Notes

Transcriber's note: References to Notes in Volume I are shown as in the

printed book, with the resequenced footnote numbers in the Project

Gutenberg Edition (EText-No. 23100) added thus {123}.

[1] See Vol. I, page 255, note 6 {584}.

[2] "I have no need for this hypothesis."

[3] "Ah, it is a beautiful hypothesis; it explains many things."

[4] "What we know is very slight; what we don't know is immense."

[5] Brewster relates (_Life of Sir Isaac Newton_, Vol. II, p. 407) that, a

short time before his death, Newton remarked: "I do not know what I may

appear to the world, but to myself I seem to have been only like a boy

playing on the seashore, and diverting myself in now and then finding a

smoother pebble or a prettier shell than ordinary, whilst the great ocean

of truth lay all undiscovered before me."

[6] See Vol. I, p. 292, note 1 {632}.

[7] "What is all that!"

[8] "I have some good news to tell you: at the Bureau of Longitudes they

have just received a letter from Germany announcing that M. Bessel has

verified by observation your theoretical discoveries on the satellites of

Jupiter."

[9] "Man follows only phantoms."

[10] See Vol. I, page 382, note 13 {786}.

[11] Dieudonne Thiebault (1733-1807) was a Jesuit in his early life, but he

left the order and took up the study of law. In 1765 he went to Prussia and

became a favorite of Frederick the Great. He returned to France in 1785 and

became head of the Lycee at Versailles.

[12] _Memories of Twenty Years of Residence in Berlin._ There was a second

French and an English edition in 1805.

[13] Richard Joachim Heinrich von Mollendorff (1724-1816) began his career

as a page of Frederick the Great (1740) and became field marshal (1793) and

commander of the Prussian army on the Rhine (1794).

[14] Hugues Bernard Maret (1763-1839) was not Duc de Bassano in 1807, this

title not being conferred upon him until 1809. He was ambassador to England

in 1792 and to Naples in 1793. Napoleon made him head of the cabinet and

his special confidant. The Bourbons exiled him in 1816.

[15] Denis Diderot (1713-1784), whose _Lettre sur les aveugles_ (1749)

introduced him to the world as a philosopher, and whose work on the

_Encyclopedie_ is so well known.

[16] "Sir, (a + b^{n}) / n = x, whence God exists; answer!"

[17] This was one James Laurie of Musselburgh.

[18] Jelinger Cookson Symons (1809-1860) was an office-holder with a

decided leaning towards the improvement of education and social conditions.

He wrote _A Plea for Schools_ (1847), _The Industrial Capacities of South

Wales_ (1855), and _Lunar Motion_ (1856), to which last work the critic

probably refers.

[19] "Protimalethes" followed this by another work along the same line the

following year, _The Independence of the Testimony of St. Matthew and St.

John tested and vindicated by the theory of chances_.

[20] Wilson had already taken up the lance against science in his

_Strictures on Geology and Astronomy, in reference to a supposed want of

harmony between these sciences and some parts of Divine Revelation_,

Glasgow, 1843. He had also ventured upon poetry in his _Pleasures of

Piety_, Glasgow, 1837.

[21] Mrs. Borron was Elizabeth Willesford Mills before her marriage. She

made an attempt at literature in her _Sibyl's Leaves_, London (printed at

Devonport), 1826.

[22] See Vol. I, page 386, note 10 {801}.

[23] See Vol. I, page 43, notes 7 {32} and 8 {33}.

[24] His flying machine, designed in 1843, was one of the earliest attempts

at aviation on any extensive scale.

[25] Erasmus Darwin (1731-1802) was the grandfather of Charles Darwin. The

work here mentioned had great influence, being translated into French,

Portuguese, and Italian. Canning parodied it in his _Loves of the

Triangles_.

[26] See Vol. I, page 147, note 1 {312}.

[27] The notes on this page were written on the day of the funeral of

Wilbur Wright, June 1, 1912, the man who realized all of these prophecies,

and then died a victim of municipal crime,--of typhoid fever.

[28] John Charles, third Earl Spencer (1782-1845), to whose efforts the

Reform Bill was greatly indebted for its final success.

[29] This was published in London in 1851 instead of 1848.

[30] This appeared in 1846.

[31] This was done in _The Circle Squared_, published at Brighton in 1865.

