Notes

[1] See Mrs. De Morgan's _Memoir of Augustus De Morgan_, London, 1882, p

61.

[2] In the first edition this reference was to page 11.

[3] In the first edition this read "at page 438," the work then appearing

in a single volume.

[4] "Just as it would surely have been better not to have considered it

(i.e., the trinity) as a mystery, and with Cl. Kleckermann to have

investigated by the aid of philosophy according to the teaching of true

logic what it might be, before they determined what it was; just so would

it have been better to withdraw zealously and industriously into the

deepest caverns and darkest recesses of metaphysical speculations and

suppositions in order to establish their opinion beyond danger from the

weapons of their adversaries.... Indeed that great man so explains and

demonstrates this dogma (although to theologians the word has not much

charm) from the immovable foundations of philosophy, that with but few

changes and additions a mind sincerely devoted to truth can desire nothing

more."

[5] Mrs. Wititterly, in _Nicholas Nickleby_.--A. De M.

[6] The brackets mean that the paragraph is substantially from some one of

the _Athenaeum Supplements_.--S. E. De M.

[7] "It is annoying that this ingenious naturalist who has already given us

more useful works and has still others in preparation, uses for this odious

task, a pen dipped in gall and wormwood. It is true that many of his

remarks have some foundation, and that to each error that he points out he

at the same time adds its correction. But he is not always just and never

fails to insult. After all, what does his book prove except that a

forty-fifth part of a very useful review is not free from mistakes? Must we

confuse him with those superficial writers whose liberty of body does not

permit them to restrain their fruitfulness, that crowd of savants of the

highest rank whose writings have adorned and still adorn the

_Transactions_? Has he forgotten that the names of the Boyles, Newtons,

Halleys, De Moivres, Hans Sloanes, etc. have been seen frequently? and that

still are found those of the Wards, Bradleys, Grahams, Ellicots, Watsons,

and of an author whom Mr. Hill prefers to all others, I mean Mr. Hill

himself?"

[8] "Let no free man be seized or imprisoned or in any way harmed except by

trial of his peers."

[9] "The master can rob, wreck and punish his slave according to his

pleasure save only that he may not maim him."

[10] An Irish antiquary informs me that Virgil is mentioned in annals at

A.D. 784, as "Verghil, i.e., the geometer, Abbot of Achadhbo [and Bishop of

Saltzburg] died in Germany in the thirteenth year of his bishoprick." No

allusion is made to his opinions; but it seems he was, by tradition, a

mathematician. The Abbot of Aghabo (Queen's County) was canonized by

Gregory IX, in 1233. The story of the second, or scapegoat, Virgil would be

much damaged by the character given to the real bishop, if there were

anything in it to dilapidate.--A. De M.

[11] "He performed many acts befitting the Papal dignity, and likewise many

excellent (to be sure!) works."

[12] "After having been on the throne during ten years of pestilence."

[13] The work is the _Questiones Joannis Buridani super X libros

Aristotelis ad Nicomachum, curante Egidio Delfo_ ... Parisiis, 1489, folio.

It also appeared at Paris in editions of 1499, 1513, and 1518, and at

Oxford in 1637.

[14] Jean Buridan was born at Bethune about 1298, and died at Paris about

1358. He was professor of philosophy at the University of Paris and several

times held the office of Rector. As a philosopher he was classed among the

nominalists.

[15] So in the original.

[16] Baruch Spinoza, or Benedict de Spinoza as he later called himself, the

pantheistic philosopher, excommunicated from the Jewish faith for heresy,

was born at Amsterdam in 1632 and died there in 1677.

[17] Michael Scott, or Scot, was born about 1190, probably in Fifeshire,

Scotland, and died about 1291. He was one of the best known savants of the

court of Emperor Frederick II, and wrote upon astrology, alchemy, and the

occult sciences. He was looked upon as a great magician and is mentioned

among the wizards in Dante's _Inferno_.

"That other, round the loins

So slender of his shape, was Michael Scot,

Practised in every slight of magic wile." _Inferno_, XX.

Boccaccio also speaks of him: "It is not long since there was in this city

(Florence) a great master in necromancy, who was called Michele Scotto,

because he was a Scot." _Decameron_, Dec. Giorno.

Scott's mention of him in Canto Second of his _Lay of the Last Minstrel_,

is well known:

"In these fair climes, it was my lot

To meet the wondrous Michael Scott;

A wizard of such dreaded fame,

That when, in Salamanca's cave,

Him listed his magic wand to wave,

The bells would ring in Notre Dame!"

Sir Walter's notes upon him are of interest.

[18] These were some of the forgeries which Michel Chasles (1793-1880) was

duped into buying. They purported to be a correspondence between Pascal and

Newton and to show that the former had anticipated some of the discoveries

of the great English physicist and mathematician. That they were forgeries

was shown by Sir David Brewster in 1855.

[19] "Let the serpent also break from its appointed path."

[20] Guglielmo Brutus Icilius Timoleon Libri-Carucci della Sommaja, born at

Florence in 1803; died at Fiesole in 1869. His _Histoire des Sciences

Mathematiques_ appeared at Paris in 1838, the entire first edition of

volume I, save some half dozen that he had carried home, being burned on

the day that the printing was completed. He was a great collector of early

printed works on mathematics, and was accused of having stolen large

numbers of them from other libraries. This accusation took him to London,

where he bitterly attacked his accusers. There were two auction sales of

his library, and a number of his books found their way into De Morgan's

collection.

[21] Philo of Gadara lived in the second century B.C. He was a pupil of

Sporus, who worked on the problem of the two mean proportionals.

[22] In his _Histoire des Mathematiques_, the first edition of which

appeared in 1758. Jean Etienne Montucla was born at Lyons in 1725 and died

at Versailles in 1799. He was therefore only thirty-three years old when

his great work appeared. The second edition, with additions by D'Alembert,

appeared in 1799-1802. He also wrote a work on the quadrature of the

circle, _Histoire des recherches sur la Quadrature du Cercle_, which

appeared in 1754.

[23] Eutocius of Ascalon was born in 480 A.D. He wrote commentaries on the

first four books of the conics of Apollonius of Perga (247-222 B.C.). He

also wrote on the Sphere and Cylinder and the Quadrature of the Circle, and

on the two books on Equilibrium of Archimedes (287-212 B.C.)

[24] Edward Cocker was born in 1631 and died between 1671 and 1677. His

famous arithmetic appeared in 1677 and went through many editions. It was

written in a style that appealed to teachers, and was so popular that the

expression "According to Cocker" became a household phrase. Early in the

nineteenth century there was a similar saying in America, "According to

Daboll," whose arithmetic had some points of analogy to that of Cocker.

Each had a well-known prototype in the ancient saying, "He reckons like

Nicomachus of Gerasa."

[25] So in the original, for Barreme. Francois Barreme was to France what

Cocker was to England. He was born at Lyons in 1640, and died at Paris in

1703. He published several arithmetics, dedicating them to his patron,

Colbert. One of the best known of his works is _L'arithmetique, ou le livre

facile pour apprendre l'arithmetique soi-meme_, 1677. The French word

_bareme_ or _barreme_, a ready-reckoner, is derived from his name.

[26] Born at Rome, about 480 A.D.; died at Pavia, 524. Gibbon speaks of him

as "the last of the Romans whom Cato or Tully could have acknowledged for

their countryman." His works on arithmetic, music, and geometry were

classics in the medieval schools.

[27] Johannes Campanus, of Novarra, was chaplain to Pope Urban IV

(1261-1264). He was one of the early medieval translators of Euclid from

the Arabic into Latin, and the first printed edition of the _Elements_

(Venice, 1482) was from his translation. In this work he probably depended

not a little upon at least two or three earlier scholars. He also wrote _De

computo ecclesiastico Calendarium_, and _De quadratura circuli_.

[28] Archimedes gave 3-1/7, and 3-10/71 as the limits of the ratio of the

circumference to the diameter of a circle.

[29] Friedrich W. A. Murhard was born at Cassel in 1779 and died there in

1853. His _Bibliotheca Mathematica_, Leipsic, 1797-1805, is ill arranged

and inaccurate, but it is still a helpful bibliography. De Morgan speaks

somewhere of his indebtedness to it.

[30] Abraham Gotthelf Kaestner was born at Leipsic in 1719, and died at

Goettingen in 1800. He was professor of mathematics and physics at

Goettingen. His _Geschichte der Mathematik_ (1796-1800) was a work of

considerable merit. In the text of the _Budget of Paradoxes_ the name

appears throughout as Kastner instead of Kaestner.

[31] Lucas Gauricus, or Luca Gaurico, born at Giffoni, near Naples, in

1476; died at Rome in 1558. He was an astrologer and mathematician, and was

professor of mathematics at Ferrara in 1531. In 1545 he became bishop of

Civita Ducale.

[32] John Couch Adams was born at Lidcot, Cornwall, in 1819, and died in

1892. He and Leverrier predicted the discovery of Neptune from the

perturbations in Uranus.

[33] Urbain-Jean-Joseph Leverrier was born at Saint-Lo, Manche, in 1811,

and died at Paris in 1877. It was his data respecting the perturbations of

Uranus that were used by Adams and himself in locating Neptune.

[34] Joseph-Juste Scaliger, the celebrated philologist, was born at Agen in

1540, and died at Leyden in 1609. His _Cyclometrica elementa_, to which De

Morgan refers, appeared at Leyden in 1594.

