A Budget of Paradoxes Volume I Part 46

[488] Sir John Wilson (1741-1793) was knighted in 1786 and became Commissioner of the Great Seal in 1792. He was a lawyer and jurist of recognized merit. He stated his theorem without proof, the first demonstration having been given by Lagrange in the Memoirs of the Berlin Academy for 1771,--_Demonstration d'un theoreme nouveau concernant les nombres premiers_. Euler also gave a proof in his _Miscellanea a.n.a.lytica_ (1773). Fermat's works should be consulted in connection with the early history of this theorem.

[489] He wrote, in 1760, a tract in defense of Waring, a point of whose algebra had been a.s.sailed by a Dr. Powell. Waring wrote another tract of the same date.--A. De M.

William Samuel Powell (1717-1775) was at this time a fellow of St. John's College, Cambridge. In 1765 he became Vice Chancellor of the University.

Waring was a Magdalene man, and while candidate for the Lucasian professorship he circulated privately his _Miscellanea a.n.a.lytica_. Powell attacked this in his _Observations on the First Chapter of a Book called Miscellanea_ (1760). This attack was probably in the interest of another candidate, a man of his own college (St. John's), William Ludlam.

[490] William Paley (1743-1805) was afterwards a tutor at Christ's College, Cambridge. He never contributed anything to mathematics, but his _Evidences of Christianity_ (1794) was long considered somewhat of a cla.s.sic. He also wrote _Principles of Morality and Politics_ (1785), and _Natural Theology_ (1802).

[491] Edward, first Baron Thurlow (1731-1806) is known to Americans because of his strong support of the Royal prerogative during the Revolution. He was a favorite of George III, and became Lord Chancellor in 1778.

[492] George Wilson Meadley (1774-1818) published his _Memoirs of ...

Paley_ in 1809. He also published _Memoirs of Algernon Sidney_ in 1813. He was a merchant and banker, and had traveled extensively in Europe and the East. He was a convert to unitarianism, to which sect Paley had a strong leaning.

[493] Watson (1737-1816) was a strange kind of man for a bishopric. He was professor of chemistry at Cambridge (1764) at the age of twenty-seven. It was his experiments that led to the invention of the black-bulb thermometer. He is said to have saved the government 100,000 a year by his advice on the manufacture of gunpowder. Even after he became professor of divinity at Cambridge (1771) he published four volumes of _Chemical Essays_ (vol. I, 1781). He became Bishop of Llandaff in 1782.

[494] James Adair (died in 1798) was counsel for the defense in the trial of the publishers of the _Letters of Junius_ (1771). As King's Serjeant he a.s.sisted in prosecuting Hardy and Horne Tooke.

[495] Morgan (1750-1833) was actuary of the Equitable a.s.surance Society of London (1774-1830), and it was to his great abilities that the success of that company was due at a time when other corporations of similar kind were meeting with disaster. The Royal Society awarded him a medal (1783) for a paper on _Probability of Survivorship_. He wrote several important works on insurance and finance.

[496] Dr. Price (1723-1791) was a non-conformist minister and a writer on ethics, economics, politics, and insurance. He was a defender of the American Revolution and a personal friend of Franklin. In 1778 Congress invited him to America to a.s.sist in the financial administration of the new republic, but he declined. His famous sermon on the French Revolution is said to have inspired Burke's _Reflections on the Revolution in France_.

[497] Elizabeth Gurney (1780-1845), a Quaker, who married Joseph Fry (1800), a London merchant. She was the prime mover in the a.s.sociation for the Improvement of the Female Prisoners in Newgate, founded in 1817. Her influence in prison reform extended throughout Europe, and she visited the prisons of many countries in her efforts to improve the conditions of penal servitude. The friendship of Mrs. Fry with the De Morgans began in 1837.

Her scheme for a female benefit society proved worthless from the actuarial standpoint, and would have been disastrous to all concerned if it had been carried out, and it was therefore fortunate that De Morgan was consulted in time. Mrs. De Morgan speaks of the consultation in these words: "My husband, who was very sensitive on such points, was charmed with Mrs. Fry's voice and manner as much as by the simple self-forgetfulness with which she entered into this business; her own very uncomfortable share of it not being felt as an element in the question, as long as she could be useful in promoting good or preventing mischief. I can see her now as she came into our room, took off her little round Quaker cap, and laying it down, went at once into the matter. 'I have followed thy advice, and I think nothing further can be done in this case; but all harm is prevented.' In the following year I had an opportunity of seeing the effect of her most musical tones. I visited her at Stratford, taking my little baby and nurse with me, to consult her on some articles on prison discipline, which I had written for a periodical. The baby--three months old--was restless, and the nurse could not quiet her, neither could I entirely, until Mrs. Fry began to read something connected with the subject of my visit, when the infant, fixing her large eyes on the reader, lay listening till she fell asleep."