[32] It first appeared in 1847, under the title, _The Scriptural Calendar

and Chronological Reformer, 1848. Including a review of tracts by Dr.

Wardlaw and others on the Sabbath question. By W. H. Black._ The one above

mentioned, for 1849, was printed in 1848, and was also by Black

(1808-1872). He was pastor of the Seventh Day Baptists and was interested

in archeology and in books. He catalogued the manuscripts of the Ashmolean

Museum at Oxford.

[33] William Upton, a Trinity College man, Dublin. He also wrote _Upton's

Physioglyphics_, London, 1844; _Pars prima. Geometria vindicata;

antiquorumque Problematum, ad hoc tempus desperatorum, Trisectionis Anguli,

Circulique Quadraturae, Solutio, per Eucliden effecta, London_ (printed at

Southampton), 1847; _The Uptonian Trisection_, London, 1866; and _The

Circle Squared_, London, 1872.

[34] For example, if [theta] = 90 deg. we should have 3 cos 30 deg. = 1

+ [root](4 - sin^2 90 deg.), or 3. 1/2 [root]3 = 1 + [root]3, or

1/2 [root]3 = 1.

[35] Nathaniel Wallich (1786-1854) was surgeon at the Danish settlement at

Serampore when the East India Company took over the control in 1807. He

entered the British medical service and was invalided to England in 1828.

His _Plantae Asiaticae Rariores_ (3 vols., London, 1830-1832) was

recognized as a standard. He became vice-president of the Linnean Society,

F. R. S., and fellow of the Royal Asiatic Society.

[36] But if [theta] = 90 deg. this asserts that

cos 30 deg. = (sin 270 deg. . cos 225 deg. + sin^2 90 deg.

. sin 225 deg.) / [root](sin^2

270 deg. . cos^2 225 deg. + sin^{4} 90 deg. + sin 270 deg.

. sin 450 deg. . sin^2 90 deg.),

or that

1/2 [root]3 = (-1 . (-1 /[root]2) + 1 . (-1/[root]2) / [root]1

. 1/2 + 1 - 1 . 1 . 1) = 0 / [root](1/2),

so that De Morgan must have made some error in copying.

[37] John Bonnycastle (died in 1821) was professor of mathematics at

Woolwich. His edition of Bossut's _History of Mathematics_ (1803), and his

works on elementary mathematics were well known.

[38] The bibliographies give Husain Rifki as the translator, a practical

geometry as the work, and 1802 as the date.

[39] See Vol. I, page 309, note 2 {670}.

[40] Probably in _The Improvement of the Mind_ which Isaac Watts

(1674-1748) published in 1741. His _Horae Lyricae_ appeared in 1706, and

the _Hymns_, by which he is still well known, in 1707.

[41] Spencer Joshua Alwyne Compton, second Marquis of Northampton

(1790-1851), was a poet, a scientist, and a statesman. He was president of

the Royal Society from 1838 to 1849.

[42] Besides the writings here mentioned Perigal published a work on

_Geometric Maps_ (London, 1853), and _Graphic Demonstrations of Geometric

Problems_ (1891).

[43] See Vol. II, page 5, note 18.

[44] James Ferguson (1710-1776) was a portrait painter, an astronomer, and

a popular writer and lecturer on various subjects.

[45] In the old ballad of King Alfred and the Shepherd, when the latter is

tempting the disguised king into his service, he says:

"Of whig and whey we have good store,

And keep good pease-straw fire."

_Whig_ is then a preparation of milk. But another commonly cited derivation

may be suspected from the word _whiggamor_ being used before _whig_, as

applied to the political party; _whig_ may be a contraction. Perhaps both

derivations conspired: the word _whiggamor_, said to be a word of command

to the horses, might contract into _whig_, and the contraction might be

welcomed for its own native meaning.--A. De M.

[46] This was p. 147 in the first edition.

[47] St. Augustine (354-430) was bishop of Hippo. His _Confessiones_, in

13 books, was written in 397, and his _De Civitate Dei_ in 426.

[48] "He was wont to indulge in certain Punic subtleties lest he should

weary the reader by much speaking."

[49] John Milner (1751-1826), bishop of Castabala, a well-known

antiquarian.