[35] The title is: _In hoc libra contenta.... Introductio i

geometri[=a].... Liber de quadratura circuli. Liber de cubicatione sphere.

Perspectiva introductio_. Carolus Bovillus, or Charles Bouvelles (Boueelles,

Bouilles, Bouvel), was born at Saucourt, Picardy, about 1470, and died at

Noyon about 1533. He was canon and professor of theology at Noyon. His

_Introductio_ contains considerable work on star polygons, a favorite study

in the Middle Ages and early Renaissance. His work _Que hoc volumine

contin[=e]tur. Liber de intellectu. Liber de sensu_, etc., appeared at

Paris in 1509-10.

[36] Nicolaus Cusanus, Nicolaus Chrypffs or Krebs, was born at Kues on the

Mosel in 1401, and died at Todi, Umbria, August 11, 1464. He held positions

of honor in the church, including the bishopric of Brescia. He was made a

cardinal in 1448. He wrote several works on mathematics, his _Opuscula

varia_ appearing about 1490, probably at Strasburg, but published without

date or place. His _Opera_ appeared at Paris in 1511 and again in 1514, and

at Basel in 1565.

[37] Henry Stephens (born at Paris about 1528, died at Lyons in 1598) was

one of the most successful printers of his day. He was known as

_Typographus Parisiensis_, and to his press we owe some of the best works

of the period.

[38] Jacobus Faber Stapulensis (Jacques le Fevre d'Estaples) was born at

Estaples, near Amiens, in 1455, and died at Nerac in 1536. He was a priest,

vicar of the bishop of Meaux, lecturer on philosophy at the College Lemoine

in Paris, and tutor to Charles, son of Francois I. He wrote on philosophy,

theology, and mathematics.

[39] Claude-Francois Milliet de Challes was born at Chambery in 1621, and

died at Turin in 1678. He edited _Euclidis Elementorum libri octo_ in 1660,

and published a _Cursus seu mundus mathematicus_, which included a short

history of mathematics, in 1674. He also wrote on mathematical geography.

[40] This date should be 1503, if he refers to the first edition. It is

well known that this is the first encyclopedia worthy the name to appear in

print. It was written by Gregorius Reisch (born at Balingen, and died at

Freiburg in 1487), prior of the cloister at Freiburg and confessor to

Maximilian I. The first edition appeared at Freiburg in 1503, and it passed

through many editions in the sixteenth and seventeenth centuries. The title

of the 1504 edition reads: _Aepitoma omnis phylosophiae. alias Margarita

phylosophica tractans de omni genere scibili: Cum additionibus: Quae in

alijs non habentur_.

[41] This is the _Introductio in arithmeticam Divi S. Boetii.... Epitome

rerum geometricarum ex geometrica introductio C. Bovilli. De quadratura

circuli demonstratio ex Campano_, that appeared without date about 1507.

[42] Born at Liverpool in 1805, and died there about 1872. He was a

merchant, and in 1865 he published, at Liverpool, a work entitled _The

Quadrature of the Circle, or the True Ratio between the Diameter and

Circumference geometrically and mathematically demonstrated_. In this he

gives the ratio as exactly 3-1/8.

[43] "That it would be impossible to tell him exactly, since no one had yet

been able to find precisely the ratio of the circumference to the

diameter."

[44] This is the Paris edition: "Parisiis: ex officina Ascensiana anno

Christi ... MDXIIII," as appears by the colophon of the second volume to

which De Morgan refers.

[45] Regiomontanus, or Johann Mueller of Koenigsberg (Regiomontanus), was

born at Koenigsberg in Franconia, June 5, 1436, and died at Rome July 6,

1476. He studied at Vienna under the great astronomer Peuerbach, and was

his most famous pupil. He wrote numerous works, chiefly on astronomy. He is

also known by the names Ioannes de Monte Regio, de Regiomonte, Ioannes

Germanus de Regiomonte, etc.

[46] Henry Cornelius Agrippa was born at Cologne in 1486 and died either at

Lyons in 1534 or at Grenoble in 1535. He was professor of theology at

Cologne and also at Turin. After the publication of his _De Occulta

Philosophia_ he was imprisoned for sorcery. Both works appeared at Antwerp

in 1530, and each passed through a large number of editions. A French

translation appeared in Paris in 1582, and an English one in London in

1651.

[47] Nicolaus Remegius was born in Lorraine in 1554, and died at Nancy in

1600. He was a jurist and historian, and held the office of procurator

general to the Duke of Lorraine.

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

From his having been born in India, all this appealed strongly to the

interests of De Morgan.

[49] Orontius Finaeus, or Oronce Fine, was born at Briancon in 1494 and

died at Paris, October 6, 1555. He was imprisoned by Francois I for

refusing to recognize the concordat (1517). He was made professor of

mathematics in the College Royal (later called the College de France) in

1532. He wrote extensively on astronomy and geometry, but was by no means a

great scholar. He was a pretentious man, and his works went through several

editions. His _Protomathesis_ appeared at Paris in 1530-32. The work

referred to by De Morgan is the _Quadratura circuli tandem inventa &

clarissime demonstrata_ ... Lutetiae Parisiorum, 1544, fol. In the 1556

edition of his _De rebus mathematicis, hactenus desideratis, Libri IIII_,

published at Paris, the subtitle is: _Quibus inter caetera, Circuli

quadratura Centum modis, & supra, per eundem Orontium recenter excogitatis,

demonstratus_, so that he kept up his efforts until his death.

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

1485-1489, and died in a cloister in 1560 or 1564. Some writers give

Charpey as the place and 1492 as the date of his birth, and state that he

died at Canar in 1572. He belonged to the order of St. Anthony, and wrote

chiefly on geometry, exposing the pretenses of Finaeus. His _Opera

geometrica_ appeared at Lyons in 1554, and his _Logistica_ and _De

quadratura circuli libri duo_ at Lyons in 1559.

[51] This is the great French algebraist, Francois Viete (Vieta), who was

born at Fontenay-le-Comte in 1540, and died at Paris, December 13, 1603.

His well-known _Isagoge in artem analyticam_ appeared at Tours in 1591. His

_Opera mathematica_ was edited by Van Schooten in 1646.

[52] This is the _De Rebus mathematicis hactenus desideratis, Libri IIII_,

that appeared in Paris in 1556. For the title page see Smith, D. E., _Rara

Arithmetica_, Boston, 1908, p. 280.

[53] The title is correct except for a colon after _Astronomicum_. Nicolaus

Raimarus Ursus was born in Henstede or Hattstede, in Dithmarschen, and died

at Prague in 1599 or 1600. He was a pupil of Tycho Brahe. He also wrote _De

astronomis hypothesibus_ (1597) and _Arithmetica analytica vulgo Cosa oder

Algebra_ (1601).

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

The work to which reference is made is the _Quadrature du cercle, ou

maniere de trouver un quarre egal au cercle donne_, which appeared at Delft

in 1584. Duchesne had the courage of his convictions, not only on

circle-squaring but on religion as well, for he was obliged to leave France

because of his conversion to Calvinism. De Morgan's statement that his real

name is Van der Eycke is curious, since he was French born. The Dutch may

have translated his name when he became professor at Delft, but we might

equally well say, that his real name was Quercetanus or a Quercu.

[55] This was the father of Adriaan Metius (1571-1635). He was a

mathematician and military engineer, and suggested the ratio 355/113 for

[pi], a ratio afterwards published by his son. The ratio, then new to

Europe, had long been known and used in China, having been found by Tsu

Ch'ung-chih (428-499 A.D.).

[56] This was Jost Buergi, or Justus Byrgius, the Swiss mathematician of

whom Kepler wrote in 1627: "Apices logistici Justo Byrgio multis annis ante

editionem Neperianam viam praeiverunt ad hos ipsissimos logarithmos." He

constructed a table of antilogarithms (_Arithmetische und geometrische

Progress-Tabulen_), but it was not published until after Napier's work

appeared.

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

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

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

[59] I do not know this edition. There was one "Antverpiae apud Petrum

Bellerum sub scuto Burgundiae," 4to, in 1591.

[60] Archytas of Tarentum (430-365 B.C.) who wrote on proportions,

irrationals, and the duplication of the cube.

[61]

_The Circle Speaks._

"At first a circle I was called,

And was a curve around about

Like lofty orbit of the sun

Or rainbow arch among the clouds.

A noble figure then was I--

And lacking nothing but a start,

And lacking nothing but an end.

But now unlovely do I seem

Polluted by some angles new.

This thing Archytas hath not done

Nor noble sire of Icarus

Nor son of thine, Iapetus.

What accident or god can then

Have quadrated mine area?"

_The Author Replies._

"By deepest mouth of Turia

And lake of limpid clearness, lies

A happy state not far removed

From old Saguntus; farther yet

A little way from Sucro town.

In this place doth a poet dwell,

Who oft the stars will closely scan,

And always for himself doth claim

What is denied to wiser men;--

An old man musing here and there

And oft forgetful of himself,

Not knowing how to rightly place

The compasses, nor draw a line,

As he doth of himself relate.

This craftsman fine, in sooth it is

Hath quadrated thine area."

