[33] Urbain-Jean-Joseph Leverrier was born at Saint-Lo, Manche, in 1811, and died at Paris in 1877. It was his data respecting the perturbations of Ura.n.u.s that were used by Adams and himself in locating Neptune.

[34] Joseph-Juste Scaliger, the celebrated philologist, was born at Agen in 1540, and died at Leyden in 1609. His _Cyclometrica elementa_, to which De Morgan refers, appeared at Leyden in 1594.

[35] The t.i.tle is: _In hoc libra contenta.... Introductio i geometri[=a].... Liber de quadratura circuli. Liber de cubicatione sphere.

Perspectiva introductio_. Carolus Bovillus, or Charles Bouvelles (Bouelles, Bouilles, Bouvel), was born at Saucourt, Picardy, about 1470, and died at Noyon about 1533. He was canon and professor of theology at Noyon. His _Introductio_ contains considerable work on star polygons, a favorite study in the Middle Ages and early Renaissance. His work _Que hoc volumine contin[=e]tur. Liber de intellectu. Liber de sensu_, etc., appeared at Paris in 1509-10.

[36] Nicolaus Cusa.n.u.s, Nicolaus Chrypffs or Krebs, was born at Kues on the Mosel in 1401, and died at Todi, Umbria, August 11, 1464. He held positions of honor in the church, including the bishopric of Brescia. He was made a cardinal in 1448. He wrote several works on mathematics, his _Opuscula varia_ appearing about 1490, probably at Strasburg, but published without date or place. His _Opera_ appeared at Paris in 1511 and again in 1514, and at Basel in 1565.

[37] Henry Stephens (born at Paris about 1528, died at Lyons in 1598) was one of the most successful printers of his day. He was known as _Typographus Parisiensis_, and to his press we owe some of the best works of the period.

[38] Jacobus Faber Stapulensis (Jacques le Fevre d'Estaples) was born at Estaples, near Amiens, in 1455, and died at Nerac in 1536. He was a priest, vicar of the bishop of Meaux, lecturer on philosophy at the College Lemoine in Paris, and tutor to Charles, son of Francois I. He wrote on philosophy, theology, and mathematics.

[39] Claude-Francois Milliet de Challes was born at Chambery in 1621, and died at Turin in 1678. He edited _Euclidis Elementorum libri octo_ in 1660, and published a _Cursus seu mundus mathematicus_, which included a short history of mathematics, in 1674. He also wrote on mathematical geography.

[40] This date should be 1503, if he refers to the first edition. It is well known that this is the first encyclopedia worthy the name to appear in print. It was written by Gregorius Reisch (born at Balingen, and died at Freiburg in 1487), prior of the cloister at Freiburg and confessor to Maximilian I. The first edition appeared at Freiburg in 1503, and it pa.s.sed through many editions in the sixteenth and seventeenth centuries. The t.i.tle of the 1504 edition reads: _Aepitoma omnis phylosophiae. alias Margarita phylosophica tractans de omni genere scibili: c.u.m additionibus: Quae in alijs non habentur_.

[41] This is the _Introductio in arithmeticam Divi S. Boetii.... Epitome rerum geometricarum ex geometrica introductio C. Bovilli. De quadratura circuli demonstratio ex Campano_, that appeared without date about 1507.

[42] Born at Liverpool in 1805, and died there about 1872. He was a merchant, and in 1865 he published, at Liverpool, a work ent.i.tled _The Quadrature of the Circle, or the True Ratio between the Diameter and Circ.u.mference geometrically and mathematically demonstrated_. In this he gives the ratio as exactly 3-1/8.

[43] "That it would be impossible to tell him exactly, since no one had yet been able to find precisely the ratio of the circ.u.mference to the diameter."

[44] This is the Paris edition: "Parisiis: ex officina Ascensiana anno Christi ... MDXIIII," as appears by the colophon of the second volume to which De Morgan refers.

[45] Regiomonta.n.u.s, or Johann Muller of Konigsberg (Regiomonta.n.u.s), was born at Konigsberg in Franconia, June 5, 1436, and died at Rome July 6, 1476. He studied at Vienna under the great astronomer Peuerbach, and was his most famous pupil. He wrote numerous works, chiefly on astronomy. He is also known by the names Ioannes de Monte Regio, de Regiomonte, Ioannes Germa.n.u.s de Regiomonte, etc.

