[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 isArithmeticae Libri II et Geometriae Libri VI. The work on which it is based is theArithmeticae 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 forpiae memoriae! The ratio 355/113 was known in China hundreds of years before his time. See note55, page52.[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. HugeniiΚοσμοθεωρος,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 hisHistory of the Inductive Sciences(1837) andPhilosophy 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 theDictionary of National Biography.[177]The late Greek satirist and poet, c. 120-c. 200 A.D.[178]François 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 wroteThe 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 Académie des Sciences, and member of the Académie Française. HisEntretien sur la pluralité des mondesappeared 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 theBudget. 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. HisCyclometria e lunulis reciproce demonstrataappeared 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 Collège Gervais at Paris, and later at the Collège Royal. He claimed to have discovered the theory of indivisibles before Cavalieri, and his work is set forth in hisTraité des indivisibleswhich 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. HisLeviathan(1651) is said to have influenced Spinoza, Leibnitz, and Rousseau. HisQuadratura circuli, cubatio sphaerae, duplicatio cubi ...(London, 1669),Rosetum geometricum ...(London, 1671), andLux 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 Académie 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 hisBudget 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), wroteHarmonicorum Libri XII(1636), andCogitata 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, calledFratres Polonorumbecause they took refuge in Poland. Some of his works appear in theBibliotheca 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'sGéométrie 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 titleInstitutio 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 thatmirandulaof his age, Sir Kenelm Digby (1603-1665), with the famouspoudre 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 célèbre assemblée par le chevalier Digby .... touchant la guérison 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 hisHistory 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 thebon motof Dr. Holmes: "I firmly believe that if the wholemateria medicacould 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 theEncyclopaedia Britannica.[198]This is hisAnimadversions upon Mr. Hobbes' late book De principiis et ratiocinatione geometrarum, 1666, or hisHobbianae 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 hisOpus geometricum quadraturae circuli et sectionum coniat Antwerp in 1647.[201]This appears inJ. Scaligeri cyclometrica elementa duo, Lugduni Batav., 1594.[202]Adriaen van Roomen (1561-1615) gave the value ofπto sixteen decimal places in hisIdeae mathematicae pars prima(1593), and wrote hisIn Archimedis circuli dimensionem expositio & analysisin 1597.[203]Kästner. See note30on page43.[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) wroteThe 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 hisEloges des hommes savants, tirés de l'histoire de M. de Thouin 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 Scévole 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 theHistoria et Antiquitates Universitatis Oxoniensis(1674). See note163, page98.[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 theAnimal Cornatum, or the Horn'd Beast(1654) andThe Nativity of the late King Charls(1659).[223]Isaac D'Israeli (1766-1848), in hisCuriosities 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. HisMerlini 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 entitledMercurio-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 note171on page100.[226]This is theArs 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 note200on page110.[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 ofaandbto the basee. E.g., in the case of the hyperbolaxy= 1, the area betweenx=aandx= 1 is loga.[229]"On ne peut lui refuser la justice de remarquer que personne avant lui ne s'est porté dans cette recherche avec autant de génie, & même, si nous en exceptons son objet principal, avec autant de succès."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.... René Francois, Baron de Sluse (1622-1685) was canon and chancellor of Liège, and a member of the Royal Society. He also published a work on tangents (1672). The wordmesolabiumis from the Greekμεσολάβιονorμεσόλαβον, 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 hisOptica 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 hisVera quadraturais his use of an infinite converging series, a plan that Archimedes used with the parabola.[232]Jean de Beaulieu wrote several works on mathematics, includingLa lumière de l'arithmétique(n.d.),La lumière des mathématiques(1673),Nouvelle invention d'arithmétique(1677), and some mathematical tables.[233]A just estimate. There were several works published by Gérard Desargues (1593-1661), of which the greatest was theBrouillon Proiect(Paris, 1639). There is an excellent edition of theŒuvres de Desarguesby 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 forπ. One of the latest pretended geometric proofs resulting in this value appeared in New York in 1910, entitledQuadrimetry(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 meansplusin commerce andpikemenin the army; M meansminus, andmusketeerin the art of war;... R signifiesrootin the measurement of a cube, andrankinthe army; Q meanssquare(Frenchquarè, as then spelled) in both cases; C meanscubein mensuration, andcavalryin arranging batallions and squadrons. As for the operations of this science, they are as follows: to add aplusand aplus, the sum will beplus; to addminuswithplus, 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 theJoannis 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 isVegetable 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'sPrincipiaprinted.