes de mathématiques(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. HisMethodus 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 wroteSur 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, note483.[534]Thomas Baker (c. 1625-1689) gave a geometric solution of the biquadratic in hisGeometrical 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. HisEpistola 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) wroteAn Arithmeticall Militare Treatise, named Stratioticos(1579), and completedA 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 hisArtis Analyticæ 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'sArtis 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, note509.[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 Braunmühl'sGeschichte der Trigonometrie.[558]See Vol. I, page 377, note 3 {768}.[559]See Vol. I, page 108, note 2 {192}.[560]Michael Dary wroteDary's Miscellanies(1669),Gauging epitomised(1669), andThe 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 wroteL'usage de la règle de proportion(Paris, 1624, with an English translation in 1626),Arithmétique Logarithmétique(Paris, 1626, with an English translation in 1635), andOf 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 isThe 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, note547.[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. TheAnti-Logarithmic Canonwas 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, page208.[586]"Whatever objections one may make to the above arguments, one always falls into an absurdity."[587]See Vol. II. page 11, note29.The Circle Squared; and the solution of the problem adapted to explain the difference between square and superficial measurementappeared 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 wroteAn 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), andHebrew 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. HisApologia 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]ConsultTo 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. HisCorrelation 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. HisSermonsfirst 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 hisPrecedents of Pleadingin 1808 and hisReports of Cases on Practice and Pleadingin 1820-23 (2 volumes).[604]See Vol. I, page 44, note 1 {35}.[605]See Vol. I, page 44, note 4 {38}.[606]Jean Pèlerin, 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. HisGrounde of Artes, published about 1540, was the first arithmetic published in English that had any influence. It went through many editions. TheCastle of Knowledgeappeared 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. HisWhetstone of Witte ... containying thextraction of Rootes: The Cosike practise, with the rule of Equation: and the woorkes of Surde Nombresappeared 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 Italiancosa, 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 Clüver (d. 1708 at Hamburg) was a nephew, not a grandson, of Philippe Cluvier, or Philipp Clüver (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 theActa Eruditorum(1686) hisSchediasma geometricum de nova infinitorum scientia.Quadratura circuli infinitis modis demonstrata, and hisMonitum ad geometras(1687). Philippe was geographer of the Academy of Leyden. HisIntroductionis in universam geographiam tam veterem quam novam libri sexappeared 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. HisConsiderationes circa Analyseos ad quantitates infinite parvas applicatæ Principia et Calculi Differentialis usum(Amsterdam, 1694) was attacked by Leibnitz. He replied in hisConsiderationes secundæ(1694), and also wrote theAnalysis Infinitorum, seu Curvilineorum Proprietates ex Polygonorum Natura deductæ(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 Collège du Plessis, in Paris, for 34 years. The work to which De Morgan refers is probably theFameux Problème de la quadrature du cercle, résolu géometriquement par le cercle et a ligne droitethat appeared in 1683.[621]On Tycho Brahe see Vol. I, page 76, note 3 {112}.[622]Wilhelm Frederik von Zytphen also published theTidens Ström, a chronological table, in 1840. The work to which De Morgan refers, theSolens Bevægelse i Verdensrummet, appeared first in 1861. De Morgan seems to have missed hisNogl Ord om Cirkelens Quadraturwhich 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, note349.[626]See Vol. I, page 76, note 3 {112}.[627]See Vol. I, page 46, note 1 {42}.[628]See Vol. II, page 183, note318.[629]See Vol. I, page 321, note 2 {691}.[630]James Mill, born 1773, died 1836.[631]See Vol. II, page 3, note11.[632]See Vol. II, page 3, note13.[633]See Vol. II, page 3, note14.[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, note15.[636]See Vol. I, page 382, note 13 {786}.[637]"Monsieur, (a+bn)/n=x, whence God exists; answer that!"[638]"Monsieur, you know very well that your argument requires the development ofxaccording to integral powers ofn."[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 ofTen 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 Mælius (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-knownChoice and Chance(Cambridge, 1867), and other works.[649]James Maurice Wilson, whoseElementary Geometryappeared in 1868 and went through several editions.[650]See Vol. II, page 183, note315.[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 thePrinciples of Human Knowledge(1710),The Analyst, or a Discourse addressed to an Infidel Mathematician(1734), andA 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'sHandbook of Astronomy(1869) and Milner'sThe Heavens and the Earth(1873) and wroteThe 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]
"O sweet soul, what good shall I declareThat heretofore was thine, since such are thy remains!"