[62] Pietro Bongo, or Petrus Bungus, was born at Bergamo, and died there in

1601. His work on the Mystery of Numbers is one of the most exhaustive and

erudite ones of the mystic writers. The first edition appeared at Bergamo

in 1583-84; the second, at Bergamo in 1584-85; the third, at Venice in

1585; the fourth, at Bergamo in 1590; and the fifth, which De Morgan calls

the second, in 1591. Other editions, before the Paris edition to which he

refers, appeared in 1599 and 1614; and the colophon of the Paris edition is

dated 1617. See the editor's _Rara Arithmetica_, pp. 380-383.

[63] William Warburton (1698-1779), Bishop of Gloucester, whose works got

him into numerous literary quarrels, being the subject of frequent satire.

[64] Thomas Galloway (1796-1851), who was professor of mathematics at

Sandhurst for a time, and was later the actuary of the Amicable Life

Assurance Company of London. In the latter capacity he naturally came to be

associated with De Morgan.

[65] Giordano Bruno was born near Naples about 1550. He left the Dominican

order to take up Calvinism, and among his publications was _L'expulsion de

la bete triomphante_. He taught philosophy at Paris and Wittenberg, and

some of his works were published in England in 1583-86. Whether or not he

was roasted alive "for the maintenance and defence of the holy Church," as

De Morgan states, depends upon one's religious point of view. At any rate,

he was roasted as a heretic.

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

[67] Bartholomew Legate, who was born in Essex about 1575. He denied the

divinity of Christ and was the last heretic burned at Smithfield.

[68] Edward Wightman, born probably in Staffordshire. He was

anti-Trinitarian, and claimed to be the Messiah. He was the last man burned

for heresy in England.

[69] Gaspar Schopp, born at Neumarck in 1576, died at Padua in 1649;

grammarian, philologist, and satirist.

[70] Konrad Ritterhusius, born at Brunswick in 1560; died at Altdorf in

1613. He was a jurist of some power.

[71] Johann Jakob Brucker, born at Augsburg in 1696, died there in 1770. He

wrote on the history of philosophy (1731-36, and 1742-44).

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

He was rector of the University of Kiel, and professor of eloquence,

poetry, and history.

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

416-435 of the 1841 edition.

[74] Colenso (1814-1883), missionary bishop of Natal, was one of the

leaders of his day in the field of higher biblical criticism. De Morgan

must have admired his mathematical works, which were not without merit.

[75] Samuel Roffey Maitland, born at London in 1792; died at Gloucester in

1866. He was an excellent linguist and a critical student of the Bible. He

became librarian at Lambeth in 1838.

[76] Archbishop Howley (1766-1848) was a thorough Tory. He was one of the

opponents of the Roman Catholic Relief bill, the Reform bill, and the

Jewish Civil Disabilities Relief bill.

[77] We have, in America at least, almost forgotten the great stir made by

Edward B. Pusey (1800-1882) in the great Oxford movement in the middle of

the nineteenth century. He was professor of Hebrew at Oxford, and canon of

Christ Church.

[78] That is, his _Magia universalis naturae et artis sive recondita

naturalium et artificialium rerum scientia_, Wuerzburg, 1657, 4to, with

editions at Bamberg in 1671, and at Frankfort in 1677. Gaspard Schott

(Koenigshofen 1608, Wuerzburg 1666) was a physicist and mathematician,

devoting most of his attention to the curiosities of his sciences. His type

of mind must have appealed to De Morgan.

[79] _Salicetti Quadratura circuli nova, perspicua, expedita, veraque tum

naturalis, tum geometrica_, etc., 1608.--_Consideratio nova in opusculum

Archimedis de circuli dimensione_, etc., 1609.

[80] Melchior Adam, who died at Heidelberg in 1622, wrote a collection of

biographies which was published at Heidelberg and Frankfort from 1615 to

1620.

[81] Born at Baden in 1524; died at Basel in 1583. The Erastians were

related to the Zwinglians, and opposed all power of excommunication and the

infliction of penalties by a church.

[82] See Acts xii. 20.

[83] Theodore de Bese, a French theologian; born at Vezelay, in Burgundy,

in 1519; died at Geneva, in 1605.

[84] Dr. Robert Lee (1804-1868) had some celebrity in De Morgan's time

through his attempt to introduce music and written prayers into the service

of the Scotch Presbyterian church.

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

[86] Born at Kinnairdie, Bannfshire, in 1661; died at London in 1708. His

_Astronomiae Physicae et Geometriae Elementa_, Oxford, 1702, was an

influential work.

[87] The title was carelessly copied by De Morgan, not an unusual thing in

his case. The original reads: A Plaine Discovery, of the whole Revelation

of S. Iohn: set downe in two treatises ... set foorth by John Napier L. of

Marchiston ... whereunto are annexed, certaine Oracles of Sibylla ...

London ... 1611.

[88] I have not seen the first edition, but it seems to have appeared in

Edinburgh, in 1593, with a second edition there in 1594. The 1611 edition

was the third.

[89] It seems rather certain that Napier felt his theological work of

greater importance than that in logarithms. He was born at Merchiston, near

(now a part of) Edinburgh, in 1550, and died there in 1617, three years

after the appearance of his _Mirifici logarithmorum canonis descriptio_.

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

[91] There was an edition published at Stettin in 1633. An English

translation by P. F. Mottelay appeared at London in 1893. Gilbert

(1540-1603) was physician to Queen Elizabeth and President of the College

of Physicians at London. His _De Magnete_ was the first noteworthy treatise

on physics printed in England. He treated of the earth as a spherical

magnet and suggested the variation and declination of the needle as a means

of finding latitude at sea.

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

by J. Gruterus.

[93] Porta was born at Naples in 1550 and died there in 1615. He studied

the subject of lenses and the theory of sight, did some work in hydraulics

and agriculture, and was well known as an astrologer. His _Magiae naturalis

libri XX_ was published at Naples in 1589. The above title should read

_curvilineorum_.

[94] Cataldi was born in 1548 and died at Bologna in 1626. He was professor

of mathematics at Perugia, Florence, and Bologna, and is known in

mathematics chiefly for his work in continued fractions. He was one of the

scholarly men of his day.

[95] Georg Joachim Rheticus was born at Feldkirch in 1514 and died at

Caschau, Hungary, in 1576. He was one of the most prominent pupils of

Copernicus, his _Narratio de libris revolutionum Copernici_ (Dantzig, 1540)

having done much to make the theory of his master known.

[96] Henry Briggs, who did so much to make logarithms known, and who used

the base 10, was born at Warley Wood, in Yorkshire, in 1560, and died at

Oxford in 1630. He was Savilian professor of mathematics at Oxford, and his

grave may still be seen there.

[97] He lived at "Reggio nella Emilia" in the 16th and 17th centuries. His

_Regola e modo facilissimo di quadrare il cerchio_ was published at Reggio

in 1609.

[98] Christoph Klau (Clavius) was born at Bamberg in 1537, and died at Rome

in 1612. He was a Jesuit priest and taught mathematics in the Jesuit

College at Rome. He wrote a number of works on mathematics, including

excellent text-books on arithmetic and algebra.

[99] Christopher Gruenberger, or Grienberger, was born at Halle in Tyrol in

1561, and died at Rome in 1636. He was, like Clavius, a Jesuit and a

mathematician, and he wrote a little upon the subject of projections. His

_Prospectiva nova coelestis_ appeared at Rome in 1612.

[100] The name should, of course, be Lansbergii in the genitive, and is so

in the original title. Philippus Lansbergius was born at Ghent in 1560, and

died at Middelburg in 1632. He was a Protestant theologian, and was also a

physician and astronomer. He was a well-known supporter of Galileo and

Copernicus. His _Commentationes in motum terrae diurnum et annuum_ appeared

at Middelburg in 1630 and did much to help the new theory.

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

[102] The African explorer, born in Somersetshire in 1827, died at Bath in

1864. He was the first European to cross Central Africa from north to

south. He investigated the sources of the Nile.

[103] Prester (Presbyter, priest) John, the legendary Christian king whose

realm, in the Middle Ages, was placed both in Asia and in Africa, is first

mentioned in the chronicles of Otto of Freisingen in the 12th century. In

the 14th century his kingdom was supposed to be Abyssinia.

[104] "It is a profane and barbarous nation, dirty and slovenly, who eat

their meat half raw and drink mare's milk, and who use table-cloths and

napkins only to wipe their hands and mouths."

