A Budget of Paradoxes Volume I Part 39

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 t.i.tle 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 ent.i.tled: _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 ent.i.tled: _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 G.o.dwin (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 Ca.s.sandra 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 t.i.tle. 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 ma.n.u.scripts 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] Christia.n.u.s Longomonta.n.u.s (Christen Longberg or Lumborg) was born in 1569 at Longberg, Jutland, and died in 1647 at Copenhagen. He was an a.s.sistant 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 n.o.blemen, 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 geometric.u.m ..._ (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 ma.n.u.scripts on mathematics, which his widow promptly disposed of for waste paper. If De Morgan's ma.n.u.scripts 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 Ta.s.se (Ta.s.sius) 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 f.a.gnano 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 friends.h.i.+p 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.

Ga.s.sendi (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 t.i.tle _Inst.i.tutio 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 t.i.tle: _Discours fait en une celebre a.s.semblee 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 t.i.tle 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 s.e.x 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 geometric.u.m quadraturae circuli et sectionum coni_ at Antwerp in 1647.