[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 passed through many editions in the sixteenth and seventeenth centuries. The title of the 1504 edition reads: Aepitoma omnis phylosophiae. alias Margarita phylosophica tractans de omni genere scibili: Cum 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 entitled The Quadrature of the Circle, or the True Ratio between the Diameter and Circumference 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 circumference 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] Regiomontanus, or Johann Mueller of Koenigsberg (Regiomontanus), was born at Koenigsberg 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 Germanus de Regiomonte, etc.

[46] Henry Cornelius Agrippa was born at Cologne in 1486 and died either at Lyons in 1534 or at Grenoble 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 passed 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 subtitle 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 analyticam 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 title page see Smith, D. E., Rara Arithmetica, Boston, 1908, p. 280.

[53] The title is correct except for a colon after Astronomicum. 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 analytica 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. Duchesne 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 Quercetanus 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 Buergi, or Justus Byrgius, the Swiss mathematician of whom Kepler wrote in 1627: "Apices logistici Justo Byrgio 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 noble 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 noble sire of Icarus Nor son of thine, Iapetus. What accident or god 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 compasses, 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 Assurance Company of London. In the latter capacity he naturally came to be associated 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 Essex 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 Luebeck 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.

[74] Colenso (1814-1883), missionary bishop of Natal, was one of the leaders of his day in the field of higher biblical criticism. De Morgan must have admired his mathematical works, which were not without merit.

[75] Samuel Roffey Maitland, born at London in 1792; died at Gloucester in 1866. He was an excellent linguist and a critical student of the Bible. He became librarian at Lambeth in 1838.

[76] Archbishop Howley (1766-1848) was a thorough Tory. He was one of the opponents of the Roman Catholic Relief bill, the Reform bill, and the Jewish Civil Disabilities Relief bill.

[77] We have, in America at least, almost forgotten the great stir made by Edward B. Pusey (1800-1882) in the great Oxford movement in the middle of the nineteenth century. He was professor of Hebrew at Oxford, and canon of Christ Church.

[78] That is, his Magia universalis naturae et artis sive recondita naturalium et artificialium rerum scientia, Wuerzburg, 1657, 4to, with editions at Bamberg in 1671, and at Frankfort in 1677. Gaspard Schott (Koenigshofen 1608, Wuerzburg 1666) was a physicist and mathematician, devoting most of his attention to the curiosities of his sciences. His type of mind must have appealed to De Morgan.

[79] Salicetti Quadratura circuli nova, perspicua, expedita, veraque tum naturalis, tum geometrica, etc., 1608.—Consideratio nova in opusculum Archimedis de circuli dimensione, etc., 1609.

[80] Melchior Adam, who died at Heidelberg in 1622, wrote a collection of biographies which was published at Heidelberg and Frankfort from 1615 to 1620.

[81] Born at Baden in 1524; died at Basel in 1583. The Erastians were related to the Zwinglians, and opposed all power of excommunication and the infliction of penalties by a church.

[82] See Acts xii. 20.

[83] Theodore de Bese, a French theologian; born at Vezelay, in Burgundy, in 1519; died at Geneva, in 1605.

[84] Dr. Robert Lee (1804-1868) had some celebrity in De Morgan's time through his attempt to introduce music and written prayers into the service of the Scotch Presbyterian church.

[85] Born at Veringen, Hohenzollern, in 1512; died at Roeteln in 1564.

[86] Born at Kinnairdie, Bannfshire, in 1661; died at London in 1708. His Astronomiae Physicae et Geometriae Elementa, Oxford, 1702, was an influential work.

[87] The title was carelessly copied by De Morgan, not an unusual thing in his case. The original reads: A Plaine Discovery, of the whole Revelation of S. Iohn: set downe in two treatises ... set foorth by John Napier L. of Marchiston ... whereunto are annexed, certaine Oracles of Sibylla ... London ... 1611.

[88] I have not seen the first edition, but it seems to have appeared in Edinburgh, in 1593, with a second edition there in 1594. The 1611 edition was the third.

[89] It seems rather certain that Napier felt his theological work of greater importance than that in logarithms. He was born at Merchiston, near (now a part of) Edinburgh, in 1550, and died there in 1617, three years after the appearance of his Mirifici logarithmorum canonis descriptio.

[90] Followed, in the third edition, from which he quotes, by a comma.

[91] There was an edition published at Stettin in 1633. An English translation by P. F. Mottelay appeared at London in 1893. Gilbert (1540-1603) was physician to Queen Elizabeth and President of the College of Physicians at London. His De Magnete was the first noteworthy treatise on physics printed in England. He treated of the earth as a spherical magnet and suggested the variation and declination of the needle as a means of finding latitude at sea.

[92] The title says "ab authoris fratre collectum," although it was edited by J. Gruterus.

[93] Porta was born at Naples in 1550 and died there in 1615. He studied the subject of lenses and the theory of sight, did some work in hydraulics and agriculture, and was well known as an astrologer. His Magiae naturalis libri XX was published at Naples in 1589. The above title should read curvilineorum.

[94] Cataldi was born in 1548 and died at Bologna in 1626. He was professor of mathematics at Perugia, Florence, and Bologna, and is known in mathematics chiefly for his work in continued fractions. He was one of the scholarly men of his day.

[95] Georg Joachim Rheticus was born at Feldkirch in 1514 and died at Caschau, Hungary, in 1576. He was one of the most prominent pupils of Copernicus, his Narratio de libris revolutionum Copernici (Dantzig, 1540) having done much to make the theory of his master known.

[96] Henry Briggs, who did so much to make logarithms known, and who used the base 10, was born at Warley Wood, in Yorkshire, in 1560, and died at Oxford in 1630. He was Savilian professor of mathematics at Oxford, and his grave may still be seen there.

[97] He lived at "Reggio nella Emilia" in the 16th and 17th centuries. His Regola e modo facilissimo di quadrare il cerchio was published at Reggio in 1609.

[98] Christoph Klau (Clavius) was born at Bamberg in 1537, and died at Rome in 1612. He was a Jesuit priest and taught mathematics in the Jesuit College at Rome. He wrote a number of works on mathematics, including excellent text-books on arithmetic and algebra.

[99] Christopher Gruenberger, or Grienberger, was born at Halle in Tyrol in 1561, and died at Rome in 1636. He was, like Clavius, a Jesuit and a mathematician, and he wrote a little upon the subject of projections. His Prospectiva nova coelestis appeared at Rome in 1612.

[100] The name should, of course, be Lansbergii in the genitive, and is so in the original title. Philippus Lansbergius was born at Ghent in 1560, and died at Middelburg in 1632. He was a Protestant theologian, and was also a physician and astronomer. He was a well-known supporter of Galileo and Copernicus. His Commentationes in motum terrae diurnum et annuum appeared at Middelburg in 1630 and did much to help the new theory.

[101] I have never seen the work. It is rare.

[102] The African explorer, born in Somersetshire in 1827, died at Bath in 1864. He was the first European to cross Central Africa from north to south. He investigated the sources of the Nile.

[103] Prester (Presbyter, priest) John, the legendary Christian king whose realm, in the Middle Ages, was placed both in Asia and in Africa, is first mentioned in the chronicles of Otto of Freisingen in the 12th century. In the 14th century his kingdom was supposed to be Abyssinia.

[104] "It is a profane and barbarous nation, dirty and slovenly, who eat their meat half raw and drink mare's milk, and who use table-cloths and napkins only to wipe their hands and mouths."

[105] "The great Prester John, who is the fourth in rank, is emperor of Ethiopia and of the Abyssinians, and boasts of his descent from the race of David, as having descended from the Queen of Sheba, Queen of Ethiopia. She, having gone to Jerusalem to see the wisdom of Solomon, about the year of the world 2952, returned pregnant with a son whom they called Moylech, from whom they claim descent in a direct line. And so he glories in being the most ancient monarch in the world, saying that his empire has endured for more than three thousand years, which no other empire is able to assert. He also puts into his titles the following: 'We, the sovereign in my realms, uniquely beloved of God, pillar of the faith, sprung from the race of Judah, etc.' The boundaries of this empire touch the Red Sea and the mountains of Azuma on the east, and on the western side it is bordered by the River Nile which separates it from Nubia. To the north lies Egypt, and to the south the kingdoms of Congo and Mozambique. It extends forty degrees in length, or one thousand twenty-five leagues, from Congo or Mozambique on the south to Egypt on the north; and in width it reaches from the Nile on the west to the mountains of Azuma on the east, seven hundred twenty-five leagues, or twenty-nine degrees. This empire contains thirty large provinces, namely Medra, Gaga, Alchy, Cedalon, Mantro, Finazam, Barnaquez, Ambiam, Fungy, Angote, Cigremaon, Gorga, Cafatez, Zastanla, Zeth, Barly, Belangana, Tygra, Gorgany, Barganaza, d'Ancut, Dargaly, Ambiacatina, Caracogly, Amara, Maon (sic), Guegiera, Bally, Dobora, and Macheda. All of these provinces are situated directly under the equinoctial line between the tropics of Capricorn and Cancer; but they are two hundred fifty leagues nearer our tropic than the other. The name of Prester John signifies Great Lord, and is not Priest [Presbyter] as many think. He has always been a Christian, but often schismatic. At the present time he is a Catholic and recognizes the Pope as sovereign pontiff. I met one of his bishops in Jerusalem, and often conversed with him through the medium of our guide. He was of grave and serious bearing, pleasant of speech, but wonderfully subtle in everything he said. He took great delight in what I had to relate concerning our beautiful ceremonies and the dignity of our prelates in their pontifical vestments. As to other matters I will only say that the Ethiopian is joyous and merry, not at all like the Tartar in the matter of filth, nor like the wretched Arab. They are refined and subtle, trusting no one, wonderfully suspicious, and very devout. They are not at all black as is commonly supposed, by which I refer to those who do not live under the equator or too near to it, for these are Moors as we shall see."