[105] "The great Prester John, who is the fourth in rank, is emperor of

Ethiopia and of the Abyssinians, and boasts of his descent from the race of

David, as having descended from the Queen of Sheba, Queen of Ethiopia. She,

having gone to Jerusalem to see the wisdom of Solomon, about the year of

the world 2952, returned pregnant with a son whom they called Moylech, from

whom they claim descent in a direct line. And so he glories in being the

most ancient monarch in the world, saying that his empire has endured for

more than three thousand years, which no other empire is able to assert. He

also puts into his titles the following: 'We, the sovereign in my realms,

uniquely beloved of God, pillar of the faith, sprung from the race of

Judah, etc.' The boundaries of this empire touch the Red Sea and the

mountains of Azuma on the east, and on the western side it is bordered by

the River Nile which separates it from Nubia. To the north lies Egypt, and

to the south the kingdoms of Congo and Mozambique. It extends forty degrees

in length, or one thousand twenty-five leagues, from Congo or Mozambique on

the south to Egypt on the north; and in width it reaches from the Nile on

the west to the mountains of Azuma on the east, seven hundred twenty-five

leagues, or twenty-nine degrees. This empire contains thirty large

provinces, namely Medra, Gaga, Alchy, Cedalon, Mantro, Finazam, Barnaquez,

Ambiam, Fungy, Angote, Cigremaon, Gorga, Cafatez, Zastanla, Zeth, Barly,

Belangana, Tygra, Gorgany, Barganaza, d'Ancut, Dargaly, Ambiacatina,

Caracogly, Amara, Maon (_sic_), Guegiera, Bally, Dobora, and Macheda. All

of these provinces are situated directly under the equinoctial line between

the tropics of Capricorn and Cancer; but they are two hundred fifty leagues

nearer our tropic than the other. The name of Prester John signifies Great

Lord, and is not Priest [Presbyter] as many think. He has always been a

Christian, but often schismatic. At the present time he is a Catholic and

recognizes the Pope as sovereign pontiff. I met one of his bishops in

Jerusalem, and often conversed with him through the medium of our guide. He

was of grave and serious bearing, pleasant of speech, but wonderfully

subtle in everything he said. He took great delight in what I had to relate

concerning our beautiful ceremonies and the dignity of our prelates in

their pontifical vestments. As to other matters I will only say that the

Ethiopian is joyous and merry, not at all like the Tartar in the matter of

filth, nor like the wretched Arab. They are refined and subtle, trusting no

one, wonderfully suspicious, and very devout. They are not at all black as

is commonly supposed, by which I refer to those who do not live under the

equator or too near to it, for these are Moors as we shall see."

With respect to this translation it should be said that the original forms

of the proper names have been preserved, although they are not those found

in modern works. It should also be stated that the meaning of Prester is

not the one that was generally accepted by scholars at the time the work

was written, nor is it the one accepted to-day. There seems to be no doubt

that the word is derived from Presbyter as stated in note 103 on page 71,

since the above-mentioned chronicles of Otto, bishop of Freisingen about

the middle of the twelfth century, states this fact clearly. Otto received

his information from the bishop of Gabala (the Syrian Jibal) who told him

the story of John, _rex et sacerdos_, or Presbyter John as he liked to be

called. He goes on to say "Should it be asked why, with all this power and

splendor, he calls himself merely 'presbyter,' this is because of his

humility, and because it was not fitting for one whose server was a primate

and king, whose butler an archbishop and king, whose chamberlain a bishop

and king, whose master of the horse an archimandrite and king, whose chief

cook an abbot and king, to be called by such titles as these."

[106] Thomas Fienus (Fyens) was born at Antwerp in 1567 and died in 1631.

He was professor of medicine at Louvain. Besides the editions mentioned

below, his _De cometis anni 1618_ appeared at Leipsic in 1656. He also

wrote a _Disputatio an coelum moveatur et terra quiescat_, which appeared

at Antwerp in 1619, and again at Leipsic in 1656.

[107] Libertus Fromondus (1587-c 1653), a Belgian theologian, dean of the

College Church at Harcourt, and professor at Louvain. The name also appears

as Froidmont and Froimont.

[108] _L. Fromondi ... meteorologicorum libri sex.... Cui accessit T. Fieni

et L. Fromondi dissertationes de cometa anni 1618...._ This is from the

1670 edition. The 1619 edition was published at Antwerp. The

_Meteorologicorum libri VI_, appeared at Antwerp in 1627. He also wrote

_Anti-Aristarchus sive orbis terrae immobilis liber unicus_ (Antwerp,

1631); _Labyrrinthus sive de compositione continui liber unus, Philosophis,

Mathematicis, Theologis utilis et jucundus_ (Antwerp, 1631) and _Vesta sive

Anti-Aristarchi vindex adversus Jac. Lansbergium (Philippi filium) et

copernicanos_ (Antwerp, 1634).

[109] Snell was born at Leyden in 1591, and died there in 1626. He studied

under Tycho Brahe and Kepler, and is known for Snell's law of the

refraction of light. He was the first to determine the size of the earth by

measuring the arc of a meridian with any fair degree of accuracy. The title

should read: _Willebrordi Snellii R. F. Cyclometricus, de circuli

dimensione secundum Logistarum abacos, et ad Mechanicem accuratissima...._

[110] Bacon was born at York House, London, in 1561, and died near

Highgate, London, in 1626. His _Novum Organum Scientiarum or New Method of

employing the reasoning faculties in the pursuits of Truth_ appeared at

London in 1620. He had previously published a work entitled _Of the

Proficience and Advancement of Learning, divine and humane_ (London, 1605),

which again appeared in 1621. His _De augmentis scientiarum Libri IX_

appeared at Paris in 1624, and his _Historia naturalis et experimentalis de

ventis_ at Leyden in 1638. He was successively solicitor general, attorney

general, lord chancellor (1619), Baron Verulam and Viscount St. Albans. He

was deprived of office and was imprisoned in the Tower of London in 1621,

but was later pardoned.

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

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

to his edition of Bacon.

[113] R. Leslie Ellis (1817-1859), editor of the _Cambridge Mathematical

Journal_. He also wrote on Roman aqueducts, on Boole's Laws of Thought, and

on the formation of a Chinese dictionary.

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

scholar.

[115] There have been numerous editions of Bacon's complete works,

including the following: Frankfort, 1665; London, 1730, 1740, 1764, 1765,

1778, 1803, 1807, 1818, 1819, 1824, 1825-36, 1857-74, 1877. The edition to

which De Morgan refers is that of 1857-74, 14 vols., of which five were

apparently out at the time he wrote. There were also French editions in

1800 and 1835.

[116] So in the original for Tycho Brahe.

[117] In general these men acted before Baron wrote, or at any rate, before

he wrote the _Novum Organum_, but the statement must not be taken too

literally. The dates are as follows: Copernicus, 1473-1543; Tycho Brahe,

1546-1601; Gilbert, 1540-1603; Kepler, 1571-1630; Galileo, 1564-1642;

Harvey, 1578-1657. For example, Harvey's _Exercitatio Anatomica de Motu

Cordis et Sanguinis_ did not appear until 1628, and his _Exercitationes de

Generatione_ until 1651.

[118] Robert Hooke (1635-1703) studied under Robert Boyle at Oxford. He was

"Curator of Experiments" to the Royal Society and its secretary, and was

professor of geometry at Gresham College, London. It is true that he was

"very little of a mathematician" although he wrote on the motion of the

earth (1674), on helioscopes and other instruments (1675), on the rotation

of Jupiter (1666), and on barometers and sails.

[119] The son of the Sir William mentioned below. He was born in 1792 and

died in 1871. He wrote a treatise on light (1831) and one on astronomy

(1836), and established an observatory at the Cape of Good Hope where he

made observations during 1834-1838, publishing them in 1847. On his return

to England he was knighted, and in 1848 was made president of the Royal

Society. The title of the work to which reference is made is: _A

preliminary discourse on the Study of Natural Philosophy_. It appeared at

London in 1831.

[120] Sir William was horn at Hanover in 1738 and died at Slough, near

Windsor in 1822. He discovered the planet Uranus and six satellites,

besides two satellites of Saturn. He was knighted by George III.

[121] This was the work of 1836. He also published a work entitled

_Outlines of Astronomy_ in 1849.

[122] While Newton does not tell the story, he refers in the _Principia_

(1714 edition, p. 293) to the accident caused by his cat.

[123] Marino Ghetaldi (1566-1627), whose _Promotus Archimedes_ appeared at

Rome in 1603, _Nonnullae propositiones de parabola_ at Rome in 1603. and

_Apollonius redivivus_ at Venice in 1607. He was a nobleman and was

ambassador from Venice to Rome.

[124] Simon Stevin (born at Bruges, 1548; died at the Hague, 1620). He was

an engineer and a soldier, and his _La Disme_ (1585) was the first separate

treatise on the decimal fraction. The contribution referred to above is

probably that on the center of gravity of three bodies (1586).

[125] Habakuk Guldin (1577-1643), who took the name Paul on his conversion

to Catholicism. He became a Jesuit, and was professor of mathematics at

Vienna and later at Gratz. In his _Centrobaryca seu de centro gravitatis

trium specierum quantitatis continuae_ (1635), of the edition of 1641,

appears the Pappus rule for the volume of a solid formed by the revolution

of a plane figure about an axis, often spoken of as Guldin's Theorem.

[126] Edward Wright was born at Graveston, Norfolkshire, in 1560, and died

at London in 1615. He was a fellow of Caius College, Cambridge, and in his

work entitled _The correction of certain errors in Navigation_ (1599) he

gives the principle of Mercator's projection. He translated the _Portuum

investigandorum ratio_ of Stevin in 1599.

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

for his generation alone.

[128] The eminent French physicist, Jean Baptiste Biot (1779-1862),

professor in the College de France. His work _Sur les observatoires

meteorologiques_ appeared in 1855.

[129] George Biddell Airy (1801-1892), professor of astronomy and physics

at Cambridge, and afterwards director of the Observatory at Greenwich.

[130] De Morgan would have rejoiced in the role played by Intuition in the

mathematics of to-day, notably among the followers of Professor Klein.