"O sweet soul, what good shall I declareThat heretofore was thine, since such are thy remains!"
"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 theNew 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, theSumario compendioso ... con algunas reglas tocantes al Aritmética, 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 Abbé but was really nothing more than a "clerc tonsuré." 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 theAboriginal 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 aMonody 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. HisBozzy 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. HisAnalytical Inquiry into the Principles of Tasteappeared in 1808.
[437]Mario Nizzoli (1498-1566), a well-known student of Cicero, was for a time professor at the University of Parma. HisObservationes in M. Tullium Ciceronemappeared at Pratalboino in 1535. It was revised by his nephew under the titleThesaurus Ciceronianus(Venice, 1570).
[438]See Vol. I, page 314, note 4 {681}.
[439]
"Like the geometer, who bends all his powersTo measure the circle, and does not succeed,Thinking what principle he needs."
"Like the geometer, who bends all his powersTo measure the circle, and does not succeed,Thinking what principle he needs."
"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 theEmblems(1635), with illustrations by William Marshall.
[441]Regnault de Bécourt wroteLa Création du monde, ou Système d'organisation primitive suivi de l'interprétation des principaux phénomènes et accidents que se sont opérés dans la nature depuis l'origine de univers jusqu'à nos jours(1816). This may be the work translated by Dalmas.
[442]"Because it lacks a holy prophet."
[443]Angherà. See Vol. II, page 60, note127.
[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 theDunciadfor 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, note206.
[446]Encyclopædia.
[447]Author of theHistoria Naturalis(77 A.D.)
[448]Author of theDe Institutione Oratorio LibriXII (c. 91 A.D.)
[449]HisDe Architectures LibriX 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 hisGame and Playe of Chesse(1474). TheMyrrour of the Worlde and th'ymage of the sameappeared 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 theMargarita 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. HisInstitutionum astronomicarum libri IIIappeared at Basel in 1528, hisCosmographiaat Paris in 1529, and hisOperaat 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 theElementale mathematicum(1611),Systema physicae harmonicae(1612),Methodus admirandorum mathematicorum(1613),Encyclopædia 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 theEpitome metrica historiæ universalis civilis et sacræ ab orbe condito(1686).
[457]Ephraim Chambers (c. 1680-1740), a crotchety, penurious, but kind-hearted freethinker. HisCyclopædia, or an Universal Dictionarywas translated into French and is said to have suggested the greatEncyclopédie.
[458]Encyclopédie, ou Dictionnaire raisonné des sciences, des arts et des métiers, par un société de gens de lettres. Mis en ordre et publié par M. Diderot, et quant à la partie mathématique, 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, note15.
[462]"In morals nothing should serve man as a model but God; in the arts, nothing but nature."
[463]Encyclopédie Méthodique, ou par ordre de matières.Paris, 1782-1832, 166½ volumes.
[464]See Vol. II, page 193, note336.
[465]Encyclopædia 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. HisViews of the Architecture of the Heavens(1838) was a very popular work, and hisPlanetary System(1848, 1850) contains the first suggestion for the study of sun spots by the aid of photography.
[470]See Vol. II, page 109, note206.
[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 thePenny Cyclopædia. 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, note56.
[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 toThe Sphere of Marcus Manilius, in the appendix to which is aCatalogue 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, note263.
[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. HisArithmeticæ in Numero & Speciebus Institutio ... quasi Clavis Mathematicæ est(1631) went through many editions and appeared in English asThe Key to the Mathematicks new forged and filedin 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 hisAstronomia geometricain 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 thePhilosophical Transactions.
[510]Thomas Brancker, or Branker (1636-1676) wrote theDoctrinæ sphæricæ adumbratio et usus globorum artificialium(1662) and translated the algebra of Rhonius with the help of Pell. The latter work appeared under the title ofAn 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 Collège de France. He wrote chiefly on geography.
[513]See Vol. II, page 297, note487.
[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 Collège of Pau, and afterwards professor of rhetoric at the Collège 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 hisVaria 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'sPrincipiainto English. His computation ofπto 100 places is given in William Jones'sSynopsis palmariorum matheseos(1706).
[523]Pierre Rémond 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'sPrincipia. His posthumousHarmonia 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 Réné Reyneau (1656-1728) was professor of mathematics at Angers. HisAnalyse démontrée, ou Manière de resoudre les problèmes de mathématiques(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. HisMethodus 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 wroteSur 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, note483.