[46] Henry Cornelius Agrippa was born at Cologne in 1486 and died either at Lyons in 1534 or at Gren.o.ble in 1535. He was professor of theology at Cologne and also at Turin. After the publication of his _De Occulta Philosophia_ he was imprisoned for sorcery. Both works appeared at Antwerp in 1530, and each pa.s.sed through a large number of editions. A French translation appeared in Paris in 1582, and an English one in London in 1651.

[47] Nicolaus Remegius was born in Lorraine in 1554, and died at Nancy in 1600. He was a jurist and historian, and held the office of procurator general to the Duke of Lorraine.

[48] This was at the storming of the city by the British on May 4, 1799.

From his having been born in India, all this appealed strongly to the interests of De Morgan.

[49] Orontius Finaeus, or Oronce Fine, was born at Briancon in 1494 and died at Paris, October 6, 1555. He was imprisoned by Francois I for refusing to recognize the concordat (1517). He was made professor of mathematics in the College Royal (later called the College de France) in 1532. He wrote extensively on astronomy and geometry, but was by no means a great scholar. He was a pretentious man, and his works went through several editions. His _Protomathesis_ appeared at Paris in 1530-32. The work referred to by De Morgan is the _Quadratura circuli tandem inventa & clarissime demonstrata_ ... Lutetiae Parisiorum, 1544, fol. In the 1556 edition of his _De rebus mathematicis, hactenus desideratis, Libri IIII_, published at Paris, the subt.i.tle is: _Quibus inter caetera, Circuli quadratura Centum modis, & supra, per eundem Orontium recenter excogitatis, demonstratus_, so that he kept up his efforts until his death.

[50] Johannes Buteo (Boteo, Buteon, Bateon) was born in Dauphine c.

1485-1489, and died in a cloister in 1560 or 1564. Some writers give Charpey as the place and 1492 as the date of his birth, and state that he died at Canar in 1572. He belonged to the order of St. Anthony, and wrote chiefly on geometry, exposing the pretenses of Finaeus. His _Opera geometrica_ appeared at Lyons in 1554, and his _Logistica_ and _De quadratura circuli libri duo_ at Lyons in 1559.

[51] This is the great French algebraist, Francois Viete (Vieta), who was born at Fontenay-le-Comte in 1540, and died at Paris, December 13, 1603.

His well-known _Isagoge in artem a.n.a.lyticam_ appeared at Tours in 1591. His _Opera mathematica_ was edited by Van Schooten in 1646.

[52] This is the _De Rebus mathematicis hactenus desideratis, Libri IIII_, that appeared in Paris in 1556. For the t.i.tle page see Smith, D. E., _Rara Arithmetica_, Boston, 1908, p. 280.

[53] The t.i.tle is correct except for a colon after _Astronomic.u.m_. Nicolaus Raimarus Ursus was born in Henstede or Hattstede, in Dithmarschen, and died at Prague in 1599 or 1600. He was a pupil of Tycho Brahe. He also wrote _De astronomis hypothesibus_ (1597) and _Arithmetica a.n.a.lytica vulgo Cosa oder Algebra_ (1601).

[54] Born at Dole, Franche-Comte, about 1550, died in Holland about 1600.

The work to which reference is made is the _Quadrature du cercle, ou maniere de trouver un quarre egal au cercle donne_, which appeared at Delft in 1584. d.u.c.h.esne had the courage of his convictions, not only on circle-squaring but on religion as well, for he was obliged to leave France because of his conversion to Calvinism. De Morgan's statement that his real name is Van der Eycke is curious, since he was French born. The Dutch may have translated his name when he became professor at Delft, but we might equally well say, that his real name was Querceta.n.u.s or a Quercu.

[55] This was the father of Adriaan Metius (1571-1635). He was a mathematician and military engineer, and suggested the ratio 355/113 for [pi], a ratio afterwards published by his son. The ratio, then new to Europe, had long been known and used in China, having been found by Tsu Ch'ung-chih (428-499 A.D.).