With respect to this translation it should be said that the original forms of the proper names have been preserved, although they are not those found in modern works. It should also be stated that the meaning of Prester is not the one that was generally accepted by scholars at the time the work was written, nor is it the one accepted to-day. There seems to be no doubt that the word is derived from Presbyter as stated in note 103 on page 71, since the above-mentioned chronicles of Otto, bishop of Freisingen about the middle of the twelfth century, states this fact clearly. Otto received his information from the bishop of Gabala (the Syrian Jibal) who told him the story of John, rex et sacerdos, or Presbyter John as he liked to be called. He goes on to say "Should it be asked why, with all this power and splendor, he calls himself merely 'presbyter,' this is because of his humility, and because it was not fitting for one whose server was a primate and king, whose butler an archbishop and king, whose chamberlain a bishop and king, whose master of the horse an archimandrite and king, whose chief cook an abbot and king, to be called by such titles as these."

[106] Thomas Fienus (Fyens) was born at Antwerp in 1567 and died in 1631. He was professor of medicine at Louvain. Besides the editions mentioned below, his De cometis anni 1618 appeared at Leipsic in 1656. He also wrote a Disputatio an coelum moveatur et terra quiescat, which appeared at Antwerp in 1619, and again at Leipsic in 1656.

[107] Libertus Fromondus (1587-c 1653), a Belgian theologian, dean of the College Church at Harcourt, and professor at Louvain. The name also appears as Froidmont and Froimont.

[108] L. Fromondi ... meteorologicorum libri sex.... Cui accessit T. Fieni et L. Fromondi dissertationes de cometa anni 1618.... This is from the 1670 edition. The 1619 edition was published at Antwerp. The Meteorologicorum libri VI, appeared at Antwerp in 1627. He also wrote Anti-Aristarchus sive orbis terrae immobilis liber unicus (Antwerp, 1631); Labyrrinthus sive de compositione continui liber unus, Philosophis, Mathematicis, Theologis utilis et jucundus (Antwerp, 1631) and Vesta sive Anti-Aristarchi vindex adversus Jac. Lansbergium (Philippi filium) et copernicanos (Antwerp, 1634).

[109] Snell was born at Leyden in 1591, and died there in 1626. He studied under Tycho Brahe and Kepler, and is known for Snell's law of the refraction of light. He was the first to determine the size of the earth by measuring the arc of a meridian with any fair degree of accuracy. The title should read: Willebrordi Snellii R. F. Cyclometricus, de circuli dimensione secundum Logistarum abacos, et ad Mechanicem accuratissima....

[110] Bacon was born at York House, London, in 1561, and died near Highgate, London, in 1626. His Novum Organum Scientiarum or New Method of employing the reasoning faculties in the pursuits of Truth appeared at London in 1620. He had previously published a work entitled Of the Proficience and Advancement of Learning, divine and humane (London, 1605), which again appeared in 1621. His De augmentis scientiarum Libri IX appeared at Paris in 1624, and his Historia naturalis et experimentalis de ventis at Leyden in 1638. He was successively solicitor general, attorney general, lord chancellor (1619), Baron Verulam and Viscount St. Albans. He was deprived of office and was imprisoned in the Tower of London in 1621, but was later pardoned.

[111] The Greek form, Organon, is sometimes used.

[112] James Spedding (1808-1881), fellow of Cambridge, who devoted his life to his edition of Bacon.

[113] R. Leslie Ellis (1817-1859), editor of the Cambridge Mathematical Journal. He also wrote on Roman aqueducts, on Boole's Laws of Thought, and on the formation of a Chinese dictionary.

[114] Douglas Derion Heath (1811-1897), a classical and mathematical scholar.

[115] There have been numerous editions of Bacon's complete works, including the following: Frankfort, 1665; London, 1730, 1740, 1764, 1765, 1778, 1803, 1807, 1818, 1819, 1824, 1825-36, 1857-74, 1877. The edition to which De Morgan refers is that of 1857-74, 14 vols., of which five were apparently out at the time he wrote. There were also French editions in 1800 and 1835.

[116] So in the original for Tycho Brahe.

[117] In general these men acted before Baron wrote, or at any rate, before he wrote the Novum Organum, but the statement must not be taken too literally. The dates are as follows: Copernicus, 1473-1543; Tycho Brahe, 1546-1601; Gilbert, 1540-1603; Kepler, 1571-1630; Galileo, 1564-1642; Harvey, 1578-1657. For example, Harvey's Exercitatio Anatomica de Motu Cordis et Sanguinis did not appear until 1628, and his Exercitationes de Generatione until 1651.

[118] Robert Hooke (1635-1703) studied under Robert Boyle at Oxford. He was "Curator of Experiments" to the Royal Society and its secretary, and was professor of geometry at Gresham College, London. It is true that he was "very little of a mathematician" although he wrote on the motion of the earth (1674), on helioscopes and other instruments (1675), on the rotation of Jupiter (1666), and on barometers and sails.

[119] The son of the Sir William mentioned below. He was born in 1792 and died in 1871. He wrote a treatise on light (1831) and one on astronomy (1836), and established an observatory at the Cape of Good Hope where he made observations during 1834-1838, publishing them in 1847. On his return to England he was knighted, and in 1848 was made president of the Royal Society. The title of the work to which reference is made is: A preliminary discourse on the Study of Natural Philosophy. It appeared at London in 1831.

[120] Sir William was horn at Hanover in 1738 and died at Slough, near Windsor in 1822. He discovered the planet Uranus and six satellites, besides two satellites of Saturn. He was knighted by George III.

[121] This was the work of 1836. He also published a work entitled Outlines of Astronomy in 1849.

[122] While Newton does not tell the story, he refers in the Principia (1714 edition, p. 293) to the accident caused by his cat.

[123] Marino Ghetaldi (1566-1627), whose Promotus Archimedes appeared at Rome in 1603, Nonnullae propositiones de parabola at Rome in 1603. and Apollonius redivivus at Venice in 1607. He was a nobleman and was ambassador from Venice to Rome.

[124] Simon Stevin (born at Bruges, 1548; died at the Hague, 1620). He was an engineer and a soldier, and his La Disme (1585) was the first separate treatise on the decimal fraction. The contribution referred to above is probably that on the center of gravity of three bodies (1586).

[125] Habakuk Guldin (1577-1643), who took the name Paul on his conversion to Catholicism. He became a Jesuit, and was professor of mathematics at Vienna and later at Gratz. In his Centrobaryca seu de centro gravitatis trium specierum quantitatis continuae (1635), of the edition of 1641, appears the Pappus rule for the volume of a solid formed by the revolution of a plane figure about an axis, often spoken of as Guldin's Theorem.

[126] Edward Wright was born at Graveston, Norfolkshire, in 1560, and died at London in 1615. He was a fellow of Caius College, Cambridge, and in his work entitled The correction of certain errors in Navigation (1599) he gives the principle of Mercator's projection. He translated the Portuum investigandorum ratio of Stevin in 1599.

[127] De Morgan never wrote a more suggestive sentence. Its message is not for his generation alone.

[128] The eminent French physicist, Jean Baptiste Biot (1779-1862), professor in the College de France. His work Sur les observatoires meteorologiques appeared in 1855.

[129] George Biddell Airy (1801-1892), professor of astronomy and physics at Cambridge, and afterwards director of the Observatory at Greenwich.

[130] De Morgan would have rejoiced in the role played by Intuition in the mathematics of to-day, notably among the followers of Professor Klein.

[131] Colburn was the best known of the calculating boys produced in America. He was born at Cabot, Vermont, in 1804, and died at Norwich, Vermont, in 1840. Having shown remarkable skill in numbers as early as 1810, he was taken to London in 1812, whence he toured through Great Britain and to Paris. The Earl of Bristol placed him in Westminster School (1816-1819). On his return to America he became a preacher, and later a teacher of languages.

[132] The history of calculating boys is interesting. Mathieu le Coc (about 1664), a boy of Lorraine, could extract cube roots at sight at the age of eight. Tom Fuller, a Virginian slave of the eighteenth century, although illiterate, gave the number of seconds in 7 years 17 days 12 hours after only a minute and a half of thought. Jedediah Buxton, an Englishman of the eighteenth century, was studied by the Royal Society because of his remarkable powers. Ampere, the physicist, made long calculations with pebbles at the age of four. Gauss, one of the few infant prodigies to become an adult prodigy, corrected his father's payroll at the age of three. One of the most remarkable of the French calculating boys was Henri Mondeux. He was investigated by Arago, Sturm, Cauchy, and Liouville, for the Academie des Sciences, and a report was written by Cauchy. His specialty was the solution of algebraic problems mentally. He seems to have calculated squares and cubes by a binomial formula of his own invention. He died in obscurity, but was the subject of a Biographie by Jacoby (1846). George P. Bidder, the Scotch engineer (1806-1878), was exhibited as an arithmetical prodigy at the age of ten, and did not attend school until he was twelve. Of the recent cases two deserve special mention, Inaudi and Diamandi. Jacques Inaudi (born in 1867) was investigated for the Academie in 1892 by a commission including Poincare, Charcot, and Binet. (See the Revue des Deux Mondes, June 15, 1892, and the laboratory bulletins of the Sorbonne). He has frequently exhibited his remarkable powers in America. Pericles Diamandi was investigated by the same commission in 1893. See Alfred Binet, Psychologie des Grands Calculateurs et Joueurs d'Echecs, Paris, 1894.

[133] John Flamsteed's (1646-1719) "old white house" was the first Greenwich observatory. He was the Astronomer Royal and first head of this observatory.

[134] It seems a pity that De Morgan should not have lived to lash those of our time who are demanding only the immediately practical in mathematics. His satire would have been worth the reading against those who seek to stifle the science they pretend to foster.