[50] It will be said that when the final happiness is spoken of in "sure

and certain hope," it is _the_ Resurrection, generally; but when afterwards

application is made to the individual, simple "hope" is all that is

predicated which merely means "wish?" I know it: but just before the

general declaration, it is declared that it _has_ pleased God of his great

mercy to _take unto Himself_, the soul of our dear brother: and between the

"hopes" hearty thanks are given that it _has_ pleased God to deliver our

dear brother out of the miseries of this wicked world, with an additional

prayer that the number of the elect may shortly be accomplished. All which

means, that our dear brother is declared to be taken to God, to be in a

place not so miserable as this world--a description which excludes the

"wicked place"--and to be of the elect. Yes, but it will be said again! do

you not know that when this Liturgy was framed, all who were not in the

road to Heaven were excommunicated burial service read over them. Supposing

the fact to have been true in old time, which is a very spicy supposition,

how does that excuse the present practice? Have you a right _always_ to say

what you believe _cannot always_ be true, because you think it was once

_always_ true? Yes, but, choose whom you please, you cannot be _certain_ He

is _not_ gone to Heaven. True, and choose which Bishop you please, you

cannot be demonstratively _certain_, he is _not_ a concealed unbeliever:

may I therefore say of the whole bench, _singulatim et seriatim_, that they

_are_ unbelievers? No! No! The voice of common sense, of which common logic

is a part, is slowly opening the eyes of the multitude to the unprincipled

reasoning of theologians. Remember 1819. What chance had Parliamentary

Reform when the House of Commons thanked the Manchester sabre-men? If you

do not reform your Liturgy, it will be reformed for you, and sooner than

you think! The dishonest interpretations, by defence of which even the

minds of children are corrupted, and which throw their shoots into

literature and commerce, will be sent to the place whence they came: and

over the door of the established organization for teaching religion will be

posted the following notice:

"Shift and Subterfuge, Shuffle and Dodge,

No longer here allowed to lodge!"

All this ought to be written by some one who belongs to the Establishment:

in him, it would be quite prudent and proper; in me, it is kind and

charitable.--A. De M.

[51] But few do have access to it, for the work is not at all common, and

this Piscator is rarely mentioned.

[52] This derivation has been omitted.--S. E. De M.

[53] A blow for a blow. Roland and Oliver were two of the paladins of

Charlemagne whose exploits were so alike that each was constantly receiving

credit for what the other did. Finally they met and fought for five days on

an island in the Rhine, but even at the end of that period it was merely a

drawn battle.

[54] "In the name of the church."

[55] "From the chair," officially.

[56] Nicholas Patrick Stephen Wiseman (1802-1865), whose elevation to the

archbishopric of Westminster and the cardinalate (1850) led to the act

prohibiting Roman Catholics from assuming episcopal titles in England, a

law that was never enforced.

[57] He was born in 1812 and was converted to Catholicism in 1839. He

founded the _Tablet_ in London in 1840, removing its office to Dublin in

1849. He became M. P. in 1852, and at the time of his death (1855) he was

preparing a memorial to the Pope asking him to annul the proclamation of an

Irish bishop prohibiting his priests from taking part in politics.

[58] John Guillim (1565-1621) was the first to systematize and illustrate

the whole science of heraldry. He published _A display of Heraldrie:

manifesting a more easie accesse to the knowledge thereof_ in 1610.

[59] "Faith."

[60] "Faithful."

[61] "For the faith vindicated."

[62] The words are of the same root, and hence our word _fiddle_. Some

suppose this root means a _rope_, which, as that to which you trust,

becomes, in one divergence, confidence itself--just as a _rock_, and other

words, come to mean reliance--and in another, a little string.--A. De M.

[63] The Greek lexicographer, a Christian, living after 1000 A. D. His

lexicon was first printed at Milan in 1499.

[64] _Skindapsos._

[65] This was John William Burgon (1813-1888), Gresham professor of

theology (1867) and dean of Chichester. He was an ultra-conservative,

opposing the revised version of the New Testament, and saying of the

admission of women to the university examinations that it was "a thing

inexpedient and immodest."

[66] _Ekklesia_, or _ecclesia_.

[67] _Ennomos ekklesia._

[68] "Without doubt I shall perish forever."