[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. HisCurrus triumphalis antimoniiappeared 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 theChariot.[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 isThe Secret of the Immortal Liquor Alkahest or Ignis-Aqua. See note260,infra.[255]Johann Baptist van Helmont, Herr von Merode, Royenborg etc. (1577-1644). His chemical discoveries appeared in hisOrtus medicinae(1648), which went through many editions.[256]De Morgan should have written up Francis Anthony (1550-1623), whosePanacea 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),Traité 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. HisLiber de mercuris philosophicoand other tracts first appeared inOpuscula quaedam chymica(Frankfort, 1614).[259]Besides theOpus majus, and other of the better known works of this celebrated Franciscan (1214-1294), there are numerous tracts on alchemy that appeared in theThesaurus 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 note254above) 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 theLiquor 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 entitledDelights 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 inThe 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, Père Claude François 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 wasA 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, theCompendium 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 ofπ.[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 theMethodus Figurarum ... Quadraturas determinandi(1685),Tractatus ... de Figurarum Curvilinearum Quadraturis et locis Geometricis(1693), andDe 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 memoirOn the Curve of the quickest descent(1700),On the Solid of least resistance(1700), and theSolution 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 hisCatalogue of the Royal and Noble Authors of Englandin 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. HisTreatise on Fluxions(London, 1704) was the first work in English to explain Newton's calculus. He wrote a work entitledThe Moon(1723) to prove that our satellite shines by its own as well as by reflected light. HisChronographia Asiatica & Aegyptica(1758) gives the results of his travels.[275]Publickin 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 onPrimitive Christianityappeared 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 whoseSynopsis Palmariorum Matheseos(1706) the symbolπis first used for the circle ratio.[282]This was theGeometrica solidorum, sive materiae, seu de varia compositione, progressione, rationeque velocitatum, Cambridge, 1712. The work was parodied inA 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 Académie, 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 proposof Mrs. Conduitt's life of her illustrious uncle, Sir George Greenhill tells a very good story on Poincaré, 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. Poincaré looked blank and said, "Newton, et la nièce 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 theCollections 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 theIsaaci 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 wroteAn historical Essay on first publication of Sir Isaac Newton's Principia, Oxford, 1838, and a two-volume work entitledCorrespondence 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 theCorrespondence 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 thePhilosophical Works of Francis Baconappeared 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 theSacred Classics) and one in 1836 (vol. 2 of theChristian Library).[302]I use the wordSocinianbecause 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 forallUnitarians. I suspect they have a kind of liking for theword; it sounds likeso 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 ownInstitutio, 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 thatPatremshould 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 Dávid. The only result of his efforts was the imprisonment of Dávid 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 theBibliotheca Fratres Polonorum. TheRacovian 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 Jonchère. He was a man of some merit, proposing (1718) an important canal in Burgundy, and publishing a work on theDécouverte des longitudes estimées généralement impossible à 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 theMemoirs 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 publishedThe 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 heconstructeda 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 hisClavecin oculaire, an instrument on the order of the harpsichord, intended to produce melodies and harmonies of color. He also wroteL'Optique des couleurs(1740) andSur 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 hisTreatise 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 thattmust = 34,y= 1, andz= 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, thevia lacteaas 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 wrotePhilosophia Britannica or a new and comprehensive system of the Newtonian Philosophy(1759).[336]Jean Théophile 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.