[56] This was Jost Burgi, or Justus Byrgius, the Swiss mathematician of whom Kepler wrote in 1627: "Apices logistici Jus...o...b..rgio multis annis ante editionem Neperianam viam praeiverunt ad hos ipsissimos logarithmos." He constructed a table of antilogarithms (_Arithmetische und geometrische Progress-Tabulen_), but it was not published until after Napier's work appeared.

[57] Ludolphus Van Ceulen, born at Hildesheim, and died at Leyden in 1610.

It was he who first carried the computation of [pi] to 35 decimal places.

[58] Jens Jenssen Dodt, van Flensburg, a Dutch historian, who died in 1847.

[59] I do not know this edition. There was one "Antverpiae apud Petrum Bellerum sub scuto Burgundiae," 4to, in 1591.

[60] Archytas of Tarentum (430-365 B.C.) who wrote on proportions, irrationals, and the duplication of the cube.

[61]

_The Circle Speaks._ "At first a circle I was called, And was a curve around about Like lofty orbit of the sun Or rainbow arch among the clouds.

A n.o.ble figure then was I-- And lacking nothing but a start, And lacking nothing but an end.

But now unlovely do I seem Polluted by some angles new.

This thing Archytas hath not done Nor n.o.ble sire of Icarus Nor son of thine, Iapetus.

What accident or G.o.d can then Have quadrated mine area?"

_The Author Replies._ "By deepest mouth of Turia And lake of limpid clearness, lies A happy state not far removed From old Saguntus; farther yet A little way from Sucro town.

In this place doth a poet dwell, Who oft the stars will closely scan, And always for himself doth claim What is denied to wiser men;-- An old man musing here and there And oft forgetful of himself, Not knowing how to rightly place The compa.s.ses, nor draw a line, As he doth of himself relate.

This craftsman fine, in sooth it is Hath quadrated thine area."

[62] Pietro Bongo, or Petrus Bungus, was born at Bergamo, and died there in 1601. His work on the Mystery of Numbers is one of the most exhaustive and erudite ones of the mystic writers. The first edition appeared at Bergamo in 1583-84; the second, at Bergamo in 1584-85; the third, at Venice in 1585; the fourth, at Bergamo in 1590; and the fifth, which De Morgan calls the second, in 1591. Other editions, before the Paris edition to which he refers, appeared in 1599 and 1614; and the colophon of the Paris edition is dated 1617. See the editor's _Rara Arithmetica_, pp. 380-383.

[63] William Warburton (1698-1779), Bishop of Gloucester, whose works got him into numerous literary quarrels, being the subject of frequent satire.

[64] Thomas Galloway (1796-1851), who was professor of mathematics at Sandhurst for a time, and was later the actuary of the Amicable Life a.s.surance Company of London. In the latter capacity he naturally came to be a.s.sociated with De Morgan.

[65] Giordano Bruno was born near Naples about 1550. He left the Dominican order to take up Calvinism, and among his publications was _L'expulsion de la bete triomphante_. He taught philosophy at Paris and Wittenberg, and some of his works were published in England in 1583-86. Whether or not he was roasted alive "for the maintenance and defence of the holy Church," as De Morgan states, depends upon one's religious point of view. At any rate, he was roasted as a heretic.

[66] Referring to part of his _Discours de la methode_, Leyden, 1637.

[67] Bartholomew Legate, who was born in Ess.e.x about 1575. He denied the divinity of Christ and was the last heretic burned at Smithfield.

[68] Edward Wightman, born probably in Staffordshire. He was anti-Trinitarian, and claimed to be the Messiah. He was the last man burned for heresy in England.

[69] Gaspar Schopp, born at Neumarck in 1576, died at Padua in 1649; grammarian, philologist, and satirist.

[70] Konrad Ritterhusius, born at Brunswick in 1560; died at Altdorf in 1613. He was a jurist of some power.

[71] Johann Jakob Brucker, born at Augsburg in 1696, died there in 1770. He wrote on the history of philosophy (1731-36, and 1742-44).

[72] Daniel Georg Morhof, born at Wismar in 1639, died at Lubeck in 1691.

He was rector of the University of Kiel, and professor of eloquence, poetry, and history.

[73] In the _Histoire des Sciences Mathematiques_, vol. IV, note X, pp.

416-435 of the 1841 edition.