[135] Ismael Bouillaud, or Boulliau, was born in 1605 and died at Paris in 1694. He was well known as an astronomer, mathematician, and jurist. He lived with De Thou at Paris, and accompanied him to Holland. He traveled extensively, and was versed in the astronomical work of the Persians and Arabs. It was in his Astronomia philolaica, opus novum (Paris, 1645) that he attacked Kepler's laws. His tables were shown to be erroneous by the fact that the solar eclipse did not take place as predicted by him in 1645.

[136] As it did, until 1892, when Airy had reached the ripe age of ninety-one.

[137] Didaci a Stunica ... In Job commentaria appeared at Toledo in 1584.

[138] "The false Pythagorean doctrine, absolutely opposed to the Holy Scriptures, concerning the mobility of the earth and the immobility of the sun."

[139] Paolo Antonio Foscarini (1580-1616), who taught theology and philosophy at Naples and Messina, was one of the first to champion the theories of Copernicus. This was in his Lettera sopra l'opinione de' Pittagorici e del Copernico, della mobilita della Terra e stabilita del Sole, e il nuovo pittagorico sistema del mondo, 4to, Naples, 1615. The condemnation of the Congregation was published in the following spring, and in the year of Foscarini's death at the early age of thirty-six.

[140] "To be wholly prohibited and condemned," because "it seeks to show that the aforesaid doctrine is consonant with truth and is not opposed to the Holy Scriptures."

[141] "As repugnant to the Holy Scriptures and to its true and Catholic interpretation (which in a Christian man cannot be tolerated in the least), he does not hesitate to treat (of his subject) 'by hypothesis', but he even adds 'as most true'!"

[142] "To the places in which he discusses not by hypothesis but by making assertions concerning the position and motion of the earth."

[143] "Copernicus. If by chance there shall be vain talkers who, although ignorant of all mathematics, yet taking it upon themselves to sit in judgment upon the subject on account of a certain passage of Scripture badly distorted for their purposes, shall have dared to criticize and censure this teaching of mine, I pay no attention to them, even to the extent of despising their judgment as rash. For it is not unknown that Lactantius, a writer of prominence in other lines although but little versed in mathematics, spoke very childishly about the form of the earth when he ridiculed those who declared that it was spherical. Hence it should not seem strange to the learned if some shall look upon us in the same way. Mathematics is written for mathematicians, to whom these labors of ours will seem, if I mistake not, to add something even to the republic of the Church.... Emend. Here strike out everything from 'if by chance' to the words 'these labors of ours,' and adapt it thus: 'But these labors of ours.'"

[144] "Copernicus. However if we consider the matter more carefully it will be seen that the investigation is not yet completed, and therefore ought by no means to be condemned. Emend. However, if we consider the matter more carefully it is of no consequence whether we regard the earth as existing in the center of the universe or outside of the center, so far as the solution of the phenomena of celestial movements is concerned."

[145] "The whole of this chapter may be cut out, since it avowedly treats of the earth's motion, while it refutes the reasons of the ancients proving its immobility. Nevertheless, since it seems to speak problematically, in order that it may satisfy the learned and keep intact the sequence and unity of the book let it be emended as below."

[146] "Copernicus. Therefore why do we still hesitate to concede to it motion which is by nature consistent with its form, the more so because the whole universe is moving, whose end is not and cannot be known, and not confess that there is in the sky an appearance of daily revolution, while on the earth there is the truth of it? And in like manner these things are as if Virgil's AEneas should say, 'We are borne from the harbor' ... Emend. Hence I cannot concede motion to this form, the more so because the universe would fall, whose end is not and cannot be known, and what appears in the heavens is just as if ..."

[147] "Copernicus. I also add that it would seem very absurd that motion should be ascribed to that which contains and locates, and not rather to that which is contained and located, that is the earth. Emend. I also add that it is not more difficult to ascribe motion to the contained and located, which is the earth, than to that which contains it."

[148] "Copernicus. You see, therefore, that from all these things the motion of the earth is more probable than its immobility, especially in the daily revolution which is as it were a particular property of it. Emend. Omit from 'You see' to the end of the chapter."

[149] "Copernicus. Therefore, since there is nothing to hinder the motion of the earth, it seems to me that we should consider whether it has several motions, to the end that it may be looked upon as one of the moving stars. Emend. Therefore, since I have assumed that the earth moves, it seems to me that we should consider whether it has several motions."

[150] "Copernicus. We are not ashamed to acknowledge ... that this is preferably verified in the motion of the earth. Emend. We are not ashamed to assume ... that this is consequently verified in the motion."

[151] "Copernicus. So divine is surely this work of the Best and Greatest. Emend. Strike out these last words."

[152] This should be Cap. 11, lib. i, p. 10.

[153] "Copernicus. Demonstration of the threefold motion of the earth. Emend. On the hypothesis of the threefold motion of the earth and its demonstration."

[154] This should be Cap. 20, lib. iv, p. 122.

[155] "Copernicus. Concerning the size of these three stars, the sun, the moon and the earth. Emend. Strike out the words 'these three stars,' because the earth is not a star as Copernicus would make it."

[156] He seems to speak problematically in order to satisfy the learned.

[157] One of the Church Fathers, born about 250 A.D., and died about 330, probably at Treves. He wrote Divinarum Institutionum Libri VII. and other controversial and didactic works against the learning and philosophy of the Greeks.

[158] Giovanni Battista Riccioli (1598-1671) taught philosophy and theology at Parma and Bologna, and was later professor of astronomy. His Almagestum novum appeared in 1651, and his Argomento fisico-matematico contro il moto diurno della terra in 1668.

[159] He was a native of Arlington, Sussex, and a pensioner of Christ's College, Cambridge. In 1603 he became a master of arts at Oxford.

[160] Straying, i.e., from the right way.

[161] "Private subjects may, in the presence of danger, defend themselves or their families against a monarch as against any malefactor, if the monarch assaults them like a bandit or a ravisher, and provided they are unable to summon the usual protection and cannot in any way escape the danger."

[162] Daniel Neal (1678-1743), an independent minister, wrote a History of the Puritans that appeared in 1732. The account may be found in the New York edition of 1843-44, vol. I, p. 271.

[163] Anthony Wood (1632-1695), whose Historia et Antiquitates Universitatis Oxoniensis (1674) and Athenae Oxoniensis (1691) are among the classics on Oxford.

[164] Part of the title, not here quoted, shows the nature of the work more clearly: "liber unicus, in quo decretum S. Congregationis S. R. E. Cardinal. an. 1616, adversus Pythagorico-Copernicanos editum defenditur."

[165] This was John Elliot Drinkwater Bethune (1801-1851), the statesman who did so much for legislative and educational reform in India. His father, John Drinkwater Bethune, wrote a history of the siege of Gibraltar.

[166] The article referred to is about thirty years old; since it appeared another has been given (Dubl. Rev., Sept. 1865) which is of much greater depth. In it will also be found the Roman view of Bishop Virgil (ante, p. 32).—A. De M.

[167] Jean Baptiste Morin (1583-1656), in his younger days physician to the Bishop of Boulogne and the Duke of Luxemburg, became in 1630 professor of mathematics at the College Royale. His chief contribution to the problem of the determination of longitude is his Longitudinum terrestrium et coelestium nova et hactenus optata scientia (1634). He also wrote against Copernicus in his Famosi problematis de telluris motu vel quiete hactenus optata solutio (1631), and against Lansberg in his Responsio pro telluris quiete (1634).

[168] The work appeared at Leyden in 1626, at Amsterdam in 1634, at Copenhagen in 1640 and again at Leyden in 1650. The title of the 1640 edition is Arithmeticae Libri II et Geometriae Libri VI. The work on which it is based is the Arithmeticae et Geometriae Practica, which appeared in 1611.

[169] The father's name was Adriaan, and Lalande says that it was Montucla who first made the mistake of calling him Peter, thinking that the initials P. M. stood for Petrus Metius, when in reality they stood for piae memoriae! The ratio 355/113 was known in China hundreds of years before his time. See note 55, page 52.

[170] Adrian Metius (1571-1635) was professor of medicine at the University of Franeker. His work was, however, in the domain of astronomy, and in this domain he published several treatises.

[171] The first edition was entitled: The Discovery of a World in the Moone. Or, a Discourse Tending to prove that 'tis probable there may be another habitable World in that Planet. 1638, 8vo. The fourth edition appeared in 1684. John Wilkins (1614-1672) was Warden of Wadham College, Oxford; master of Trinity, Cambridge; and, later, Bishop of Chester. He was influential in founding the Royal Society.

[172] The first edition was entitled: C. Hugenii [Greek: Kosmotheoros], sive de Terris coelestibus, earumque ornatu, conjecturae, The Hague, 1698, 4to. There were several editions. It was also translated into French (1718), and there was another English edition (1722). Huyghens (1629-1695) was one of the best mathematical physicists of his time.

[173] It is hardly necessary to say that science has made enormous advance in the chemistry of the universe since these words were written.

[174] William Whewell (1794-1866) is best known through his History of the Inductive Sciences (1837) and Philosophy of the Inductive Sciences (1840).

[175] Thomas Chalmers (1780-1847), the celebrated Scotch preacher. These discourses were delivered while he was minister in a large parish in the poorest part of Glasgow, and in them he attempted to bring science into harmony with the Bible. He was afterwards professor of moral philosophy at St. Andrew's (1823-28), and professor of theology at Edinburgh (1828). He became the leader of a schism from the Scotch Presbyterian Church,—the Free Church.

[176] That is, in Robert Watt's (1774-1819) Bibliotheca Britannica (posthumous, 1824). Nor is it given in the Dictionary of National Biography.

[177] The late Greek satirist and poet, c. 120-c. 200 A.D.

[178] Francois Rabelais (c. 1490-1553) the humorist who created Pantagruel (1533) and Gargantua (1532). His work as a physician and as editor of the works of Galen and Hippocrates is less popularly known.

[179] Francis Godwin (1562-1633) bishop of Llandaff and Hereford. Besides some valuable historical works he wrote The Man in the Moone, or a Discourse of a voyage thither by Domingo Gonsales, the Speed Messenger of London, 1638.

