A Budget of Paradoxes Volume I Part 45

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

[442] George Peac.o.c.k (1791-1858), Fellow of Trinity College, Cambridge, Lowndean professor of astronomy, and Dean of Ely Cathedral (1839). His tomb may be seen at Ely where he spent the latter part of his life. He was one of the group that introduced the modern continental notation of the calculus into England, replacing the c.u.mbersome notation of Newton, pa.s.sing from "the _dot_age of fluxions to the _de_ism of the calculus."

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

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

[445] These appeared annually from 1804 to 1822.

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

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

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

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

He was born in 1757 and died in 1839. On the trial of Frend he publicly protested against testifying against a personal confidant, and was excused.

He was one of the first of the English clergy to study modern higher criticism of the Bible, and amid much opposition he wrote numerous works on the subject. He was professor of theology at Cambridge (1707), Bishop of Llandaff (1816), and Bishop of Peterborough.

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

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

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

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

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

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

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

[457] See note 443 on page 197.

[458] See note 444 on page 197.

[459] See note 439 on page 193.

[460] Edward Waring (1736-1796) was Lucasian professor of mathematics at Cambridge. He published several works on a.n.a.lysis and curves. The work referred to was the _Miscellanea a.n.a.lytica de aequationibus algebraicis et curvarum proprietatibus_, Cambridge, 1762.

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

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

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

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

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

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

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

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

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

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

[471] George Sinclair, probably a native of East Lothian, who died in 1696.

He was professor of philosophy and mathematics at Glasgow, and was one of the first to use the barometer in measuring alt.i.tudes. The work to which De Morgan refers is his _Hydrostaticks_ (1672). He was a firm believer in evil spirits, his work on the subject going through four editions: _Satan's Invisible World Discovered; or, a choice collection of modern relations, proving evidently against the Saducees and Athiests of this present age, that there are Devils, Spirits, Witches, and Apparitions_, Edinburgh, 1685.

[472] This was probably William Sanders, Regent of St. Leonard's College, whose _Theses philosophicae_ appeared in 1674, and whose _Elementa geometriae_ came out a dozen years later.

[473] _Ars nova et magna gravitatis et levitatis; sive dialogorum philosophicorum libri s.e.x de aeris vera ac reali gravitate_, Rotterdam, 1669, 4to.

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

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

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

[477] See page 86, note 132.

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

[479] _Recherches sur les courbes a double courbure_, Paris, 1731. Clairaut was then only eighteen, and was in the same year made a member of the Academie des sciences. His _Elemens de geometrie_ appeared in 1741.

Meantime he had taken part in the measurement of a degree in Lapland (1736-1737). His _Traite de la figure de la terre_ was published in 1741.

The Academy of St. Petersburg awarded him a prize for his _Theorie de la lune_ (1750). His various works on comets are well known, particularly his _Theorie du mouvement des cometes_ (1760) in which he applied the "problem of three bodies" to Halley's comet as r.e.t.a.r.ded by Jupiter and Saturn.

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

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

[482] Blaise Pascal (1623-1662), the well-known French philosopher and mathematician. He lived for some time with the Port Royalists, and defended them against the Jesuits in his _Provincial Letters_. Among his works are the following: _Essai pour les coniques_ (1640); _Recit de la grande experience de l'equilibre des liqueurs_ (1648), describing his experiment in finding alt.i.tudes by barometric readings; _Histoire de la roulette_ (1658); _Traite du triangle arithmetique_ (1665); _Aleae geometria_ (1654).

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

[484] Jacques Curabelle, _Examen des Oeuvres du Sr. Desargues_, Paris, 1644. He also published without date a work ent.i.tled: _Foiblesse pitoyable du Sr. G. Desargues employee contre l'examen fait de ses oeuvres_.

[485] See page 119, note 233.

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

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