[534]Thomas Baker (c. 1625-1689) gave a geometric solution of the biquadratic in hisGeometrical 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. HisEpistola 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) wroteAn Arithmeticall Militare Treatise, named Stratioticos(1579), and completedA 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 hisArtis Analyticæ 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'sArtis 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, note509.
[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 Braunmühl'sGeschichte der Trigonometrie.
[558]See Vol. I, page 377, note 3 {768}.
[559]See Vol. I, page 108, note 2 {192}.
[560]Michael Dary wroteDary's Miscellanies(1669),Gauging epitomised(1669), andThe 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 wroteL'usage de la règle de proportion(Paris, 1624, with an English translation in 1626),Arithmétique Logarithmétique(Paris, 1626, with an English translation in 1635), andOf 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 isThe 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, note547.
[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. TheAnti-Logarithmic Canonwas 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, page208.
[586]"Whatever objections one may make to the above arguments, one always falls into an absurdity."
[587]See Vol. II. page 11, note29.The Circle Squared; and the solution of the problem adapted to explain the difference between square and superficial measurementappeared 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 wroteAn 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), andHebrew 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. HisApologia 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]ConsultTo 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. HisCorrelation 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. HisSermonsfirst 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 hisPrecedents of Pleadingin 1808 and hisReports of Cases on Practice and Pleadingin 1820-23 (2 volumes).
[604]See Vol. I, page 44, note 1 {35}.
[605]See Vol. I, page 44, note 4 {38}.
[606]Jean Pèlerin, 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. HisGrounde of Artes, published about 1540, was the first arithmetic published in English that had any influence. It went through many editions. TheCastle of Knowledgeappeared 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. HisWhetstone of Witte ... containying thextraction of Rootes: The Cosike practise, with the rule of Equation: and the woorkes of Surde Nombresappeared 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 Italiancosa, 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 Clüver (d. 1708 at Hamburg) was a nephew, not a grandson, of Philippe Cluvier, or Philipp Clüver (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 theActa Eruditorum(1686) hisSchediasma geometricum de nova infinitorum scientia.Quadratura circuli infinitis modis demonstrata, and hisMonitum ad geometras(1687). Philippe was geographer of the Academy of Leyden. HisIntroductionis in universam geographiam tam veterem quam novam libri sexappeared 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. HisConsiderationes circa Analyseos ad quantitates infinite parvas applicatæ Principia et Calculi Differentialis usum(Amsterdam, 1694) was attacked by Leibnitz. He replied in hisConsiderationes secundæ(1694), and also wrote theAnalysis Infinitorum, seu Curvilineorum Proprietates ex Polygonorum Natura deductæ(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 Collège du Plessis, in Paris, for 34 years. The work to which De Morgan refers is probably theFameux Problème de la quadrature du cercle, résolu géometriquement par le cercle et a ligne droitethat appeared in 1683.
[621]On Tycho Brahe see Vol. I, page 76, note 3 {112}.
[622]Wilhelm Frederik von Zytphen also published theTidens Ström, a chronological table, in 1840. The work to which De Morgan refers, theSolens Bevægelse i Verdensrummet, appeared first in 1861. De Morgan seems to have missed hisNogl Ord om Cirkelens Quadraturwhich 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, note349.
[626]See Vol. I, page 76, note 3 {112}.
[627]See Vol. I, page 46, note 1 {42}.
[628]See Vol. II, page 183, note318.
[629]See Vol. I, page 321, note 2 {691}.
[630]James Mill, born 1773, died 1836.
[631]See Vol. II, page 3, note11.
[632]See Vol. II, page 3, note13.
[633]See Vol. II, page 3, note14.
[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, note15.
[636]See Vol. I, page 382, note 13 {786}.
[637]"Monsieur, (a+bn)/n=x, whence God exists; answer that!"
[638]"Monsieur, you know very well that your argument requires the development ofxaccording to integral powers ofn."
[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 ofTen 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 Mælius (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-knownChoice and Chance(Cambridge, 1867), and other works.
[649]James Maurice Wilson, whoseElementary Geometryappeared in 1868 and went through several editions.
[650]See Vol. II, page 183, note315.
[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 thePrinciples of Human Knowledge(1710),The Analyst, or a Discourse addressed to an Infidel Mathematician(1734), andA 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'sHandbook of Astronomy(1869) and Milner'sThe Heavens and the Earth(1873) and wroteThe 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]