Chapter XIV: Part 14

[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).