[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 isArithmeticae Libri II et Geometriae Libri VI. The work on which it is based is theArithmeticae 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 forpiae memoriae! The ratio 355/113 was known in China hundreds of years before his time. See note55, page52.
[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. HugeniiΚοσμοθεωρος,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 hisHistory of the Inductive Sciences(1837) andPhilosophy 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 theDictionary of National Biography.
[177]The late Greek satirist and poet, c. 120-c. 200 A.D.
[178]François 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 wroteThe 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 Académie des Sciences, and member of the Académie Française. HisEntretien sur la pluralité des mondesappeared 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 theBudget. 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. HisCyclometria e lunulis reciproce demonstrataappeared 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 Collège Gervais at Paris, and later at the Collège Royal. He claimed to have discovered the theory of indivisibles before Cavalieri, and his work is set forth in hisTraité des indivisibleswhich 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. HisLeviathan(1651) is said to have influenced Spinoza, Leibnitz, and Rousseau. HisQuadratura circuli, cubatio sphaerae, duplicatio cubi ...(London, 1669),Rosetum geometricum ...(London, 1671), andLux 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 Académie 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 hisBudget 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), wroteHarmonicorum Libri XII(1636), andCogitata 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, calledFratres Polonorumbecause they took refuge in Poland. Some of his works appear in theBibliotheca 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'sGéométrie 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 titleInstitutio 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 thatmirandulaof his age, Sir Kenelm Digby (1603-1665), with the famouspoudre 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 célèbre assemblée par le chevalier Digby .... touchant la guérison 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 hisHistory 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 thebon motof Dr. Holmes: "I firmly believe that if the wholemateria medicacould 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 theEncyclopaedia Britannica.
[198]This is hisAnimadversions upon Mr. Hobbes' late book De principiis et ratiocinatione geometrarum, 1666, or hisHobbianae 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 hisOpus geometricum quadraturae circuli et sectionum coniat Antwerp in 1647.
[201]This appears inJ. Scaligeri cyclometrica elementa duo, Lugduni Batav., 1594.
[202]Adriaen van Roomen (1561-1615) gave the value ofπto sixteen decimal places in hisIdeae mathematicae pars prima(1593), and wrote hisIn Archimedis circuli dimensionem expositio & analysisin 1597.
[203]Kästner. See note30on page43.
[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) wroteThe 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 hisEloges des hommes savants, tirés de l'histoire de M. de Thouin 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 Scévole 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 theHistoria et Antiquitates Universitatis Oxoniensis(1674). See note163, page98.
[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 theAnimal Cornatum, or the Horn'd Beast(1654) andThe Nativity of the late King Charls(1659).
[223]Isaac D'Israeli (1766-1848), in hisCuriosities 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. HisMerlini 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 entitledMercurio-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 note171on page100.
[226]This is theArs 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 note200on page110.
[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 ofaandbto the basee. E.g., in the case of the hyperbolaxy= 1, the area betweenx=aandx= 1 is loga.
[229]"On ne peut lui refuser la justice de remarquer que personne avant lui ne s'est porté dans cette recherche avec autant de génie, & même, si nous en exceptons son objet principal, avec autant de succès."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.... René Francois, Baron de Sluse (1622-1685) was canon and chancellor of Liège, and a member of the Royal Society. He also published a work on tangents (1672). The wordmesolabiumis from the Greekμεσολάβιονorμεσόλαβον, 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 hisOptica 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 hisVera quadraturais his use of an infinite converging series, a plan that Archimedes used with the parabola.
[232]Jean de Beaulieu wrote several works on mathematics, includingLa lumière de l'arithmétique(n.d.),La lumière des mathématiques(1673),Nouvelle invention d'arithmétique(1677), and some mathematical tables.