[180] Bernard Le Bovier de Fontenelle (1657-1757), historian, critic, mathematician, Secretary of the Academie des Sciences, and member of the Academie Francaise. His Entretien sur la pluralite des mondes appeared at Paris in 1686.

[181] Athanasius Kircher (1602-1680), Jesuit, professor of mathematics and philosophy, and later of Hebrew and Syriac, at Wurzburg; still later professor of mathematics and Hebrew at Rome. He wrote several works on physics. His collection of mathematical instruments and other antiquities became the basis of the Kircherian Museum at Rome.

[182] "Both belief and non-belief are dangerous. Hippolitus died because his stepmother was believed. Troy fell because Cassandra was not believed. Therefore the truth should be investigated long before foolish opinion can properly judge." (Prove = probe?).

[183] Jacobus Grandamicus (Jacques Grandami) was born at Nantes in 1588 and died at Paris in 1672. He was professor of theology and philosophy in the Jesuit colleges at Rennes, Tours, Rouen, and other places. He wrote several works on astronomy.

[184] "And I, if I be lifted up from the earth, will draw all men unto me." John xii. 32.

[185] Andrea Argoli (1568-1657) wrote a number of works on astronomy, and computed ephemerides from 1621 to 1700.

[186] So in the original edition of the Budget. It is Johannem Pellum in the original title. John Pell (1610 or 1611-1685) studied at Cambridge and Oxford, and was professor of mathematics at Amsterdam (1643-46) and Breda (1646-52). He left many manuscripts but published little. His name attaches by accident to an interesting equation recently studied with care by Dr. E. E. Whitford (New York, 1912).

[187] Christianus Longomontanus (Christen Longberg or Lumborg) was born in 1569 at Longberg, Jutland, and died in 1647 at Copenhagen. He was an assistant of Tycho Brahe and accepted the diurnal while denying the orbital motion of the earth. His Cyclometria e lunulis reciproce demonstrata appeared in 1612 under the name of Christen Severin, the latter being his family name. He wrote several other works on the quadrature problem, and some treatises on astronomy.

[188] The names are really pretty well known. Giles Persone de Roberval was born at Roberval near Beauvais in 1602, and died at Paris in 1675. He was professor of philosophy at the College Gervais at Paris, and later at the College Royal. He claimed to have discovered the theory of indivisibles before Cavalieri, and his work is set forth in his Traite des indivisibles which appeared posthumously in 1693.

Hobbes (1588-1679), the political and social philosopher, lived a good part of his time (1610-41) in France where he was tutor to several young noblemen, including the Cavendishes. His Leviathan (1651) is said to have influenced Spinoza, Leibnitz, and Rousseau. His Quadratura circuli, cubatio sphaerae, duplicatio cubi ... (London, 1669), Rosetum geometricum ... (London, 1671), and Lux Mathematica, censura doctrinae Wallisianae contra Rosetum Hobbesii (London, 1674) are entirely forgotten to-day. (See a further note, infra.)

Pierre de Carcavi, a native of Lyons, died at Paris in 1684. He was a member of parliament, royal librarian, and member of the Academie des Sciences. His attempt to prove the impossibility of the quadrature appeared in 1645. He was a frequent correspondent of Descartes.

Cavendish (1591-1654) was Sir (not Lord) Charles. He was, like De Morgan himself, a bibliophile in the domain of mathematics. His life was one of struggle, his term as member of parliament under Charles I being followed by gallant service in the royal army. After the war he sought refuge on the continent where he met most of the mathematicians of his day. He left a number of manuscripts on mathematics, which his widow promptly disposed of for waste paper. If De Morgan's manuscripts had been so treated we should not have had his revision of his Budget of Paradoxes.

Marin Mersenne (1588-1648), a minorite, living in the cloisters at Nevers and Paris, was one of the greatest Franciscan scholars. He edited Euclid, Apollonius, Archimedes, Theodosius, and Menelaus (Paris, 1626), translated the Mechanics of Galileo into French (1634), wrote Harmonicorum Libri XII (1636), and Cogitata physico-mathematica (1644), and taught theology and philosophy at Nevers.

Johann Adolph Tasse (Tassius) was born in 1585 and died at Hamburg in 1654. He was professor of mathematics in the Gymnasium at Hamburg, and wrote numerous works on astronomy, chronology, statics, and elementary mathematics.

Johann Ludwig, Baron von Wolzogen, seems to have been one of the early unitarians, called Fratres Polonorum because they took refuge in Poland. Some of his works appear in the Bibliotheca Fratrum Polonorum (Amsterdam, 1656). I find no one by the name who was contributing to mathematics at this time.

Descartes is too well known to need mention in this connection.

Bonaventura Cavalieri (1598-1647) was a Jesuit, a pupil of Galileo, and professor of mathematics at Bologna. His greatest work, Geometria indivisibilibus continuorum nova quadam ratione promota, in which he makes a noteworthy step towards the calculus, appeared in 1635.

Jacob (Jacques) Golius was born at the Hague in 1596 and died at Leyden in 1667. His travels in Morocco and Asia Minor (1622-1629) gave him such knowledge of Arabic that he became professor of that language at Leyden. After Snell's death he became professor of mathematics there. He translated Arabic works on mathematics and astronomy into Latin.

[189] It would be interesting to follow up these rumors, beginning perhaps with the tomb of Archimedes. The Ludolph van Ceulen story is very likely a myth. The one about Fagnano may be such. The Bernoulli tomb does have the spiral, however (such as it is), as any one may see in the cloisters at Basel to-day.

[190] Collins (1625-1683) was secretary of the Royal Society, and was "a kind of register of all new improvements in mathematics." His office brought him into correspondence with all of the English scientists, and he was influential in the publication of various important works, including Branker's translation of the algebra by Rhonius, with notes by Pell, which was the first work to contain the present English-American symbol of division. He also helped in the publication of editions of Archimedes and Apollonius, of Kersey's Algebra, and of the works of Wallis. His profession was that of accountant and civil engineer, and he wrote three unimportant works on mathematics (one published posthumously, and the others in 1652 and 1658).

Heinrich Christian Schumacher (1780-1850) was professor of astronomy at Copenhagen and director of the observatory at Altona. His translation of Carnot's Geometrie de position (1807) brought him into personal relations with Gauss, and the friendship was helpful to Schumacher. He was a member of many learned societies and had a large circle of acquaintances. He published numerous monographs and works on astronomy.

Gassendi (1592-1655) might well have been included by De Morgan in the group, since he knew and was a friend of most of the important mathematicians of his day. Like Mersenne, he was a minorite, but he was a friend of Galileo and Kepler, and wrote a work under the title Institutio astronomica, juxta hypotheses Copernici, Tychonis-Brahaei et Ptolemaei (1645). He taught philosophy at Aix, and was later professor of mathematics at the College Royal at Paris.

Burnet is the Bishop Gilbert Burnet (1643-1715) who was so strongly anti-Romanistic that he left England during the reign of James II and joined the ranks of the Prince of Orange. William made him bishop of Salisbury.

[191] There is some substantial basis for De Morgan's doubts as to the connection of that mirandula of his age, Sir Kenelm Digby (1603-1665), with the famous poudre de sympathie. It is true that he was just the one to prepare such a powder. A dilletante in everything,—learning, war, diplomacy, religion, letters, and science—he was the one to exploit a fraud of this nature. He was an astrologer, an alchemist, and a fabricator of tales, and well did Henry Stubbes characterize him as "the very Pliny of our age for lying." He first speaks of the powder in a lecture given at Montpellier in 1658, and in the same year he published the address at Paris under the title: Discours fait en une celebre assemblee par le chevalier Digby .... touchant la guerison de playes par la poudre de sympathie. The London edition referred to by De Morgan also came out in 1658, and several editions followed it in England, France and Germany. But Nathaniel Highmore in his History of Generation (1651) referred to the concoction as "Talbot's Powder" some years before Digby took it up. The basis seems to have been vitriol, and it was claimed that it would heal a wound by simply being applied to a bandage taken from it.

[192] This work by Thomas Birch (1705-1766) came out in 1756-57. Birch was a voluminous writer on English history. He was a friend of Dr. Johnson and of Walpole, and he wrote a life of Robert Boyle.

[193] We know so much about John Evelyn (1620-1706) through the diary which he began at the age of eleven, that we forget his works on navigation and architecture.

[194] I suppose this was the seventh Earl of Shrewsbury (1553-1616).

[195] This is interesting in view of the modern aseptic practice of surgery and the antiseptic treatment of wounds inaugurated by the late Lord Lister.

[196] Perhaps De Morgan had not heard the bon mot of Dr. Holmes: "I firmly believe that if the whole materia medica could be sunk to the bottom of the sea, it would be all the better for mankind and all the worse for the fishes."

[197] The full title is worth giving, because it shows the mathematical interests of Hobbes, and the nature of the six dialogues: Examinatio et emendatio mathematicae hodiernae qualis explicatur in libris Johannis Wallisii geometriae professoris Saviliani in Academia Oxoniensi: distributa in sex dialogos (1. De mathematicae origine ...; 2. De principiis traditis ab Euclide; 3. De demonstratione operationum arithmeticarum ...; 4. De rationibus; 5. De angula contactus, de sectionibus coni, et arithmetica infinitorum; 6. Dimensio circuli tribus methodis demonstrata ... item cycloidis verae descriptio et proprietates aliquot.) Londini, 1660 (not 1666). For a full discussion of the controversy over the circle, see George Croom Robertson's biography of Hobbes in the eleventh edition of the Encyclopaedia Britannica.

[198] This is his Animadversions upon Mr. Hobbes' late book De principiis et ratiocinatione geometrarum, 1666, or his Hobbianae quadraturae circuli, cubationis sphaerae et duplicationis cubi confutatio, also of 1669.

[199] This is the work of 1669 referred to above.