_Memoirs_, p. 91.

[498] Mrs. Fry certainly believed that the writer was the old actuary of the Equitable, when she first consulted him upon the benevolent a.s.surance project; but we were introduced to her by our old and dear friend Lady Noel Byron, by whom she had been long known and venerated, and who referred her to Mr. De Morgan for advice. An unusual degree of confidence in, and appreciation of each other, arose on their first meeting between the two, who had so much that was externally different, and so much that was essentially alike, in their natures.--S. E. De M.

Anne Isabella Milbanke (1792-1860) married Lord Byron in 1815, when both took the additional name of Noel, her mother's name. They were separated in 1816.

[499] An obscure writer not mentioned in the ordinary biographies.

[500] Not mentioned in the ordinary biographies, and for obvious reasons.

[501] "Before" and "after."

[502] On Bishop Wilkins see note 171 on page 100.

[503] Provision for a journey.

[504] See note 179 on page 103.

[505] Thomas Bradwardine (1290-1349), known as _Doctor Profundus_, proctor and professor of theology at Oxford, and afterwards Chancellor of St.

Paul's and confessor to Edward III. The English ascribed their success at Crecy to his prayers.

[506] He was consecrated Archbishop of Canterbury by the Pope at Avignon, July 13, 1349, and died of the plague at London in the same year.

[507] "One paltry little year."

[508] The t.i.tle is carelessly copied, as is so frequently the case in catalogues, even of the Libri cla.s.s. It should read: _Arithmetica thome brauardini_ || _Olivier Senant_ || _Venum exponuntur ab Oliuiario senant in vico diui Jacobi sub signo beate Barbare sedente_. The colophon reads: _Explicit arithmetica speculatiua th[=o]e brauardini b[=n] reuisa et correcta a Petro sanchez Ciruelo aragonensi mathematicas leg[=e]te Parisius, [=i]pressa per Thom[=a] anguelart_. There were Paris editions of 1495, 1496, 1498, s. a. (c. 1500), 1502, 1504, 1505, s. a. (c. 1510), 1512, 1530, a Valencia edition of 1503, two Wittenberg editions of 1534 and 1536, and doubtless several others. The work is not "very rare," although of course no works of that period are common. See the editor's _Rara Arithmetica_, page 61.

[509] This is his _Tractatus de proportionibus_, Paris, 1495; Venice, 1505; Vienna, 1515, with other editions.

[510] The colophon of the 1495 edition reads: _Et sic explicit Geometria Thome brauardini c[=u] tractatulo de quadratura circuli bene reuisa a Petro sanchez ciruelo: operaqz Guidonis mercatoris dilig[=e]tissime impresse parisi^o in c[=a]po gaillardi. Anno d[=n]i. 1495. die. 20, maij._

This Petro Ciruelo was born in Arragon, and died in 1560 at Salamanca. He studied mathematics and philosophy at Paris, and took the doctor's degree there. He taught at the University of Alcala and became canon of the Cathedral at Salamanca. Besides his editions of Bradwardine he wrote several works, among them the _Liber arithmeticae practicae qui dicitur algorithmus_ (Paris, 1495) and the _Cursus quatuor mathematicarum artium liberalium_ (Alcala, 1516).

[511] Star polygons, a subject of considerable study in the later Middle Ages. See note 35 on page 44.

[512] "A new theory that adds l.u.s.tre to the fourteenth century."

[513] There is nothing in the edition of 1495 that leads to this conclusion.

[514] The full t.i.tle is: _Nouvelle theorie des paralleles, avec un appendice contenant la maniere de perfectionner la theorie des paralleles de A. M. Legendre_. The author had no standing as a scientist.

[515] Adrien Marie Legendre (1752-1833) was one of the great mathematicians of the opening of the nineteenth century. His _Elements de geometrie_ (1794) had great influence on the geometry of the United States. His _Essai sur la theorie des nombres_ (1798) is one of the cla.s.sics upon the subject.

The work to which Kircher refers is the _Nouvelle theorie des paralleles_ (1803), in which the attempt is made to avoid using Euclid's postulate of parallels, the result being merely the subst.i.tution of another a.s.sumption that was even more unsatisfactory. The best presentations of the general theory are W. B. Frankland's _Theories of Parallelism_, Cambridge, 1910, and Engel and Stackel's _Die Theorie der Parallellinien von Euclid bis auf Gauss_, Leipsic, 1895. Legendre published a second work on the theory the year of his death, _Reflexions sur ... la theorie des paralleles_ (1833).

