A Budget of Paradoxes Volume I Part 52

[753] See note 36, page 44.

[754] See note 45, page 48.

[755] The Julian year is a year of the Julian Calendar, in which there is leap year every fourth year. Its average length is therefore 365 days and a quarter.--A. De M.

[756] Ugo Buoncompagno (1502-1585) was elected pope in 1572.

[757] He was a Calabrian, and as early as 1552 was professor of medicine at Perugia. In 1576 his ma.n.u.script on the reform of the calendar was presented to the Roman Curia by his brother, Antonius. The ma.n.u.script was not printed and it has not been preserved.

[758] The t.i.tle of this work, which is the authority on all points of the new Calendar, is _Kalendarium Gregorianum Perpetuum. c.u.m Privilegio Summi Pontificis Et Aliorum Principum. Romae, Ex Officina Dominici Basae. MDLx.x.xII.

c.u.m Licentia Superiorum_ (quarto, pp. 60).--A. De M.

[759] _Manuels-Roret. Theorie du Calendrier et collection de tous les Calendriers des Annees pa.s.sees et futures_.... Par L. B. Francoeur,...

Paris, a la librairie encyclopedique de Roret, rue Hautefeuille, 10 bis.

1842. (12mo.) In this valuable manual, the 35 possible almanacs are given at length, with such preliminary tables as will enable any one to find, by mere inspection, which almanac he is to choose for any year, whether of old or new style. [1866. I may now refer to my own _Book of Almanacs_, for the same purpose].--A. De M.

Louis Benjamin Francoeur (1773-1849), after holding positions in the Ecole polytechnique (1804) and the Lycee Charlemagne (1805), became professor of higher algebra in the University of Paris (1809). His _Cours complet des mathematiques pures_ was well received, and he also wrote on mechanics, astronomy, and geodesy.

[760] Albertus Pighius, or Albert Pigghe, was born at Kempen c. 1490 and died at Utrecht in 1542. He was a mathematician and a firm defender of the faith, a.s.serting the supremacy of the Pope and attacking both Luther and Calvin. He spent some time in Rome. His greatest work was his _Hierarchiae ecclesiasticae a.s.sertio_ (1538).

[761] This was A. F. Vogel. The work was his translation from the German edition which appeared at Leipsic the same year, _Entdeckung einer numerischen General-Auflosung aller hoheren endlichen Gleichungen von jeder beliebigen algebraischen und transcendenten Form_.

[762] The latest edition of Burnside and Panton's _Theory of Equations_ has this brief summary of the present status of the problem: "Demonstrations have been given by Abel and Wantzel (see Serret's _Cours d'Algebre Superieure_, Art. 516) of the impossibility of resolving algebraically equations unrestricted in form, of a degree higher than the fourth. A transcendental solution, however, of the quintic has been given by M.

Hermite, in a form involving elliptic integrals."

[763] There was a second edition of this work in 1846. The author's _Astronomy Simplified_ was published in 1838, and the _Thoughts on Physical Astronomy_ in 1840, with a second edition in 1842.

[764] This was _The Science of the Weather, by several authors... edited by B._, Glasgow, 1867.

[765] This was Y. Ramachandra, son of Sundara L[=a]la. He was a teacher of science in Delhi College, and the work to which De Morgan refers is _A Treatise on problems of Maxima and Minima solved by Algebra_, which appeared at Calcutta in 1850. De Morgan's edition was published at London nine years later.

[766] Abraham de Moivre (1667-1754), French refugee in London, poor, studying under difficulties, was a man with tastes in some respects like those of De Morgan. For one thing, he was a lover of books, and he had a good deal of interest in the theory of probabilities to which De Morgan also gave much thought. His introduction of imaginary quant.i.ties into trigonometry was an event of importance in the history of mathematics, and the theorem that bears his name, (cos [phi] + i sin [phi])^{n} = cos n[phi]

+ i sin n[phi], is one of the most important ones in all a.n.a.lysis.