[200] Gregoire de St. Vincent (1584-1667) published his Opus geometricum quadraturae circuli et sectionum coni at Antwerp in 1647.

[201] This appears in J. Scaligeri cyclometrica elementa duo, Lugduni Batav., 1594.

[202] Adriaen van Roomen (1561-1615) gave the value of [pi] to sixteen decimal places in his Ideae mathematicae pars prima (1593), and wrote his In Archimedis circuli dimensionem expositio & analysis in 1597.

[203] Kaestner. See note 30 on page 43.

[204] Bentley (1662-1742) might have done it, for as the head of Trinity College, Cambridge, and a follower of Newton, he knew some mathematics. Erasmus (1466-1536) lived a little too early to attempt it, although his brilliant satire might have been used to good advantage against those who did try.

[205] "In grammar, to give the winds to the ships and to give the ships to the winds mean the same thing. But in geometry it is one thing to assume the circle BCD not greater than thirty-six segments BCDF, and another (to assume) the thirty-six segments BCDF not greater than the circle. The one assumption is true, the other false."

[206] The Greek scholar (1559-1614) who edited a Greek and Latin edition of Aristotle in 1590.

[207] Jacques Auguste de Thou (1553-1617), the historian and statesman.

[208] "To value Scaliger higher even when wrong, than the multitude when right."

[209] "I would rather err with Scaliger than be right with Clavius."

[210] "The perimeter of the dodecagon to be inscribed in a circle is greater than the perimeter of the circle. And the more sides a polygon to be inscribed in a circle successively has, so much the greater will the perimeter of the polygon be than the perimeter of the circle."

[211] De Morgan took, perhaps, the more delight in speaking thus of Sir William Hamilton (1788-1856) because of a spirited controversy that they had in 1847 over the theory of logic. Possibly, too, Sir William's low opinion of mathematics had its influence.

[212] Edwards (1699-1757) wrote The canons of criticism (1747) in which he gave a scathing burlesque on Warburton's Shakespeare. It went through six editions.

[213] Antoine Teissier (born in 1632) published his Eloges des hommes savants, tires de l'histoire de M. de Thou in 1683.

[214] "He boasted without reason of having found the quadrature of the circle. The glory of this admirable discovery was reserved for Joseph Scaliger, as Scevole de St. Marthe has written."

[215] Natural and political observations mentioned in the following Index, and made upon the Bills of Mortality.... With reference to the government, religion, trade, growth, ayre, and diseases of the said city. London, 1662, 4to. The book went through several editions.

[216] Ne sutor ultra crepidam, "Let the cobbler stick to his last," as we now say.

[217] The author (1632-1695) of the Historia et Antiquitates Universitatis Oxoniensis (1674). See note 163, page 98.

[218] The mathematical guild owes Samuel Pepys (1633-1703) for something besides his famous diary (1659-1669). Not only was he president of the Royal Society (1684), but he was interested in establishing Sir William Boreman's mathematical school at Greenwich.

[219] John Graunt (1620-1674) was a draper by trade, and was a member of the Common Council of London until he lost office by turning Romanist. Although a shopkeeper, he was elected to the Royal Society on the special recommendation of Charles II. Petty edited the fifth edition of his work, adding much to its size and value, and this may be the basis of Burnet's account of the authorship.

[220] Petty (1623-1687) was a mathematician and economist, and a friend of Pell and Sir Charles Cavendish. His survey of Ireland, made for Cromwell, was one of the first to be made on a large scale in a scientific manner. He was one of the founders of the Royal Society.

[221] The story probably arose from Graunt's recent conversion to the Roman Catholic faith.

[222] He was born in 1627 and died in 1704. He published a series of ephemerides, beginning in 1659. He was imprisoned in 1679, at the time of the "Popish Plot," and again for treason in 1690. His important astrological works are the Animal Cornatum, or the Horn'd Beast (1654) and The Nativity of the late King Charls (1659).

[223] Isaac D'Israeli (1766-1848), in his Curiosities of Literature (1791), speaking of Lilly, says: "I shall observe of this egregious astronomer, that there is in this work, so much artless narrative, and at the same time so much palpable imposture, that it is difficult to know when he is speaking what he really believes to be the truth." He goes on to say that Lilly relates that "those adepts whose characters he has drawn were the lowest miscreants of the town. Most of them had taken the air in the pillory, and others had conjured themselves up to the gallows. This seems a true statement of facts."

[224] It is difficult to estimate William Lilly (1602-1681) fairly. His Merlini Anglici ephemeris, issued annually from 1642 to 1681, brought him a great deal of money. Sir George Wharton (1617-1681) also published an almanac annually from 1641 to 1666. He tried to expose John Booker (1603-1677) by a work entitled Mercurio-Coelicio-Mastix; or, an Anti-caveat to all such, as have (heretofore) had the misfortune to be Cheated and Deluded by that Grand and Traiterous Impostor of this Rebellious Age, John Booker, 1644. Booker was "licenser of mathematical [astrological] publications," and as such he had quarrels with Lilly, Wharton, and others.

[225] See note 171 on page 100.

[226] This is the Ars Signorum, vulgo character universalis et lingua philosophica, that appeared at London in 1661, 8vo. George Dalgarno anticipated modern methods in the teaching of the deaf and dumb.

[227] See note 200 on page 110.

[228] If the hyperbola is referred to the asymptotes as axes, the area between two ordinates (x = a, x = b) is the difference of the logarithms of a and b to the base e. E.g., in the case of the hyperbola xy = 1, the area between x = a and x = 1 is log a.

[229] "On ne peut lui refuser la justice de remarquer que personne avant lui ne s'est porte dans cette recherche avec autant de genie, & meme, si nous en exceptons son objet principal, avec autant de succes." Quadrature du Cercle, p. 66.

[230] The title proceeds: Seu duae mediae proportionales inter extremas datas per circulum et per infinitas hyperbolas, vel ellipses et per quamlibet exhibitae.... Rene Francois, Baron de Sluse (1622-1685) was canon and chancellor of Liege, and a member of the Royal Society. He also published a work on tangents (1672). The word mesolabium is from the Greek [Greek: mesolabion] or [Greek: mesolabon], an instrument invented by Eratosthenes for finding two mean proportionals.

[231] The full title has some interest: Vera circuli et hyperbolae quadratura cui accedit geometriae pars universalis inserviens quantitatum curvarum transmutationi et mensurae. Authore Jacobo Gregorio Abredonensi Scoto ... Patavii, 1667. That is, James Gregory (1638-1675) of Aberdeen (he was really born near but not in the city), a good Scot, was publishing his work down in Padua. The reason was that he had been studying in Italy, and that this was a product of his youth. He had already (1663) published his Optica promota, and it is not remarkable that his brilliancy brought him a wide circle of friends on the continent and the offer of a pension from Louis XIV. He became professor of mathematics at St Andrews and later at Edinburgh, and invented the first successful reflecting telescope. The distinctive feature of his Vera quadratura is his use of an infinite converging series, a plan that Archimedes used with the parabola.

[232] Jean de Beaulieu wrote several works on mathematics, including La lumiere de l'arithmetique (n.d.), La lumiere des mathematiques (1673), Nouvelle invention d'arithmetique (1677), and some mathematical tables.

[233] A just estimate. There were several works published by Gerard Desargues (1593-1661), of which the greatest was the Brouillon Proiect (Paris, 1639). There is an excellent edition of the Oeuvres de Desargues by M. Poudra, Paris, 1864.

[234] "A certain M. de Beaugrand, a mathematician, very badly treated by Descartes, and, as it appears, rightly so."

[235] This is a very old approximation for [pi]. One of the latest pretended geometric proofs resulting in this value appeared in New York in 1910, entitled Quadrimetry (privately printed).

[236] "Copernicus, a German, made himself no less illustrious by his learned writings; and we might say of him that he stood alone and unique in the strength of his problems, if his excessive presumption had not led him to set forth in this science a proposition so absurd that it is contrary to faith and reason, namely that the circumference of a circle is fixed and immovable while the center is movable: on which geometrical principle he has declared in his astrological treatise that the sun is fixed and the earth is in motion."

[237] So in the original.

[238] Franciscus Maurolycus (1494-1575) was really the best mathematician produced by Sicily for a long period. He made Latin translations of Theodosius, Menelaus, Euclid, Apollonius, and Archimedes, and wrote on cosmography and other mathematical subjects.

[239] "Nicolaus Copernicus is also tolerated who asserted that the sun is fixed and that the earth whirls about it; and he rather deserves a whip or a lash than a reproof."

[240] "Algebra is the curious science of scholars, and particularly for a general of an army, or a captain, in order quickly to draw up an army in battle array and to number the musketeers and pikemen who compose it, without the figures of arithmetic. This science has five special figures of this kind: P means plus in commerce and pikemen in the army; M means minus, and musketeer in the art of war;... R signifies root in the measurement of a cube, and rank in the army; Q means square (French quare, as then spelled) in both cases; C means cube in mensuration, and cavalry in arranging batallions and squadrons. As for the operations of this science, they are as follows: to add a plus and a plus, the sum will be plus; to add minus with plus, take the less from the greater and the remainder will be the sum required or the number to be found. I say this only in passing, for the benefit of those who are wholly ignorant of it."

[241] He refers to the Joannis de Beaugrand ... Geostatice, seu de vario pondere gravium secundum varia a terrae (centro) intervalla dissertatio mathematica, Paris, 1636. Pascal relates that de Beaugrand sent all of Roberval's theorems on the cycloid and Fermat's on maxima and minima to Galileo in 1638, pretending that they were his own.

[242] More (1614-1687) was a theologian, a fellow of Christ College, Cambridge, and a Christian Platonist.

[243] Matthew Hale (1609-1676) the famous jurist, wrote a number of tracts on scientific, moral, and religious subjects. These were collected and published in 1805.