[131] Colburn was the best known of the calculating boys produced in

America. He was born at Cabot, Vermont, in 1804, and died at Norwich,

Vermont, in 1840. Having shown remarkable skill in numbers as early as

1810, he was taken to London in 1812, whence he toured through Great

Britain and to Paris. The Earl of Bristol placed him in Westminster School

(1816-1819). On his return to America he became a preacher, and later a

teacher of languages.

[132] The history of calculating boys is interesting. Mathieu le Coc (about

1664), a boy of Lorraine, could extract cube roots at sight at the age of

eight. Tom Fuller, a Virginian slave of the eighteenth century, although

illiterate, gave the number of seconds in 7 years 17 days 12 hours after

only a minute and a half of thought. Jedediah Buxton, an Englishman of the

eighteenth century, was studied by the Royal Society because of his

remarkable powers. Ampere, the physicist, made long calculations with

pebbles at the age of four. Gauss, one of the few infant prodigies to

become an adult prodigy, corrected his father's payroll at the age of

three. One of the most remarkable of the French calculating boys was Henri

Mondeux. He was investigated by Arago, Sturm, Cauchy, and Liouville, for

the Academie des Sciences, and a report was written by Cauchy. His

specialty was the solution of algebraic problems mentally. He seems to have

calculated squares and cubes by a binomial formula of his own invention. He

died in obscurity, but was the subject of a _Biographie_ by Jacoby (1846).

George P. Bidder, the Scotch engineer (1806-1878), was exhibited as an

arithmetical prodigy at the age of ten, and did not attend school until he

was twelve. Of the recent cases two deserve special mention, Inaudi and

Diamandi. Jacques Inaudi (born in 1867) was investigated for the Academie

in 1892 by a commission including Poincare, Charcot, and Binet. (See the

_Revue des Deux Mondes_, June 15, 1892, and the laboratory bulletins of the

Sorbonne). He has frequently exhibited his remarkable powers in America.

Pericles Diamandi was investigated by the same commission in 1893. See

Alfred Binet, _Psychologie des Grands Calculateurs et Joueurs d'Echecs_,

Paris, 1894.

[133] John Flamsteed's (1646-1719) "old white house" was the first

Greenwich observatory. He was the Astronomer Royal and first head of this

observatory.

[134] It seems a pity that De Morgan should not have lived to lash those of

our time who are demanding only the immediately practical in mathematics.

His satire would have been worth the reading against those who seek to

stifle the science they pretend to foster.

[135] Ismael Bouillaud, or Boulliau, was born in 1605 and died at Paris in

1694. He was well known as an astronomer, mathematician, and jurist. He

lived with De Thou at Paris, and accompanied him to Holland. He traveled

extensively, and was versed in the astronomical work of the Persians and

Arabs. It was in his _Astronomia philolaica, opus novum_ (Paris, 1645) that

he attacked Kepler's laws. His tables were shown to be erroneous by the

fact that the solar eclipse did not take place as predicted by him in 1645.

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

ninety-one.

[137] _Didaci a Stunica ... In Job commentaria_ appeared at Toledo in 1584.

[138] "The false Pythagorean doctrine, absolutely opposed to the Holy

Scriptures, concerning the mobility of the earth and the immobility of the

sun."

[139] Paolo Antonio Foscarini (1580-1616), who taught theology and

philosophy at Naples and Messina, was one of the first to champion the

theories of Copernicus. This was in his _Lettera sopra l'opinione de'

Pittagorici e del Copernico, della mobilita della Terra e stabilita del

Sole, e il nuovo pittagorico sistema del mondo_, 4to, Naples, 1615. The

condemnation of the Congregation was published in the following spring, and

in the year of Foscarini's death at the early age of thirty-six.

[140] "To be wholly prohibited and condemned," because "it seeks to show

that the aforesaid doctrine is consonant with truth and is not opposed to

the Holy Scriptures."

[141] "As repugnant to the Holy Scriptures and to its true and Catholic

interpretation (which in a Christian man cannot be tolerated in the least),

he does not hesitate to treat (of his subject) '_by hypothesis_', but he

even adds '_as most true_'!"

[142] "To the places in which he discusses not by hypothesis but by making

assertions concerning the position and motion of the earth."

[143] "_Copernicus._ If by chance there shall be vain talkers who, although

ignorant of all mathematics, yet taking it upon themselves to sit in

judgment upon the subject on account of a certain passage of Scripture

badly distorted for their purposes, shall have dared to criticize and

censure this teaching of mine, I pay no attention to them, even to the

extent of despising their judgment as rash. For it is not unknown that

Lactantius, a writer of prominence in other lines although but little

versed in mathematics, spoke very childishly about the form of the earth

when he ridiculed those who declared that it was spherical. Hence it should

not seem strange to the learned if some shall look upon us in the same way.

Mathematics is written for mathematicians, to whom these labors of ours

will seem, if I mistake not, to add something even to the republic of the

Church.... _Emend._ Here strike out everything from 'if by chance' to the

words 'these labors of ours,' and adapt it thus: 'But these labors of

ours.'"

[144] "_Copernicus._ However if we consider the matter more carefully it

will be seen that the investigation is not yet completed, and therefore

ought by no means to be condemned. _Emend._ However, if we consider the

matter more carefully it is of no consequence whether we regard the earth

as existing in the center of the universe or outside of the center, so far

as the solution of the phenomena of celestial movements is concerned."

[145] "The whole of this chapter may be cut out, since it avowedly treats

of the earth's motion, while it refutes the reasons of the ancients proving

its immobility. Nevertheless, since it seems to speak problematically, in

order that it may satisfy the learned and keep intact the sequence and

unity of the book let it be emended as below."

[146] "_Copernicus._ Therefore why do we still hesitate to concede to it

motion which is by nature consistent with its form, the more so because the

whole universe is moving, whose end is not and cannot be known, and not

confess that there is in the sky an appearance of daily revolution, while

on the earth there is the truth of it? And in like manner these things are

as if Virgil's AEneas should say, 'We are borne from the harbor' ...

_Emend._ Hence I cannot concede motion to this form, the more so because

the universe would fall, whose end is not and cannot be known, and what

appears in the heavens is just as if ..."

[147] "_Copernicus_. I also add that it would seem very absurd that motion

should be ascribed to that which contains and locates, and not rather to

that which is contained and located, that is the earth. _Emend._ I also add

that it is not more difficult to ascribe motion to the contained and

located, which is the earth, than to that which contains it."

[148] "_Copernicus._ You see, therefore, that from all these things the

motion of the earth is more probable than its immobility, especially in the

daily revolution which is as it were a particular property of it. _Emend._

Omit from 'You see' to the end of the chapter."

[149] "_Copernicus._ Therefore, since there is nothing to hinder the motion

of the earth, it seems to me that we should consider whether it has several

motions, to the end that it may be looked upon as one of the moving stars.

_Emend._ Therefore, since I have assumed that the earth moves, it seems to

me that we should consider whether it has several motions."

[150] "_Copernicus._ We are not ashamed to acknowledge ... that this is

preferably verified in the motion of the earth. _Emend._ We are not ashamed

to assume ... that this is consequently verified in the motion."

[151] "_Copernicus._ So divine is surely this work of the Best and

Greatest. _Emend._ Strike out these last words."

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

[153] "_Copernicus._ Demonstration of the threefold motion of the earth.

_Emend._ On the hypothesis of the threefold motion of the earth and its

demonstration."

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

[155] "_Copernicus._ Concerning the size of these three stars, the sun, the

moon and the earth. _Emend._ Strike out the words 'these three stars,'

because the earth is not a star as Copernicus would make it."

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

[157] One of the Church Fathers, born about 250 A.D., and died about 330,

probably at Treves. He wrote _Divinarum Institutionum Libri VII._ and other

controversial and didactic works against the learning and philosophy of the

Greeks.

[158] Giovanni Battista Riccioli (1598-1671) taught philosophy and theology

at Parma and Bologna, and was later professor of astronomy. His _Almagestum

novum_ appeared in 1651, and his _Argomento fisico-matematico contro il

moto diurno della terra_ in 1668.

[159] He was a native of Arlington, Sussex, and a pensioner of Christ's

College, Cambridge. In 1603 he became a master of arts at Oxford.

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

[161] "Private subjects may, in the presence of danger, defend themselves

or their families against a monarch as against any malefactor, if the

monarch assaults them like a bandit or a ravisher, and provided they are

unable to summon the usual protection and cannot in any way escape the

danger."

[162] Daniel Neal (1678-1743), an independent minister, wrote a _History of

the Puritans_ that appeared in 1732. The account may be found in the New

York edition of 1843-44, vol. I, p. 271.

[163] Anthony Wood (1632-1695), whose _Historia et Antiquitates

Universitatis Oxoniensis_ (1674) and _Athenae Oxoniensis_ (1691) are among

the classics on Oxford.

[164] Part of the title, not here quoted, shows the nature of the work more

clearly: "liber unicus, in quo decretum S. Congregationis S. R. E.

Cardinal. an. 1616, adversus Pythagorico-Copernicanos editum defenditur."

[165] This was John Elliot Drinkwater Bethune (1801-1851), the statesman

who did so much for legislative and educational reform in India. His

father, John Drinkwater Bethune, wrote a history of the siege of Gibraltar.

[166] The article referred to is about thirty years old; since it appeared

another has been given (_Dubl. Rev._, Sept. 1865) which is of much greater

depth. In it will also be found the Roman view of Bishop Virgil (_ante_, p.

32).--A. De M.