His other works include the _Nouvelles methodes pour la determination des...o...b..tes des cometes_ (1805), in which he uses the method of least squares; the _Traite des fonctions elliptiques et des integrales_ (1827-1832), and the _Exercises de calcul integral_ (1811, 1816, 1817).

[516] Johann Joseph Ignatz von Hoffmann (1777-1866), professor of mathematics at Aschaffenburg, published his _Theorie der Parallellinien_ in 1801. He supplemented this by his _Kritik der Parallelen-Theorie_ in 1807, and his _Das eilfte Axiom der Elemente des Euclidis neu bewiesen_ in 1859.

He wrote other works on mathematics, but none of his contributions was of any importance.

[517] Johann Karl Friedrich Hauff (1766-1846) was successively professor of mathematics at Marburg, director of the polytechnic school at Augsburg, professor at the Gymnasium at Cologne, and professor of mathematics and physics at Ghent. The work to which Kircher refers is his memoirs on the Euclidean _Theorie der Parallelen_ in Hindenburg's _Archiv_, vol. III (1799), an article of no merit in the general theory.

[518] Wenceslaus Johann Gustav Karsten (1732-1787) was professor of logic at Rostock (1758) and Butzow (1760), and later became professor of mathematics and physics at Halle. His work on parallels is the _Versuch einer vollig berichtigten Theorie der Parallellinien_ (1779). He also wrote a work ent.i.tled _Anfangsgrunde der mathematischen Wissenschaften_ (1780), but neither of these works was more than mediocre.

[519] Johann Christoph Schwab (not Schwal) was born in 1743 and died in 1821. He was professor at the Karlsschule at Stuttgart. De Morgan's wish was met, for the catalogues give "c. fig. 8," so that it evidently had eight ill.u.s.trations instead of eight volumes. He wrote several other works on the principles of geometry, none of any importance.

[520] Gaetano Rossi of Catanzaro. This was the libretto writer (1772-1855), and hence the imperfections of the work can better be condoned. De Morgan should have given a little more of the t.i.tle: _Solusione esatta e regolare ... del ... problema della quadratura del circolo_. There was a second edition, London, 1805.

[521] This identifies Rossi, for Josephine Gra.s.sini (1773-1850) was a well-known contralto, _prima donna_ at Napoleon's court opera.

[522] William Spence (1783-1860) was an entomologist and economist of some standing, a fellow of the Royal Society, and one of the founders of the Entomological Society of London. The work here mentioned was a popular one, the first edition appearing in 1807, and four editions being justified in a single year. He also wrote _Agriculture the Source of Britain's Wealth_ (1808) and _Objections against the Corn Bill refuted_ (1815), besides a work in four volumes on entomology (1815-1826) in collaboration with William Kirby.

[523] "That used to be so, but we have changed all that."

[524] "Meet the coming disease."

[525] George Douglas (or Dougla.s.s) was a Scotch writer. He got out an edition of the _Elements of Euclid_ in 1776, with an appendix on trigonometry and a set of tables. His work on _Mathematical Tables_ appeared in 1809, and his _Art of Drawing in Perspective, from mathematical principles_, in 1810.

[526] See note 443, on page 197.

[527] John Playfair (1748-1848) was professor of mathematics (1785) and natural philosophy (1805) at the University of Edinburgh. His _Elements of Geometry_ went through many editions.

[528] "Tell Apella" was an expression current in cla.s.sical Rome to indicate incredulity and to show the contempt in which the Jew was held. Horace says: _Credat Judaeus Apella_, "Let Apella the Jew believe it." Our "Tell it to the marines," is a similar phrase.

[529] As De Morgan says two lines later, "No mistake is more common than the natural one of imagining that the"--University of Virginia is at Richmond. The fact is that it is not there, and that it did not exist in 1810. It was not chartered until 1819, and was not opened until 1825, and then at Charlottesville. The act establishing the Central College, from which the University of Virginia developed, was pa.s.sed in 1816. The Jean Wood to whom De Morgan refers was one John Wood who was born about 1775 in Scotland and who emigrated to the United States in 1800. He published a _History of the Administration of J. Adams_ (New York, 1802) that was suppressed by Aaron Burr. This act called forth two works, a _Narrative of the Suppression, by Col. Burr, of the 'History of the Administration of John Adams'_ (1802), in which Wood was sustained; and the _Antidote to John Wood's Poison_ (1802), in which he was attacked. The work referred to in the "printed circular" may have been the _New theory of the diurnal rotation of the earth_ (Richmond, Va., 1809). Wood spent the last years of his life in Richmond, Va., making county maps. He died there in 1822. A careful search through works relating to the University of Virginia fails to show that Wood had any connection with it.

[530] There seems to be nothing to add to Dobson's biography beyond what De Morgan has so deliciously set forth.