[69] "Every man is an animal." "Sortes is a man." "Sortes is an animal."

[70] "For a special purpose."

[71] Heraclitus of Ephesus, the weeping philosopher, 6th century B. C.

[72] Democritus, the laughing philosopher, founder of the atomistic theory,

5th century B. C.

[73] "Ends to which."

[74] "Ends from which."

[75] "In just as many syllables," "With just as many letters," "In just as

many words."

[76] "I shall make a way," "I shall find a way."

[77] The notion that the Evil Spirit is a functionary liable to be

dismissed for not attending to his duty, is, so far as my reading goes,

utterly unknown in theology. My first wrinkle on the subject was the remark

of the Somersetshire farmer upon Palmer the poisoner-- "Well! if the Devil

don't take he, he didn't ought to be allowed to be devil no longer."--A. De

M.

William Palmer (1824-1856) was a member of the Royal College of Surgeons

and practised medicine at London. He was hanged in 1856 for having poisoned

a friend and was also suspected of having poisoned his wife and brother for

their insurance money, besides being guilty of numerous other murders. His

trial was very much in the public attention at the time.

[78] Advantages and dangers.

[79] The old priory of St. Mary of Bethlehem in London, was used as an

asylum for the insane. The name was corrupted to Bedlam.

[80] Referring to the common English pronunciation of St. John, almost

Sinjin. John St. John Long (1798-1834), an Irishman by birth, practised

medicine in London. He claimed to have found a specific for rheumatism and

tuberculosis, but upon the death of one of his patients in 1830 he was

tried for manslaughter. He died of tuberculosis four years later, refusing

to take his own treatment.

[81] William of Occam (d. 1349), so called from his birthplace, Ockham, in

Surrey. He was a Franciscan, and lectured on philosophy in the Sorbonne.

[82] He signs himself "James Hopkins, schoolmaster," and this seems to have

been his only published effort.

[83] Joseph Ady (1770-1852) was a famous swindler. One of his best-known

schemes was to send out letters informing the recipients that they would

learn something to their advantage on payment of a certain sum. He spent

some time in prison.

[84] Sir Peter Laurie (c. 1779-1861) was worth referring to, for he was

prominent as a magistrate and was honored because of his interest in all

social reforms. He made a fortune as a contractor, became sheriff of London

in 1823, and was knighted in the following year. He became Lord Mayor of

London in 1832.

[85] See Vol. I, page 321, note 2 {691}. The _Astronomy in a nutshell_

appeared in 1860. _The Herald of Astrology_ was first published in London

in 1831, "by Zadkiel the Seer." It was continued as _The Astrological

Almanac_ (London, 1834), as _Zadkiel's Almanac and Herald of Astrology_

(_ibid._, 1835, edited by R. J. Morrison, and subsequently by A. J.

Pearce), and as _Raphael's Prophetic Almanac_ (1840-1855).

[86] See Vol. I, page 172, note 3 {382}.

[87] See Vol. I, page 87, note 4 {133}.

[88] Franz Xaver, Freiherr von Zach (1754-1832) was director of the

observatory at Seeberge near Gotha. He wrote the _Tabulae speciales

aberrationis et mutationis_ (1806-7), _Novae et correctae tabulae solis_

(1792), and _L'attraction des montagnes et ses effets sur le fil a plomb_

(1814).

[89] Jean Louis Pons (1761-1831) was connected with the observatory at

Marseilles for thirty years (1789-1819). He later became director of the

observatory at Marlia, near Lucca, and subsequently filled the same office

at Florence. He was an indefatigable searcher for comets, discovering 37

between 1801 and 1827, among them being the one that bears Encke's name.

[90] This hypothesis has now become an established fact.

[91] John Chetwode Eustace (c. 1762-1815) was born in Ireland. Although a

Roman Catholic priest he lived for a time at Cambridge where he did some

tutoring. His _Classical Tour_ appeared in 1813 and went through several

editions.

[92] "Crimes should be exposed when they are punished, but disgraceful acts

should be hidden."

[93] Henri Hureau de Senarmont (1808-1862) was professor of mineralogy at

the _Ecole des mines_ and examiner at the _Ecole polytechnique_ at Paris.

[94] Augustin Jean Fresnel (1788-1827), "Ingenieur des ponts et chaussees,"

gave the first experimental proofs of the wave theory of light. He studied

the questions of interference and polarization, and determined the

approximate velocity of light.