[233]A just estimate. There were several works published by Gérard Desargues (1593-1661), of which the greatest was theBrouillon Proiect(Paris, 1639). There is an excellent edition of theŒuvres de Desarguesby 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 forπ. One of the latest pretended geometric proofs resulting in this value appeared in New York in 1910, entitledQuadrimetry(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 meansplusin commerce andpikemenin the army; M meansminus, andmusketeerin the art of war;... R signifiesrootin the measurement of a cube, andrankinthe army; Q meanssquare(Frenchquarè, as then spelled) in both cases; C meanscubein mensuration, andcavalryin arranging batallions and squadrons. As for the operations of this science, they are as follows: to add aplusand aplus, the sum will beplus; to addminuswithplus, 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 theJoannis 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 isVegetable 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'sPrincipiaprinted.
[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. HisCurrus triumphalis antimoniiappeared 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 theChariot.
[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 isThe Secret of the Immortal Liquor Alkahest or Ignis-Aqua. See note260,infra.
[255]Johann Baptist van Helmont, Herr von Merode, Royenborg etc. (1577-1644). His chemical discoveries appeared in hisOrtus medicinae(1648), which went through many editions.
[256]De Morgan should have written up Francis Anthony (1550-1623), whosePanacea 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),Traité 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. HisLiber de mercuris philosophicoand other tracts first appeared inOpuscula quaedam chymica(Frankfort, 1614).
[259]Besides theOpus majus, and other of the better known works of this celebrated Franciscan (1214-1294), there are numerous tracts on alchemy that appeared in theThesaurus 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 note254above) 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 theLiquor 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 entitledDelights 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 inThe 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, Père Claude François 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 wasA 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, theCompendium 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 ofπ.
[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 theMethodus Figurarum ... Quadraturas determinandi(1685),Tractatus ... de Figurarum Curvilinearum Quadraturis et locis Geometricis(1693), andDe 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 memoirOn the Curve of the quickest descent(1700),On the Solid of least resistance(1700), and theSolution 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 hisCatalogue of the Royal and Noble Authors of Englandin 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. HisTreatise on Fluxions(London, 1704) was the first work in English to explain Newton's calculus. He wrote a work entitledThe Moon(1723) to prove that our satellite shines by its own as well as by reflected light. HisChronographia Asiatica & Aegyptica(1758) gives the results of his travels.
[275]Publickin 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 onPrimitive Christianityappeared 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 whoseSynopsis Palmariorum Matheseos(1706) the symbolπis first used for the circle ratio.
[282]This was theGeometrica solidorum, sive materiae, seu de varia compositione, progressione, rationeque velocitatum, Cambridge, 1712. The work was parodied inA 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 Académie, 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 proposof Mrs. Conduitt's life of her illustrious uncle, Sir George Greenhill tells a very good story on Poincaré, 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. Poincaré looked blank and said, "Newton, et la nièce 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 theCollections 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 theIsaaci 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 wroteAn historical Essay on first publication of Sir Isaac Newton's Principia, Oxford, 1838, and a two-volume work entitledCorrespondence 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 theCorrespondence 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 thePhilosophical Works of Francis Baconappeared 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 theSacred Classics) and one in 1836 (vol. 2 of theChristian Library).
[302]I use the wordSocinianbecause 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 forallUnitarians. I suspect they have a kind of liking for theword; it sounds likeso 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 ownInstitutio, 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 thatPatremshould 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 Dávid. The only result of his efforts was the imprisonment of Dávid 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 theBibliotheca Fratres Polonorum. TheRacovian 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 Jonchère. He was a man of some merit, proposing (1718) an important canal in Burgundy, and publishing a work on theDécouverte des longitudes estimées généralement impossible à 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 theMemoirs 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 publishedThe 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 heconstructeda 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 hisClavecin oculaire, an instrument on the order of the harpsichord, intended to produce melodies and harmonies of color. He also wroteL'Optique des couleurs(1740) andSur 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 hisTreatise 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 thattmust = 34,y= 1, andz= 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, thevia lacteaas 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 wrotePhilosophia Britannica or a new and comprehensive system of the Newtonian Philosophy(1759).
[336]Jean Théophile 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.