[244] They might have been attributed to many a worse man than Dr. Hales (1677-1761), who was a member of the Royal Society and of the Paris Academy, and whose scheme for the ventilation of prisons reduced the mortality at the Savoy prison from one hundred to only four a year. The book to which reference is made is Vegetable Staticks or an Account of some statical experiments on the sap in Vegetables, 1727.

[245] Pleas of the Crown; or a Methodical Summary of the Principal Matters relating to the subject, 1678.

[246] Thomae Streete Astronomia Carolina, a new theory of the celestial motions, 1661. It also appeared at Nuremberg in 1705, and at London in 1710 and 1716 (Halley's editions). He wrote other works on astronomy.

[247] This was the Sir Thomas Street (1626-1696) who passed sentence of death on a Roman Catholic priest for saying mass. The priest was reprieved by the king, but in the light of the present day one would think the justice more in need of pardon. He took part in the trial of the Rye House Conspirators in 1683.

[248] Edmund Halley (1656-1742), who succeeded Wallis (1703) as Savilian professor of mathematics at Oxford, and Flamsteed (1720) as head of the Greenwich observatory. It is of interest to note that he was instrumental in getting Newton's Principia printed.

[249] Shepherd (born in 1760) was one of the most famous lawyers of his day. He was knighted in 1814 and became Attorney General in 1817.

[250] This was William Hone (1780-1842), a book publisher, who wrote satires against the government, and who was tried three times because of his parodies on the catechism, creed, and litany (illustrated by Cruikshank). He was acquitted on all of the charges.

[251] Valentinus was a Benedictine monk and was still living at Erfurt in 1413. His Currus triumphalis antimonii appeared in 1624. Synesius was Bishop of Ptolemaide, who died about 430. His works were printed at Paris in 1605. Theodor Kirckring (1640-1693) was a fellow-student of Spinoza's. Besides the commentary on Valentine he left several works on anatomy. His commentary appeared at Amsterdam in 1671. There were several editions of the Chariot.

[252] The chief difficulty with this curious "monk-bane" etymology is its absurdity. The real origin of the word has given etymologists a good deal of trouble.

[253] Robert Boyle (1627-1691), son of "the Great Earl" (of Cork). Perhaps his best-known discovery is the law concerning the volume of gases.

[254] The real name of Eirenaeus Philalethes (born in 1622) is unknown. It may have been Childe. He claimed to have discovered the philosopher's stone in 1645. His tract in this work is The Secret of the Immortal Liquor Alkahest or Ignis-Aqua. See note 260, infra.

[255] Johann Baptist van Helmont, Herr von Merode, Royenborg etc. (1577-1644). His chemical discoveries appeared in his Ortus medicinae (1648), which went through many editions.

[256] De Morgan should have written up Francis Anthony (1550-1623), whose Panacea aurea sive tractatus duo de auro potabili (Hamburg, 1619) described a panacea that he gave for every ill. He was repeatedly imprisoned for practicing medicine without a license from the Royal College of Physicians.

[257] Bernardus Trevisanus (1406-1490), who traveled even through Barbary, Egypt, Palestine, and Persia in search of the philosopher's stone. He wrote several works on alchemy,—De Chemica (1567), De Chemico Miraculo (1583), Traite de la nature de l'oeuf des philosophes (1659), etc., all published long after his death.

[258] George Ripley (1415-1490) was an Augustinian monk, later a chamberlain of Innocent VIII, and still later a Carmelite monk. His Liber de mercuris philosophico and other tracts first appeared in Opuscula quaedam chymica (Frankfort, 1614).

[259] Besides the Opus majus, and other of the better known works of this celebrated Franciscan (1214-1294), there are numerous tracts on alchemy that appeared in the Thesaurus chymicus (Frankfort, 1603).

[260] George Starkey (1606-1665 or 1666) has special interest for American readers. He seems to have been born in the Bermudas and to have obtained the bachelor's degree in England. He then went to America and in 1646 obtained the master's degree at Harvard, apparently under the name of Stirk. He met Eirenaeus Philalethes (see note 254 above) in America and learned alchemy from him. Returning to England, he sold quack medicines there, and died in 1666 from the plague after dissecting a patient who had died of the disease. Among his works was the Liquor Alcahest, or a Discourse of that Immortal Dissolvent of Paracelsus and Helmont, which appeared (1675) some nine years after his death.

[261] Platt (1552-1611) was the son of a London brewer. Although he left a manuscript on alchemy, and wrote a book entitled Delights for Ladies to adorne their Persons (1607), he was knighted for some serious work on the chemistry of agriculture, fertilizing, brewing, and the preserving of foods, published in The Jewell House of Art and Nature (1594).

[262] "Those who wish to call a man a liar and deceiver speak of him a writer of almanacs; but those who (would call him) a scoundrel and an imposter (speak of him as) a chemist."

[263] "Trust your barque to the winds but not your body to a chemist; any breeze is safer than the faith of a chemist."

[264] Probably the Jesuit, Pere Claude Francois Menestrier (1631-1705), a well known historian.

[265] The author was Christopher Nesse (1621-1705), a belligerent Calvinist, who wrote many controversial works and succeeded in getting excommunicated four times. One of his most virulent works was A Protestant Antidote against the Poison of Popery.

[266] John Case (c. 1660-1700) was a famous astrologer and physician. He succeeded to Lilly's practice in London. In a darkened room, wherein he kept an array of mystical apparatus, he pretended to show the credulous the ghosts of their departed relatives. Besides his astrological works he wrote one serious treatise, the Compendium Anatomicum nova methodo institutum (1695), in which he defends Harvey's theories of embryology.

[267] Marcelis (1636-after 1714) was a soap maker of Amsterdam. It is to be hoped that he made better soap than values of [pi].

[268] John Craig (died in 1731) was a Scotchman, but most of his life was spent at Cambridge reading and writing on mathematics. He endeavored to introduce the Leibnitz differential calculus into England. His mathematical works include the Methodus Figurarum ... Quadraturas determinandi (1685), Tractatus ... de Figurarum Curvilinearum Quadraturis et locis Geometricis (1693), and De Calculo Fluentium libri duo (1718).

[269] As is well known, this subject owes much to the Bernoullis. Craig's works on the calculus brought him into controversy with them. He also wrote on other subjects in which they were interested, as in his memoir On the Curve of the quickest descent (1700), On the Solid of least resistance (1700), and the Solution of Bernoulli's problem on Curves (1704).

[270] This is Samuel Lee (1783-1852), the young prodigy in languages. He was apprenticed to a carpenter at twelve and learned Greek while working at the trade. Before he was twenty-five he knew Hebrew, Chaldee, Syriac, Samaritan, Persian, and Hindustani. He later became Regius professor of Hebrew at Cambridge.

[271] "Where the devil, Master Ludovico, did you pick up such a collection?"

[272] Lord William Brounker (c. 1620-1684), the first president of the Royal Society, is best known in mathematics for his contributions to continued fractions.

[273] Horace Walpole (1717-1797) published his Catalogue of the Royal and Noble Authors of England in 1758. Since his time a number of worthy names in the domain of science in general and of mathematics in particular might be added from the peerage of England.

[274] It was written by Charles Hayes (1678-1760), a mathematician and scholar of no mean attainments. He travelled extensively, and was deputy governor of the Royal African Company. His Treatise on Fluxions (London, 1704) was the first work in English to explain Newton's calculus. He wrote a work entitled The Moon (1723) to prove that our satellite shines by its own as well as by reflected light. His Chronographia Asiatica & Aegyptica (1758) gives the results of his travels.

[275] Publick in the original.

[276] Whiston (1667-1752) succeeded Newton as Lucasian professor of mathematics at Cambridge. In 1710 he turned Arian and was expelled from the university. His work on Primitive Christianity appeared the following year. He wrote many works on astronomy and religion.

[277] Ditton (1675-1715) was, on Newton's recommendation, made Head of the mathematical school at Christ's Hospital, London. He wrote a work on fluxions (1706). His idea for finding longitude at sea was to place stations in the Atlantic to fire off bombs at regular intervals, the time between the sound and the flash giving the distance. He also corresponded with Huyghens concerning the use of chronometers for the purpose.

[278] This was John Arbuthnot (c. 1658-1735), the mathematician, physician and wit. He was intimate with Pope and Swift, and was Royal physician to Queen Anne. Besides various satires he published a translation of Huyghens's work on probabilities (1692) and a well-known treatise on ancient coins, weights, and measures (1727).

[279] Greene (1678-1730) was a very eccentric individual and was generally ridiculed by his contemporaries. In his will he directed that his body be dissected and his skeleton hung in the library of King's College, Cambridge. Unfortunately for his fame, this wish was never carried out.

[280] This was the historian, Robert Sanderson (1660-1741), who spent most of his life at Cambridge.

[281] I presume this was William Jones (1675-1749) the friend of Newton and Halley, vice-president of the Royal Society, in whose Synopsis Palmariorum Matheseos (1706) the symbol [pi] is first used for the circle ratio.

[282] This was the Geometrica solidorum, sive materiae, seu de varia compositione, progressione, rationeque velocitatum, Cambridge, 1712. The work was parodied in A Taste of Philosophical Fanaticism ... by a gentleman of the University of Gratz.

[283] The antiquary and scientist (1690-1754), president of the Royal Society, member of the Academie, friend of Newton, and authority on numismatics.

[284] She was Catherine Barton, Newton's step-niece. She married John Conduitt, master of the mint, who collected materials for a life of Newton.

A propos of Mrs. Conduitt's life of her illustrious uncle, Sir George Greenhill tells a very good story on Poincare, the well-known French mathematician. At an address given by the latter at the International Congress of Mathematicians held in Rome in 1908 he spoke of the story of Newton and the apple as a mere fable. After the address Sir George asked him why he had done so, saying that the story was first published by Voltaire, who had heard it from Newton's niece, Mrs. Conduitt. Poincare looked blank and said, "Newton, et la niece de Newton, et Voltaire,—non! je ne vous comprends pas!" He had thought Sir George meant Professor Volterra of Rome, whose name in French is Voltaire, and who could not possibly have known a niece of Newton without bridging a century or so.