[95] "As is my custom."

[96] Francis Heywood (1796-1858) made the first English translation of

Kant's _Critick of Pure Reason_ (1838, reprinted in 1848). The _Analysis_

came out, as here stated, in 1844.

[97] Louise Renee de Keroualle, Duchess of Portsmouth and Aubigny

(1649-1734), was a favorite of Charles II. She used her influence to keep

him under the control of Louis XIV.

[98] William Chiffinch (c. 1602-1688) was page of the king's bed-chamber

and keeper of the private closet to Charles II. He was one of the king's

intimates and was an unscrupulous henchman.

[99] "Well devised."

[100] "John Bellingham Inglis. His _Philobiblion_ "translated from the

first edition (of Ricardus d'Aungervile, Bishop of Durham), 1473," appeared

at London in 1832. It was republished in America (Albany, N. Y.) in 1864.

[101] "What are you laughing at?"

[102] See Vol. I, page 314, note 4 {681}.

[103] See Vol. I, page 112, note 7 {211}.

[104] Referring to Hamilton's edition of the _Collected Works of Dugald

Stewart_, 10 volumes, Edinburgh, 1854-58. It is not commonly remembered

that Stewart (1753-1828) taught mathematics at the University of Edinburgh

before he took up philosophy.

[105] This was Hamilton's edition of the _Works of Thomas Reid_ (2 vols.,

Edinburgh, 1846-1863). Reid (1710-1796) included mathematics in his work in

philosophy at Aberdeen. In 1764 he succeeded Adam Smith at Glasgow.

[106] Edward Irving (1792-1834), the famous preacher. At first he assisted

Dr. Chalmers at Glasgow, but in 1822 he went to London where he met with

great success. A few years later he became mentally unbalanced and was

finally expelled from his church (1832) for heresy. He was a great friend

of Carlyle.

[107] He also wrote a number of other paradoxes, including _An Essay

towards a Science of Consciousness_ (1838), _Instinctive Natural Religion_

(1858), _Popular Treatise on the structure, diseases, and treatment of the

human teeth_ (1837), and _On Headache_ (1859).

[108] James Smith (1801-1857), known as Shepherd Smith, was a socialist and

a mystic, with a philosophy that was wittily described as "Oriental

pantheism translated into Scotch." He was editor of several journals.

[109] Joanna Southcott (1750-1814) was known for her rhyming prophecies in

which she announced herself as the woman spoken of in Revelations xii. She

had at one time as many as 100,000 disciples, and she established a sect

that long survived her.

[110] Thales, c. 640-548 B. C.

[111] Pythagoras, 580-501 B. C.

[112] Anaxagoras, 499-428 B. C., the last of the Ionian school, teacher of

Euripides and Pericles. Plutarch speaks of him as having squared the

circle.

[113] Oinopides of Chios, contemporary of Anaxagoras. Proclus tells us that

Oinopides was the first to show how to let fall a perpendicular to a line

from an external point.

[114] Bryson and Antiphon, contemporaries of Socrates, invented the

so-called method of exhaustions, one of the forerunners of the calculus.

[115] He wrote, c. 440 B. C., the first elementary textbook on mathematics

in the Greek language. The "lunes of Hippocrates" are well known in

geometry.

[116] Jabir ben Aflah. He lived c. 1085, at Seville, and wrote on astronomy

and spherical trigonometry. The _Gebri filii Affla Hispalensis de

astronomia libri_ IX was published at Nuremberg in 1533.

[117] Hieronymus Cardanus, or Girolamo Cardano (1501-1576), the great

algebraist. His _Artis magnae sive de regulis Algebrae_ was published at

Nuremberg in 1545.

[118] Nicolo Tartaglia (c. 1500-1557), the great rival of Cardan.

[119] See note 5 {98}, Vol. I, page 69.

[120] See note 10 {124}, Vol. I., page 83.

[121] See note 9 {123}, Vol. I, page 83.

[122] Pierre Herigone lived in Paris the first half of the 17th century.

His _Cours mathematique_ (6 vols., 1634-1644) had some standing but was not

at all original.

[123] Franciscus van Schooten (died in 1661) was professor of mathematics

at Leyden. He edited Descartes's _La Geometrie_.