[167] Jean Baptiste Morin (1583-1656), in his younger days physician to the

Bishop of Boulogne and the Duke of Luxemburg, became in 1630 professor of

mathematics at the College Royale. His chief contribution to the problem of

the determination of longitude is his _Longitudinum terrestrium et

coelestium nova et hactenus optata scientia_ (1634). He also wrote against

Copernicus in his _Famosi problematis de telluris motu vel quiete hactenus

optata solutio_ (1631), and against Lansberg in his _Responsio pro telluris

quiete_ (1634).

[168] The work appeared at Leyden in 1626, at Amsterdam in 1634, at

Copenhagen in 1640 and again at Leyden in 1650. The title of the 1640

edition is _Arithmeticae Libri II et Geometriae Libri VI_. The work on

which it is based is the _Arithmeticae et Geometriae Practica_, which

appeared in 1611.

[169] The father's name was Adriaan, and Lalande says that it was Montucla

who first made the mistake of calling him Peter, thinking that the initials

P. M. stood for Petrus Metius, when in reality they stood for _piae

memoriae_! The ratio 355/113 was known in China hundreds of years before

his time. See note 55, page 52.

[170] Adrian Metius (1571-1635) was professor of medicine at the University

of Franeker. His work was, however, in the domain of astronomy, and in this

domain he published several treatises.

[171] The first edition was entitled: _The Discovery of a World in the

Moone. Or, a Discourse Tending to prove that 'tis probable there may be

another habitable World in that Planet_. 1638, 8vo. The fourth edition

appeared in 1684. John Wilkins (1614-1672) was Warden of Wadham College,

Oxford; master of Trinity, Cambridge; and, later, Bishop of Chester. He was

influential in founding the Royal Society.

[172] The first edition was entitled: _C. Hugenii_ [Greek: Kosmotheoros],

_sive de Terris coelestibus, earumque ornatu, conjecturae_, The Hague,

1698, 4to. There were several editions. It was also translated into French

(1718), and there was another English edition (1722). Huyghens (1629-1695)

was one of the best mathematical physicists of his time.

[173] It is hardly necessary to say that science has made enormous advance

in the chemistry of the universe since these words were written.

[174] William Whewell (1794-1866) is best known through his _History of the

Inductive Sciences_ (1837) and _Philosophy of the Inductive Sciences_

(1840).

[175] Thomas Chalmers (1780-1847), the celebrated Scotch preacher. These

discourses were delivered while he was minister in a large parish in the

poorest part of Glasgow, and in them he attempted to bring science into

harmony with the Bible. He was afterwards professor of moral philosophy at

St. Andrew's (1823-28), and professor of theology at Edinburgh (1828). He

became the leader of a schism from the Scotch Presbyterian Church,--the

Free Church.

[176] That is, in Robert Watt's (1774-1819) _Bibliotheca Britannica_

(posthumous, 1824). Nor is it given in the _Dictionary of National

Biography_.

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

[178] Francois Rabelais (c. 1490-1553) the humorist who created Pantagruel

(1533) and Gargantua (1532). His work as a physician and as editor of the

works of Galen and Hippocrates is less popularly known.

[179] Francis Godwin (1562-1633) bishop of Llandaff and Hereford. Besides

some valuable historical works he wrote _The Man in the Moone, or a

Discourse of a voyage thither by Domingo Gonsales, the Speed Messenger of

London_, 1638.

[180] Bernard Le Bovier de Fontenelle (1657-1757), historian, critic,

mathematician, Secretary of the Academie des Sciences, and member of the

Academie Francaise. His _Entretien sur la pluralite des mondes_ appeared at

Paris in 1686.

[181] Athanasius Kircher (1602-1680), Jesuit, professor of mathematics and

philosophy, and later of Hebrew and Syriac, at Wurzburg; still later

professor of mathematics and Hebrew at Rome. He wrote several works on

physics. His collection of mathematical instruments and other antiquities

became the basis of the Kircherian Museum at Rome.

[182] "Both belief and non-belief are dangerous. Hippolitus died because

his stepmother was believed. Troy fell because Cassandra was not believed.

Therefore the truth should be investigated long before foolish opinion can

properly judge." (Prove = probe?).

[183] Jacobus Grandamicus (Jacques Grandami) was born at Nantes in 1588 and

died at Paris in 1672. He was professor of theology and philosophy in the

Jesuit colleges at Rennes, Tours, Rouen, and other places. He wrote several

works on astronomy.

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

John xii. 32.

[185] Andrea Argoli (1568-1657) wrote a number of works on astronomy, and

computed ephemerides from 1621 to 1700.

[186] So in the original edition of the _Budget_. It is Johannem Pellum in

the original title. John Pell (1610 or 1611-1685) studied at Cambridge and

Oxford, and was professor of mathematics at Amsterdam (1643-46) and Breda

(1646-52). He left many manuscripts but published little. His name attaches

by accident to an interesting equation recently studied with care by Dr.

E. E. Whitford (New York, 1912).

[187] Christianus Longomontanus (Christen Longberg or Lumborg) was born in

1569 at Longberg, Jutland, and died in 1647 at Copenhagen. He was an

assistant of Tycho Brahe and accepted the diurnal while denying the orbital

motion of the earth. His _Cyclometria e lunulis reciproce demonstrata_

appeared in 1612 under the name of Christen Severin, the latter being his

family name. He wrote several other works on the quadrature problem, and

some treatises on astronomy.

[188] The names are really pretty well known. Giles Persone de Roberval was

born at Roberval near Beauvais in 1602, and died at Paris in 1675. He was

professor of philosophy at the College Gervais at Paris, and later at the

College Royal. He claimed to have discovered the theory of indivisibles

before Cavalieri, and his work is set forth in his _Traite des

indivisibles_ which appeared posthumously in 1693.

Hobbes (1588-1679), the political and social philosopher, lived a good part

of his time (1610-41) in France where he was tutor to several young

noblemen, including the Cavendishes. His _Leviathan_ (1651) is said to have

influenced Spinoza, Leibnitz, and Rousseau. His _Quadratura circuli,

cubatio sphaerae, duplicatio cubi ..._ (London, 1669), _Rosetum geometricum

..._ (London, 1671), and _Lux Mathematica, censura doctrinae Wallisianae

contra Rosetum Hobbesii_ (London, 1674) are entirely forgotten to-day. (See

a further note, _infra_.)

Pierre de Carcavi, a native of Lyons, died at Paris in 1684. He was a

member of parliament, royal librarian, and member of the Academie des

Sciences. His attempt to prove the impossibility of the quadrature appeared

in 1645. He was a frequent correspondent of Descartes.

Cavendish (1591-1654) was Sir (not Lord) Charles. He was, like De Morgan

himself, a bibliophile in the domain of mathematics. His life was one of

struggle, his term as member of parliament under Charles I being followed

by gallant service in the royal army. After the war he sought refuge on the

continent where he met most of the mathematicians of his day. He left a

number of manuscripts on mathematics, which his widow promptly disposed of

for waste paper. If De Morgan's manuscripts had been so treated we should

not have had his revision of his _Budget of Paradoxes_.

Marin Mersenne (1588-1648), a minorite, living in the cloisters at Nevers

and Paris, was one of the greatest Franciscan scholars. He edited Euclid,

Apollonius, Archimedes, Theodosius, and Menelaus (Paris, 1626), translated

the Mechanics of Galileo into French (1634), wrote _Harmonicorum Libri XII_

(1636), and _Cogitata physico-mathematica_ (1644), and taught theology and

philosophy at Nevers.

Johann Adolph Tasse (Tassius) was born in 1585 and died at Hamburg in 1654.

He was professor of mathematics in the Gymnasium at Hamburg, and wrote

numerous works on astronomy, chronology, statics, and elementary

mathematics.

Johann Ludwig, Baron von Wolzogen, seems to have been one of the early

unitarians, called _Fratres Polonorum_ because they took refuge in Poland.

Some of his works appear in the _Bibliotheca Fratrum Polonorum_ (Amsterdam,

1656). I find no one by the name who was contributing to mathematics at

this time.

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

Bonaventura Cavalieri (1598-1647) was a Jesuit, a pupil of Galileo, and

professor of mathematics at Bologna. His greatest work, _Geometria

indivisibilibus continuorum nova quadam ratione promota_, in which he makes

a noteworthy step towards the calculus, appeared in 1635.

Jacob (Jacques) Golius was born at the Hague in 1596 and died at Leyden in

1667. His travels in Morocco and Asia Minor (1622-1629) gave him such

knowledge of Arabic that he became professor of that language at Leyden.

After Snell's death he became professor of mathematics there. He translated

Arabic works on mathematics and astronomy into Latin.

[189] It would be interesting to follow up these rumors, beginning perhaps

with the tomb of Archimedes. The Ludolph van Ceulen story is very likely a

myth. The one about Fagnano may be such. The Bernoulli tomb does have the

spiral, however (such as it is), as any one may see in the cloisters at

Basel to-day.

[190] Collins (1625-1683) was secretary of the Royal Society, and was "a

kind of register of all new improvements in mathematics." His office

brought him into correspondence with all of the English scientists, and he

was influential in the publication of various important works, including

Branker's translation of the algebra by Rhonius, with notes by Pell, which

was the first work to contain the present English-American symbol of

division. He also helped in the publication of editions of Archimedes and

Apollonius, of Kersey's Algebra, and of the works of Wallis. His profession

was that of accountant and civil engineer, and he wrote three unimportant

works on mathematics (one published posthumously, and the others in 1652

and 1658).