[285] This was the Edmund Turnor (1755-1829) who wrote the Collections for the Town and Soke of Grantham, containing authentic Memoirs of Sir Isaac Newton, from Lord Portsmouth's Manuscripts, London, 1806.

[286] It may be recalled to mind that Sir David (1781-1868) wrote a life of Newton (1855).

[287] "They are in the country. We rejoice."

[288] "I am here, chatterbox, suck!"

[289] "I have been graduated! I decline!"

[290] Giovanni Castiglioni (Castillon, Castiglione), was born at Castiglione, in Tuscany, in 1708, and died at Berlin in 1791. He was professor of mathematics at Utrecht and at Berlin. He wrote on De Moivre's equations (1762), Cardan's rule (1783), and Euclid's treatment of parallels (1788-89).

[291] This was the Isaaci Newtoni, equitis aurati, opuscula mathematica, philosophica et philologica, Lausannae & Genevae, 1744.

[292] At London, 4to.

[293] "All the English attribute it to Newton."

[294] Stephen Peter Rigaud (1774-1839), Savilian professor of geometry at Oxford (1810-27) and later professor of astronomy and head of the Radcliffe Observatory. He wrote An historical Essay on first publication of Sir Isaac Newton's Principia, Oxford, 1838, and a two-volume work entitled Correspondence of Scientific Men of the 17th Century, 1841.

[295] It is no longer considered by scholars as the work of Newton.

[296] J. Edleston, the author of the Correspondence of Sir Isaac Newton and Professor Cotes, London, 1850.

[297] Palmer (1601-1647) was Master of Queen's College, Cambridge, a Puritan but not a separatist. His work, The Characters of a believing Christian, in Paradoxes and seeming contradictions, appeared in 1645.

[298] Grosart (1827-1899) was a Presbyterian clergyman. He was a great bibliophile, and issued numerous reprints of rare books.

[299] This was the year after Palmer's death. The title was, The Remaines of ... Francis Lord Verulam....; being Essays and severall Letters to severall great personages, and other pieces of various and high concernment not heretofore published, London, 1648, 4to.

[300] Shaw (1694-1763) was physician extraordinary to George II. He wrote on chemistry and medicine, and his edition of the Philosophical Works of Francis Bacon appeared at London in 1733.

[301] John Locke (1632-1704), the philosopher. This particular work appeared in 1695. There was an edition in 1834 (vol. 25 of the Sacred Classics) and one in 1836 (vol. 2 of the Christian Library).

[302] I use the word Socinian because it was so much used in Locke's time: it is used in our own day by the small fry, the unlearned clergy and their immediate followers, as a term of reproach for all Unitarians. I suspect they have a kind of liking for the word; it sounds like so sinful. The learned clergy and the higher laity know better: they know that the bulk of the modern Unitarians go farther than Socinus, and are not correctly named as his followers. The Unitarians themselves neither desire nor deserve a name which puts them one point nearer to orthodoxy than they put themselves. That point is the doctrine that direct prayer to Jesus Christ is lawful and desirable: this Socinus held, and the modern Unitarians do not hold. Socinus, in treating the subject in his own Institutio, an imperfect catechism which he left, lays much more stress on John xiv. 13 than on xv. 16 and xvi. 23. He is not disinclined to think that Patrem should be in the first citation, where some put it; but he says that to ask the Father in the name of the Son is nothing but praying to the Son in prayer to the Father. He labors the point with obvious wish to secure a conclusive sanction. In the Racovian Catechism, of which Faustus Socinus probably drew the first sketch, a clearer light is arrived at. The translation says: "But wherein consists the divine honor due to Christ? In adoration likewise and invocation. For we ought at all times to adore Christ, and may in our necessities address our prayers to him as often as we please; and there are many reasons to induce us to do this freely." There are some who like accuracy, even in aspersion—A. De M.

Socinus, or Fausto Paolo Sozzini (1539-1604), was an antitrinitarian who believed in prayer and homage to Christ. Leaving Italy after his views became known, he repaired to Basel, but his opinions were too extreme even for the Calvinists. He then tried Transylvania, attempting to convert to his views the antitrinitarian Bishop David. The only result of his efforts was the imprisonment of David and his own flight to Poland, in which country he spent the rest of his life (1579-1604). His complete works appeared first at Amsterdam in 1668, in the Bibliotheca Fratres Polonorum. The Racovian Catechism (1605) appeared after his death, but it seems to have been planned by him.

[303] "As much of faith as is necessary to salvation is contained in this article, Jesus is the Christ."

[304] Edwards (1637-1716) was a Cambridge fellow, strongly Calvinistic. He published many theological works, attacking the Arminians and Socinians. Locke and Whiston were special objects of attack.

[305] Sir I. Newton's views on points of Trinitarian Doctrine; his Articles of Faith, and the General Coincidence of his Opinions with those of J. Locke; a Selection of Authorities, with Observations, London, 1856.

[306] A Confession of the Faith, Bristol, 1752, 8vo.

[307] This was really very strange, because Laud (1573-1644), while he was Archbishop of Canterbury, forced a good deal of High Church ritual on the Puritan clergy, and even wished to compel the use of a prayer book in Scotland. It was this intolerance that led to his impeachment and execution.

[308] The name is Jonchere. He was a man of some merit, proposing (1718) an important canal in Burgundy, and publishing a work on the Decouverte des longitudes estimees generalement impossible a trouver, 1734 (or 1735).

[309] Locke invented a kind of an instrument for finding longitude, and it is described in the appendix, but I can find nothing about the man. There was published some years later (London, 1751) another work of his, A new Problem to discover the longitude at sea.

[310] Baxter, concerning whom I know merely that he was a schoolmaster, starts with the assumption of this value, and deduces from it some fourteen properties relating to the circle.

[311] John, who died in 1780, was a well-known character in his way. He was a bookseller on Fleet Street, and his shop was a general rendezvous for the literary men of his time. He wrote the Memoirs of the Life and Writings of Mr. William Whiston (1749, with another edition in 1753). He was one of the first to issue regular catalogues of books with prices affixed.

[312] The name appears both as Hulls and as Hull. He was born in Gloucestershire in 1699. In 1754 he published The Art of Measuring made Easy by the help of a new Sliding Scale.

[313] Thomas Newcomen (1663-1729) invented the first practical steam engine about 1710. It was of about five and a half horse power, and was used for pumping water from coal mines. Savery had described such an engine in 1702, but Newcomen improved upon it and made it practical.

[314] The well-known benefactor of art (1787-1863).

[315] The tract was again reprinted in 1860.

[316] Hulls made his experiment on the Avon, at Evesham, in 1737, having patented his machine in 1736. He had a Newcomen engine connected with six paddles. This was placed in the front of a small tow boat. The experiment was a failure.

[317] William Symington (1763-1831). In 1786 he constructed a working model of a steam road carriage. The machinery was applied to a small boat in 1788, and with such success as to be tried on a larger boat in 1789. The machinery was clumsy, however, and in 1801 he took out a new patent for the style of engine still used on paddle wheel steamers. This engine was successfully used in 1802, on the Charlotte Dundas. Fulton (1765-1815) was on board, and so impressed Robert Livingston with the idea that the latter furnished the money to build the Clermont (1807), the beginning of successful river navigation.

[318] Louis Bertrand Castel (1688-1757), most of whose life was spent in trying to perfect his Clavecin oculaire, an instrument on the order of the harpsichord, intended to produce melodies and harmonies of color. He also wrote L'Optique des couleurs (1740) and Sur le fond de la Musique (1754).

[319] Dr. Robinson (1680-1754) was professor of physic at Trinity College, Dublin, and three times president of King and Queen's College of Physicians. In his Treatise on the Animal Economy (1732-3, with a third edition in 1738) he anticipated the discoveries of Lavoisier and Priestley on the nature of oxygen.

[320] There was another edition, published at London in 1747, 8vo.

[321] The author seems to have shot his only bolt in this work. I can find nothing about him.

[322] Quod Deus sit, mundusque ab ipso creatus fuerit in tempore, ejusque providentia gubernetur. Selecta aliquot theoremata adversos atheos, etc., Paris, 1635, 4to.

[323] The British Museum Catalogue mentions a copy of 1740, but this is possibly a misprint.

[324] This was Johann II (1710-1790), son of Johann I, who succeeded his father as professor of mathematics at Basel.

[325] Samuel Koenig (1712-1757), who studied under Johann Bernoulli I. He became professor of mathematics at Franeker (1747) and professor of philosophy at the Hague (1749).

[326] "In accordance with the hypotheses laid down in this memoir it is so evident that t must = 34, y = 1, and z = 1, that there is no need of proof or authority for it to be recognized by every one."

[327] "I subscribe to the judgment of Mr. Bernoulli as a result of these hypotheses."

[328] "It clearly appears from my present analysis and demonstration that they have already recognized and perfectly agreed to the fact that the quadrature of the circle is mathematically demonstrated."

[329] Dr. Knight (died in 1772) made some worthy contributions to the literature of the mariner's compass. As De Morgan states, he was librarian of the British Museum.

[330] Sir Anthony Panizzi (1797-1879) fled from Italy under sentence of death (1822). He became assistant (1831) and chief (1856) librarian of the British Museum, and was knighted in 1869. He began the catalogue of printed books of the Museum.

[331] Wright (1711-1786) was a physicist. He was offered the professorship of mathematics at the Imperial Academy of St. Petersburg but declined to accept it. This work is devoted chiefly to the theory of the Milky Way, the via lactea as he calls it after the manner of the older writers.

[332] Troughton (1753-1835) was one of the world's greatest instrument makers. He was apprenticed to his brother John, and the two succeeded (1770) Wright and Cole in Fleet Street. Airy called his method of graduating circles the greatest improvement ever made in instrument making. He constructed (1800) the first modern transit circle, and his instruments were used in many of the chief observatories of the world.