[767] John Dolland (1706-1761), the silk weaver who became the greatest maker of optical instruments in his time.

[768] Thomas Simpson (1710-1761), also a weaver, taking his leisure from his loom at Spitalfields to teach mathematics. His _New Treatise on Fluxions_ (1737) was written only two years after he began working in London, and six years later he was appointed professor of mathematics at Woolwich. He wrote many works on mathematics and Simpson's Formulas for computing trigonometric tables are still given in the text-books.

[769] Nicholas Saunderson (1682-1739), the blind mathematician. He lost his eyesight through smallpox when only a year old. At the age of 25 he began lecturing at Cambridge on the principles of the Newtonian philosophy. His _Algebra_, in two large volumes, was long the standard treatise on the subject.

[770] He was not in the cla.s.s with the others mentioned.

[771] Not known in the literature of mathematics.

[772] Probably J. Butler Williams whose _Practical Geodesy_ appeared in 1842, with a third edition in 1855.

[773] Benjamin Gompertz (1779-1865) was debarred as a Jew from a university education. He studied mathematics privately and became president of the Mathematical Society. De Morgan knew him professionally through the fact that he was prominent in actuarial work.

[774] Referring to the contributions of Archimedes (287-212 B.C.) to the mensuration of the sphere.

[775] The famous Alexandrian astronomer (c. 87-c. 165 A.D.), author of the _Almagest_, a treatise founded on the works of Hipparchus.

[776] Dr. Whewell, when I communicated this song to him, started the opinion, which I had before him, that this was a very good idea, of which too little was made.--A. De M.

[777] See note 117, page 76.

[778] The common epithet of rank: _n.o.bilis Tycho_, as he was a n.o.bleman.

The writer had been at history.--A. De M.

See note 117, page 76.

[779] He lost it in a duel, with Manderupius Pasbergius. A contemporary, T. B. Laurus, insinuates that they fought to settle which was the best mathematician! This seems odd, but it must be remembered they fought in the dark, "_in tenebris densis_"; and it is a nice problem to shave off a nose in the dark, without any other harm.--A. De M.

Was this T. B. Laurus Joannes Baptista Laurus or Giovanni Battista Lauro (1581-1621), the poet and writer?

[780] See note 117, page 76.

[781] Referring to Kepler's celebrated law of planetary motion. He had previously wasted his time on a.n.a.logies between the planetary orbits and the polyhedrons.--A. De M.

[782] See note 117, page 76.

[783] "It does move though."

[784] As great a lie as ever was told: but in 1800 a compliment to Newton without a fling at Descartes would have been held a lopsided structure.--A.

De M.

[785] Jean-le-Rond D'Alembert (1717-1783), the foundling who was left on the steps of Jean-le-Rond in Paris, and who became one of the greatest mathematical physicists and astronomers of his century.

[786] Leonhard Euler (1707-1783), friend of the Bernoullis, the greatest of Swiss mathematicians, prominent in the theory of numbers, and known for discoveries in all lines of mathematics as then studied.

[787] See notes 478, 479, page 219.

[788] See note 621, page 288.

[789] See note 584, page 255.

[790] The _siderial_ day is about four minutes short of the solar; there are 366 sidereal days in the year.--A. De M.

[791] The founding of the London Mathematical Society is discussed by Mrs.

De Morgan in her _Memoir_ (p. 281). The idea came from a conversation between her brilliant son, George Campbell De Morgan, and his friend Arthur Cowper Ranyard in 1864. The meeting of organization was held on Nov. 7, 1864, with Professor De Morgan in the chair, and the first regular meeting on January 16, 1865.

[792] See note 33, page 43.

[793] See note 119, page 80.

[794] John Russell Hind (b. 1823), the astronomer. Between 1847 and 1854 he discovered ten planetoids.

[795] Sir Roderick Impey Murchison (1792-1871), the great geologist. He was knighted in 1846 and devoted the latter part of his life to the work of the Royal Geographical Society and to the geology of Scotland.