Heinrich Christian Schumacher (1780-1850) was professor of astronomy at

Copenhagen and director of the observatory at Altona. His translation of

Carnot's _Geometrie de position_ (1807) brought him into personal relations

with Gauss, and the friendship was helpful to Schumacher. He was a member

of many learned societies and had a large circle of acquaintances. He

published numerous monographs and works on astronomy.

Gassendi (1592-1655) might well have been included by De Morgan in the

group, since he knew and was a friend of most of the important

mathematicians of his day. Like Mersenne, he was a minorite, but he was a

friend of Galileo and Kepler, and wrote a work under the title _Institutio

astronomica, juxta hypotheses Copernici, Tychonis-Brahaei et Ptolemaei_

(1645). He taught philosophy at Aix, and was later professor of mathematics

at the College Royal at Paris.

Burnet is the Bishop Gilbert Burnet (1643-1715) who was so strongly

anti-Romanistic that he left England during the reign of James II and

joined the ranks of the Prince of Orange. William made him bishop of

Salisbury.

[191] There is some substantial basis for De Morgan's doubts as to the

connection of that _mirandula_ of his age, Sir Kenelm Digby (1603-1665),

with the famous _poudre de sympathie_. It is true that he was just the one

to prepare such a powder. A dilletante in everything,--learning, war,

diplomacy, religion, letters, and science--he was the one to exploit a

fraud of this nature. He was an astrologer, an alchemist, and a fabricator

of tales, and well did Henry Stubbes characterize him as "the very Pliny of

our age for lying." He first speaks of the powder in a lecture given at

Montpellier in 1658, and in the same year he published the address at Paris

under the title: _Discours fait en une celebre assemblee par le chevalier

Digby .... touchant la guerison de playes par la poudre de sympathie_. The

London edition referred to by De Morgan also came out in 1658, and several

editions followed it in England, France and Germany. But Nathaniel Highmore

in his _History of Generation_ (1651) referred to the concoction as

"Talbot's Powder" some years before Digby took it up. The basis seems to

have been vitriol, and it was claimed that it would heal a wound by simply

being applied to a bandage taken from it.

[192] This work by Thomas Birch (1705-1766) came out in 1756-57. Birch was

a voluminous writer on English history. He was a friend of Dr. Johnson and

of Walpole, and he wrote a life of Robert Boyle.

[193] We know so much about John Evelyn (1620-1706) through the diary which

he began at the age of eleven, that we forget his works on navigation and

architecture.

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

[195] This is interesting in view of the modern aseptic practice of surgery

and the antiseptic treatment of wounds inaugurated by the late Lord Lister.

[196] Perhaps De Morgan had not heard the _bon mot_ of Dr. Holmes: "I

firmly believe that if the whole _materia medica_ could be sunk to the

bottom of the sea, it would be all the better for mankind and all the worse

for the fishes."

[197] The full title is worth giving, because it shows the mathematical

interests of Hobbes, and the nature of the six dialogues: _Examinatio et

emendatio mathematicae hodiernae qualis explicatur in libris Johannis

Wallisii geometriae professoris Saviliani in Academia Oxoniensi: distributa

in sex dialogos (1. De mathematicae origine ...; 2. De principiis traditis

ab Euclide; 3. De demonstratione operationum arithmeticarum ...; 4. De

rationibus; 5. De angula contactus, de sectionibus coni, et arithmetica

infinitorum; 6. Dimensio circuli tribus methodis demonstrata ... item

cycloidis verae descriptio et proprietates aliquot.)_ Londini, 1660 (not

1666). For a full discussion of the controversy over the circle, see George

Croom Robertson's biography of Hobbes in the eleventh edition of the

_Encyclopaedia Britannica_.

[198] This is his _Animadversions upon Mr. Hobbes' late book De principiis

et ratiocinatione geometrarum_, 1666, or his _Hobbianae quadraturae

circuli, cubationis sphaerae et duplicationis cubi confutatio_, also of

1669.

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

[200] Gregoire de St. Vincent (1584-1667) published his _Opus geometricum

quadraturae circuli et sectionum coni_ at Antwerp in 1647.

[201] This appears in _J. Scaligeri cyclometrica elementa duo_, Lugduni

Batav., 1594.

[202] Adriaen van Roomen (1561-1615) gave the value of [pi] to sixteen

decimal places in his _Ideae mathematicae pars prima_ (1593), and wrote his

_In Archimedis circuli dimensionem expositio & analysis_ in 1597.

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

[204] Bentley (1662-1742) might have done it, for as the head of Trinity

College, Cambridge, and a follower of Newton, he knew some mathematics.

Erasmus (1466-1536) lived a little too early to attempt it, although his

brilliant satire might have been used to good advantage against those who

did try.

[205] "In grammar, to give the winds to the ships and to give the ships to

the winds mean the same thing. But in geometry it is one thing to assume

the circle BCD not greater than thirty-six segments BCDF, and another (to

assume) the thirty-six segments BCDF not greater than the circle. The one

assumption is true, the other false."

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

Aristotle in 1590.

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

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

right."

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

[210] "The perimeter of the dodecagon to be inscribed in a circle is

greater than the perimeter of the circle. And the more sides a polygon to

be inscribed in a circle successively has, so much the greater will the

perimeter of the polygon be than the perimeter of the circle."

[211] De Morgan took, perhaps, the more delight in speaking thus of Sir

William Hamilton (1788-1856) because of a spirited controversy that they

had in 1847 over the theory of logic. Possibly, too, Sir William's low

opinion of mathematics had its influence.

[212] Edwards (1699-1757) wrote _The canons of criticism_ (1747) in which

he gave a scathing burlesque on Warburton's Shakespeare. It went through

six editions.

[213] Antoine Teissier (born in 1632) published his _Eloges des hommes

savants, tires de l'histoire de M. de Thou_ in 1683.

[214] "He boasted without reason of having found the quadrature of the

circle. The glory of this admirable discovery was reserved for Joseph

Scaliger, as Scevole de St. Marthe has written."

[215] _Natural and political observations mentioned in the following Index,

and made upon the Bills of Mortality.... With reference to the government,

religion, trade, growth, ayre, and diseases of the said city._ London,

1662, 4to. The book went through several editions.

[216] _Ne sutor ultra crepidam_, "Let the cobbler stick to his last," as we

now say.

[217] The author (1632-1695) of the _Historia et Antiquitates Universitatis

Oxoniensis_ (1674). See note 163, page 98.

[218] The mathematical guild owes Samuel Pepys (1633-1703) for something

besides his famous diary (1659-1669). Not only was he president of the

Royal Society (1684), but he was interested in establishing Sir William

Boreman's mathematical school at Greenwich.

[219] John Graunt (1620-1674) was a draper by trade, and was a member of

the Common Council of London until he lost office by turning Romanist.

Although a shopkeeper, he was elected to the Royal Society on the special

recommendation of Charles II. Petty edited the fifth edition of his work,

adding much to its size and value, and this may be the basis of Burnet's

account of the authorship.

[220] Petty (1623-1687) was a mathematician and economist, and a friend of

Pell and Sir Charles Cavendish. His survey of Ireland, made for Cromwell,

was one of the first to be made on a large scale in a scientific manner. He

was one of the founders of the Royal Society.

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

Catholic faith.

[222] He was born in 1627 and died in 1704. He published a series of

ephemerides, beginning in 1659. He was imprisoned in 1679, at the time of

the "Popish Plot," and again for treason in 1690. His important

astrological works are the _Animal Cornatum, or the Horn'd Beast_ (1654)

and _The Nativity of the late King Charls_ (1659).

[223] Isaac D'Israeli (1766-1848), in his _Curiosities of Literature_

(1791), speaking of Lilly, says: "I shall observe of this egregious

astronomer, that there is in this work, so much artless narrative, and at

the same time so much palpable imposture, that it is difficult to know when

he is speaking what he really believes to be the truth." He goes on to say

that Lilly relates that "those adepts whose characters he has drawn were

the lowest miscreants of the town. Most of them had taken the air in the

pillory, and others had conjured themselves up to the gallows. This seems a

true statement of facts."

[224] It is difficult to estimate William Lilly (1602-1681) fairly. His

_Merlini Anglici ephemeris_, issued annually from 1642 to 1681, brought him

a great deal of money. Sir George Wharton (1617-1681) also published an

almanac annually from 1641 to 1666. He tried to expose John Booker

(1603-1677) by a work entitled _Mercurio-Coelicio-Mastix; or, an

Anti-caveat to all such, as have (heretofore) had the misfortune to be

Cheated and Deluded by that Grand and Traiterous Impostor of this

Rebellious Age, John Booker_, 1644. Booker was "licenser of mathematical

[astrological] publications," and as such he had quarrels with Lilly,

Wharton, and others.

[225] See note 171 on page 100.

[226] This is the _Ars Signorum, vulgo character universalis et lingua

philosophica_, that appeared at London in 1661, 8vo. George Dalgarno

anticipated modern methods in the teaching of the deaf and dumb.

[227] See note 200 on page 110.

[228] If the hyperbola is referred to the asymptotes as axes, the area

between two ordinates (x = a, x = b) is the difference of the logarithms of

a and b to the base e. E.g., in the case of the hyperbola xy = 1, the area

between x = a and x = 1 is log a.