[333] William Simms (1793-1860) was taken into partnership by Troughton (1826) after the death of the latter's brother. The firm manufactured some well-known instruments.

[334] This was George Horne (1730-1792), fellow of Magdalen College, Oxford, vice-Chancellor of the University (1776), Dean of Canterbury (1781), and Bishop of Norwich (1790). He was a great satirist, but most of his pamphlets against men like Adam Smith, Swedenborg, and Hume, were anonymous, as in the case of this one against Newton. He was so liberal in his attitude towards the Methodists that he would not have John Wesley forbidden to preach in his diocese. He was twenty-one when this tract appeared.

[335] Martin (1704-1782) was by no means "old Benjamin Martin" when Horne wrote this pamphlet in 1749. In fact he was then only forty-five. He was a physicist and a well-known writer on scientific instruments. He also wrote Philosophia Britannica or a new and comprehensive system of the Newtonian Philosophy (1759).

[336] Jean Theophile Desaguliers, or Des Aguliers (1683-1744) was the son of a Protestant who left France after the revocation of the Edict of Nantes. He became professor of physics at Oxford, and afterwards gave lectures in London. Later he became chaplain to the Prince of Wales. He published several works on physics.

[337] Charles Hutton (1737-1823), professor of mathematics at Woolwich (1772-1807). His Mathematical Tables (1785) and Mathematical and Philosophical Dictionary (1795-1796) are well known.

[338] James Epps (1773-1839) contributed a number of memoirs on the use and corrections of instruments. He was assistant secretary of the Astronomical Society.

[339] John Hutchinson (1674-1737) was one of the first to try to reconcile the new science of geology with Genesis. He denied the Newtonian hypothesis as dangerous to religion, and because it necessitated a vacuum. He was a mystic in his interpretation of the Scriptures, and created a sect that went under the name of Hutchinsonians.

[340] John Rowning, a Lincolnshire rector, died in 1771. He wrote on physics, and published a memoir on A machine for finding the roots of equations universally (1770).

[341] It is always difficult to sanction this spelling of the name of this Jesuit father who is so often mentioned in the analytic treatment of conics. He was born in Ragusa in 1711, and the original spelling was Ruder Josip Bošković. When he went to live in Italy, as professor of mathematics at Rome (1740) and at Pavia, the name was spelled Ruggiero Giuseppe Boscovich, although Boscovicci would seem to a foreigner more natural. His astronomical work was notable, and in his De maculis solaribus (1736) there is the first determination of the equator of a planet by observing the motion of spots on its surface. Boscovich came near having some contact with America, for he was delegated to observe in California the transit of Venus in 1755, being prevented by the dissolution of his order just at that time. He died in 1787, at Milan.

[342] James Granger (1723-1776) who wrote the Biographical History of England, London, 1769. His collection of prints was remarkable, numbering some fourteen thousand.

[343] He was curator of experiments for the Royal Society. He wrote a large number of books and monographs on physics. He died about 1713.

[344] Lee seems to have made no impression on biographers.

[345] This work appeared at London in 1852.

[346] Of course this is no longer true. The most scholarly work to-day is that of Rudio, Archimedes, Huygens, Lambert, Legendre, vier Abhandlungen ueber die Kreismessung ... mit einer Uebersicht ueber die Geschichte des Problems von der Quadratur des Zirkels, von den aeltesten Zeiten bis auf unsere Tage, Leipsic, 1892.

[347] Joseph Jerome le Francois de Lalande (1732-1807), professor of astronomy in the College de France (1753) and director of the Paris Observatory (1761). His writings on astronomy and his Bibliographie astronomique, avec l'histoire de l'astronomie depuis 1781 jusqu'en 1802 (Paris, 1803) are well known.

[348] De Morgan refers to his Histoire de l'Astronomie au 18e siecle, which appeared in 1827, five years after Delambre's death. Jean Baptiste Joseph Delambre (1749-1822) was a pupil of and a collaborator with Lalande, following his master as professor of astronomy in the College de France. His work on the measurements for the metric system is well known, and his four histories of astronomy, ancienne (1817), au moyen age (1819), moderne (1821), and au 18e siecle (posthumous, 1827) are highly esteemed.

[349] Jean-Joseph Rive (1730-1792), a priest who left his cure under grave charges, and a quarrelsome character. His attack on Montucla was a case of the pot calling the kettle black; for while he was a brilliant writer he was a careless bibliographer.

[350] Isaac Barrow (1630-1677) was quite as well known as a theologian as he was from his Lucasian professorship of mathematics at Cambridge.

[351] "Besides we can see by this that Barrow was a poor philosopher; for he believed in the immortality of the soul and in a Divinity other than universal nature."

[352] The Recreations mathematiques et physiques (Paris, 1694) of Jacques Ozanam (1640-1717) is a work that is still highly esteemed. Among various other works he wrote a Dictionnaire mathematique ou Idee generale des mathematiques (1690) that was not without merit. The Recreations went through numerous editions (Paris, 1694, 1696, 1741, 1750, 1770, 1778, and the Montucla edition of 1790; London, 1708, the Montucla-Hutton edition of 1803 and the Riddle edition of 1840; Dublin, 1790).

[353] Hendryk van Etten, the nom de plume of Jean Leurechon (1591-1670), rector of the Jesuit college at Bar, and professor of philosophy and mathematics. He wrote on astronomy (1619) and horology (1616), and is known for his Selecta Propositiones in tota sparsim mathematica pulcherrime propositae in solemni festo SS. Ignatii et Francesci Xaverii, 1622. The book to which De Morgan refers is his Recreation mathematicque, composee de plusieurs problemes plaisants et facetieux, Lyons, 1627, with an edition at Pont-a-Mousson, 1629. There were English editions published at London in 1633, 1653, and 1674, and Dutch editions in 1662 and 1672.

I do not understand how De Morgan happened to miss owning the work by Claude Gaspar Bachet de Meziriac (1581-1638), Problemes plaisans et delectables, which appeared at Lyons in 1612, 8vo, with a second edition in 1624. There was a fifth edition published at Paris in 1884.

[354] His title page closes with "Paris, Chez Ch. Ant. Jombert.... M DCC LIV."

This was Charles-Antoine Jombert (1712-1784), a printer and bookseller with some taste for painting and architecture. He wrote several works and edited a number of early treatises.

[355] The late Professor Newcomb made the matter plain even to the non-mathematical mind, when he said that "ten decimal places are sufficient to give the circumference of the earth to the fraction of an inch, and thirty decimal places would give the circumference of the whole visible universe to a quantity imperceptible with the most powerful microscope."

[356] Antinewtonianismi pars prima, in qua Newtoni de coloribus systema ex propriis principiis geometrice evertitur, et nova de coloribus theoria luculentissimis experimentis demonstrantur.... Naples, 1754; pars secunda, Naples, 1756.

[357] Celestino Cominale (1722-1785) was professor of medicine at the University of Naples.

[358] The work appeared in the years from 1844 to 1849.

[359] There was a Vienna edition in 1758, 4to, and another in 1759, 4to. This edition is described on the title page as Editio Veneta prima ipso auctore praesente, et corrigente.

[360] The first edition was entitled De solis ac lunae defectibus libri V. P. Rogerii Josephi Boscovich ... cum ejusdem auctoris adnotationibus, London, 1760. It also appeared in Venice in 1761, and in French translation by the Abbe de Baruel in 1779, and was a work of considerable influence.

[361] Paulian (1722-1802) was professor of physics at the Jesuit college at Avignon. He wrote several works, the most popular of which, the Dictionnaire de physique (Avignon, 1761), went through nine editions by 1789.

[362] This is correct.

[363] Probably referring to the fact that Hill (1795-1879), who had done so much for postal reform, was secretary to the postmaster general (1846), and his name was a synonym for the post office directory.

[364] Richard Lovett (1692-1780) was a good deal of a charlatan. He claimed to have studied electrical phenomena, and in 1758 advertised that he could effect marvelous cures, especially of sore throat, by means of electricity. Before publishing the works mentioned by De Morgan he had issued others of similar character, including The Subtile Medium proved (London, 1756) and The Reviewers Reviewed (London, 1760).

[365] Jean Sylvain Bailly (1736-1793), member of the Academie francaise and of the Academie des sciences, first deputy elected to represent Paris in the Etats-generaux (1789), president of the first National Assembly, and mayor of Paris (1789-1791). For his vigor as mayor in keeping the peace, and for his manly defence of the Queen, he was guillotined. He was an astronomer of ability, but is best known for his histories of the science.

[366] These were the Histoire de l'Astronomie ancienne (1775), Histoire de l'Astronomie moderne (1778-1783), Histoire de l'Astronomie indienne et orientale (1787), and Lettres sur l'origine des peuples de l'Asie (1775).

[367] "The sick old man of Ferney, V., a boy of a hundred years." Voltaire was born in 1694, and hence was eighty-three at this time.

[368] In Palmezeaux's Vie de Bailly, in Bailly's Ouvrage Posthume (1810), M. de Sales is quoted as saying that the Lettres sur l'Atlantide were sent to Voltaire and that the latter did not approve of the theory set forth.

[369] The British Museum catalogue gives two editions, 1781 and 1782.

[370] A mystic and a spiritualist. His chief work was the one mentioned here.

[371] Jacob Behmen, or Boehme (1575-1624), known as "the German theosophist," was founder of the sect of Boehmists, a cult allied to the Swedenborgians. He was given to the study of alchemy, and brought the vocabulary of the science into his mystic writings. His sect was revived in England in the eighteenth century through the efforts of William Law. Saint-Martin translated into French two of his Latin works under the titles L'Aurore naissante, ou la Racine de la philosophie (1800), and Les trois principes de l'essence divine (1802). The originals had appeared nearly two hundred years earlier,—Aurora in 1612, and De tribus principiis in 1619.