[229] "On ne peut lui refuser la justice de remarquer que personne avant

lui ne s'est porte dans cette recherche avec autant de genie, & meme, si

nous en exceptons son objet principal, avec autant de succes." _Quadrature

du Cercle_, p. 66.

[230] The title proceeds: _Seu duae mediae proportionales inter extremas

datas per circulum et per infinitas hyperbolas, vel ellipses et per

quamlibet exhibitae_.... Rene Francois, Baron de Sluse (1622-1685) was

canon and chancellor of Liege, and a member of the Royal Society. He also

published a work on tangents (1672). The word _mesolabium_ is from the

Greek [Greek: mesolabion] or [Greek: mesolabon], an instrument invented by

Eratosthenes for finding two mean proportionals.

[231] The full title has some interest: _Vera circuli et hyperbolae

quadratura cui accedit geometriae pars universalis inserviens quantitatum

curvarum transmutationi et mensurae. Authore Jacobo Gregorio Abredonensi

Scoto ... Patavii_, 1667. That is, James Gregory (1638-1675) of Aberdeen

(he was really born near but not in the city), a good Scot, was publishing

his work down in Padua. The reason was that he had been studying in Italy,

and that this was a product of his youth. He had already (1663) published

his _Optica promota_, and it is not remarkable that his brilliancy brought

him a wide circle of friends on the continent and the offer of a pension

from Louis XIV. He became professor of mathematics at St Andrews and later

at Edinburgh, and invented the first successful reflecting telescope. The

distinctive feature of his _Vera quadratura_ is his use of an infinite

converging series, a plan that Archimedes used with the parabola.

[232] Jean de Beaulieu wrote several works on mathematics, including _La

lumiere de l'arithmetique_ (n.d.), _La lumiere des mathematiques_ (1673),

_Nouvelle invention d'arithmetique_ (1677), and some mathematical tables.

[233] A just estimate. There were several works published by Gerard

Desargues (1593-1661), of which the greatest was the _Brouillon Proiect_

(Paris, 1639). There is an excellent edition of the _Oeuvres de Desargues_

by M. Poudra, Paris, 1864.

[234] "A certain M. de Beaugrand, a mathematician, very badly treated by

Descartes, and, as it appears, rightly so."

[235] This is a very old approximation for [pi]. One of the latest

pretended geometric proofs resulting in this value appeared in New York in

1910, entitled _Quadrimetry_ (privately printed).

[236] "Copernicus, a German, made himself no less illustrious by his

learned writings; and we might say of him that he stood alone and unique in

the strength of his problems, if his excessive presumption had not led him

to set forth in this science a proposition so absurd that it is contrary to

faith and reason, namely that the circumference of a circle is fixed and

immovable while the center is movable: on which geometrical principle he

has declared in his astrological treatise that the sun is fixed and the

earth is in motion."

[237] So in the original.

[238] Franciscus Maurolycus (1494-1575) was really the best mathematician

produced by Sicily for a long period. He made Latin translations of

Theodosius, Menelaus, Euclid, Apollonius, and Archimedes, and wrote on

cosmography and other mathematical subjects.

[239] "Nicolaus Copernicus is also tolerated who asserted that the sun is

fixed and that the earth whirls about it; and he rather deserves a whip or

a lash than a reproof."

[240] "Algebra is the curious science of scholars, and particularly for a

general of an army, or a captain, in order quickly to draw up an army in

battle array and to number the musketeers and pikemen who compose it,

without the figures of arithmetic. This science has five special figures of

this kind: P means _plus_ in commerce and _pikemen_ in the army; M means

_minus_, and _musketeer_ in the art of war;... R signifies _root_ in the

measurement of a cube, and _rank_ in _the army_; Q means _square_ (French

_quare_, as then spelled) in both cases; C means _cube_ in mensuration, and

_cavalry_ in arranging batallions and squadrons. As for the operations of

this science, they are as follows: to add a _plus_ and a _plus_, the sum

will be _plus_; to add _minus_ with _plus_, take the less from the greater

and the remainder will be the sum required or the number to be found. I say

this only in passing, for the benefit of those who are wholly ignorant of

it."

[241] He refers to the _Joannis de Beaugrand ... Geostatice, seu de vario

pondere gravium secundum varia a terrae (centro) intervalla dissertatio

mathematica_, Paris, 1636. Pascal relates that de Beaugrand sent all of

Roberval's theorems on the cycloid and Fermat's on maxima and minima to

Galileo in 1638, pretending that they were his own.

[242] More (1614-1687) was a theologian, a fellow of Christ College,

Cambridge, and a Christian Platonist.

[243] Matthew Hale (1609-1676) the famous jurist, wrote a number of tracts

on scientific, moral, and religious subjects. These were collected and

published in 1805.

[244] They might have been attributed to many a worse man than Dr. Hales

(1677-1761), who was a member of the Royal Society and of the Paris

Academy, and whose scheme for the ventilation of prisons reduced the

mortality at the Savoy prison from one hundred to only four a year. The

book to which reference is made is _Vegetable Staticks or an Account of

some statical experiments on the sap in Vegetables_, 1727.

[245] _Pleas of the Crown; or a Methodical Summary of the Principal Matters

relating to the subject_, 1678.

[246] _Thomae Streete Astronomia Carolina, a new theory of the celestial

motions_, 1661. It also appeared at Nuremberg in 1705, and at London in

1710 and 1716 (Halley's editions). He wrote other works on astronomy.

[247] This was the Sir Thomas Street (1626-1696) who passed sentence of

death on a Roman Catholic priest for saying mass. The priest was reprieved

by the king, but in the light of the present day one would think the

justice more in need of pardon. He took part in the trial of the Rye House

Conspirators in 1683.

[248] Edmund Halley (1656-1742), who succeeded Wallis (1703) as Savilian

professor of mathematics at Oxford, and Flamsteed (1720) as head of the

Greenwich observatory. It is of interest to note that he was instrumental

in getting Newton's _Principia_ printed.

[249] Shepherd (born in 1760) was one of the most famous lawyers of his

day. He was knighted in 1814 and became Attorney General in 1817.

[250] This was William Hone (1780-1842), a book publisher, who wrote

satires against the government, and who was tried three times because of

his parodies on the catechism, creed, and litany (illustrated by

Cruikshank). He was acquitted on all of the charges.

[251] Valentinus was a Benedictine monk and was still living at Erfurt in

1413. His _Currus triumphalis antimonii_ appeared in 1624. Synesius was

Bishop of Ptolemaide, who died about 430. His works were printed at Paris

in 1605. Theodor Kirckring (1640-1693) was a fellow-student of Spinoza's.

Besides the commentary on Valentine he left several works on anatomy. His

commentary appeared at Amsterdam in 1671. There were several editions of

the _Chariot_.

[252] The chief difficulty with this curious "monk-bane" etymology is its

absurdity. The real origin of the word has given etymologists a good deal

of trouble.

[253] Robert Boyle (1627-1691), son of "the Great Earl" (of Cork). Perhaps

his best-known discovery is the law concerning the volume of gases.

[254] The real name of Eirenaeus Philalethes (born in 1622) is unknown. It

may have been Childe. He claimed to have discovered the philosopher's stone

in 1645. His tract in this work is _The Secret of the Immortal Liquor

Alkahest or Ignis-Aqua_. See note 260, _infra_.

[255] Johann Baptist van Helmont, Herr von Merode, Royenborg etc.

(1577-1644). His chemical discoveries appeared in his _Ortus medicinae_

(1648), which went through many editions.

[256] De Morgan should have written up Francis Anthony (1550-1623), whose

_Panacea aurea sive tractatus duo de auro potabili_ (Hamburg, 1619)

described a panacea that he gave for every ill. He was repeatedly

imprisoned for practicing medicine without a license from the Royal College

of Physicians.

[257] Bernardus Trevisanus (1406-1490), who traveled even through Barbary,

Egypt, Palestine, and Persia in search of the philosopher's stone. He wrote

several works on alchemy,--_De Chemica_ (1567), _De Chemico Miraculo_

(1583), _Traite de la nature de l'oeuf des philosophes_ (1659), etc., all

published long after his death.

[258] George Ripley (1415-1490) was an Augustinian monk, later a

chamberlain of Innocent VIII, and still later a Carmelite monk. His _Liber

de mercuris philosophico_ and other tracts first appeared in _Opuscula

quaedam chymica_ (Frankfort, 1614).

[259] Besides the _Opus majus_, and other of the better known works of this

celebrated Franciscan (1214-1294), there are numerous tracts on alchemy

that appeared in the _Thesaurus chymicus_ (Frankfort, 1603).

[260] George Starkey (1606-1665 or 1666) has special interest for American

readers. He seems to have been born in the Bermudas and to have obtained

the bachelor's degree in England. He then went to America and in 1646

obtained the master's degree at Harvard, apparently under the name of

Stirk. He met Eirenaeus Philalethes (see note 254 above) in America and

learned alchemy from him. Returning to England, he sold quack medicines

there, and died in 1666 from the plague after dissecting a patient who had

died of the disease. Among his works was the _Liquor Alcahest, or a

Discourse of that Immortal Dissolvent of Paracelsus and Helmont_, which

appeared (1675) some nine years after his death.