[124] Florimond de Beaune (1601-1652) was the first Frenchman to write a

commentary on Descartes's _La Geometrie_. He did some noteworthy work in

the theory of curves.

[125] See note 3 {23}, Vol. I, page 41.

[126] Olivier de Serres (b. in 1539) was a writer on agriculture. Montucla

speaks of him in his _Quadrature du cercle_ (page 227) as having asserted

that the circle is twice the inscribed equilateral triangle, although, as

De Morgan points out, this did not fairly interpret his position.

[127] Anghera wrote not only the three works here mentioned, but also the

_Problemi del piu alto interesse scientifico, geometricamente risoluti e

dimostrati_, Naples, 1861. His quadrature was defended by Giovanni Motti in

a work entitled _Matematica Vera. Falsita del sistema ciclometrico

d'Archimede, quadratura del cerchio d'Anghera, ricerca algebraica dei lati

di qualunque poligono regolare inscritto in un circolo_, Voghera, 1877. The

_Problemi_ of 1861 contains Anghera's portrait, and states that he lived at

Malta from 1849 to 1861. It further states that the Malta publications are

in part reproduced in this work.

[128] This was his friend Paolo Pullicino whose _Elogio_ was pronounced by

L. Farrugia at Malta in 1890. He wrote a work _La Santa Effegie della Blata

Vergine Maria_, published at Valetta in 1868.

[129] St. Vitus, St. Modestus, and St. Crescentia were all martyred the

same day, being torn limb from limb after lions and molten lead had proved

of no avail. At least so the story runs.

[130] The reference is to Cardinal Wiseman. See Vol. II, page 26, note 56.

[131] "Worthy of esteem."

[132] Pedro de Ribadeneira (Ribadeneyra, Rivadeneira), was born at Toledo

in 1526 and died in 1611. He held high position in the Jesuit order. The

work referred to is the _Flos Sanctorum o libro de las vidas de los

santos_, of which there was an edition at Barcelona in 1643. His life of

Loyola (1572) and _Historia ecclesiastica del Cisma del reino de

Inglaterra_ were well known.

[133] Caesar Baronius (1538-1607) was made a cardinal in 1595 and became

librarian at the Vatican in 1597. The work referred to appeared at Rome in

1589.

[134] Mrs. Jameson's (1794-1860) works were very popular half a century

ago, and still have some circulation among art lovers. The first edition of

the work mentioned appeared in 1848.

[135] The barnyard cock.

[136] Shanks did nothing but computing. The title should, of course, read

"to 607 Places of _Decimals_." He later carried the computation to 707

decimal places. (_Proc. Roy. Society_, XXI, p. 319.) He also prepared a

table of prime numbers up to 60,000. (_Proc. Roy. Society_, XXII, p. 200.)

[137] See Vol. I, page 42, note 4 {24}.

[138] See Vol. I, page 64, note 1 {78}.

[139] See Vol. I, page 328, note 1 {704}.

[140] George Suffield published _Synthetic Division in Arithmetic_, to

which reference is made, in 1863.

[141] John Robert Lunn wrote chiefly on Church matters, although he

published a work on motion in 1859.

[142] Jean Baptiste Joseph, Baron Fourier (1768-1830), sometime professor

in the Military School at Paris, and later at the _Ecole polytechnique_. He

is best known by his _Theorie analytique de la chaleur_ (Paris, 1822), in

which the Fourier series is used. The work here referred to is the _Analyse

des equations determinees_ (Paris, 1831).

[143] William George Horner (1786-1837) acquired a name for himself in

mathematics in a curious manner. He was not a university man nor was he a

mathematician of any standing. He taught school near Bristol and at Bath,

and seems to have stumbled upon his ingenious method for finding the

approximate roots of numerical higher equations, including as a special

case the extracting of the various roots of numbers. Davies Gilbert

presented the method to the Royal Society in 1819, and it was reprinted in

the _Ladies' Diary_ for 1838, and in the _Mathematician_ in 1843. The

method was original as far as Horner was concerned, but it is practically

identical with the one used by the Chinese algebraist Ch'in Chiu-shang, in

his _Su-shu Chiu-chang_ of 1247. But even Ch'in Chiu-shang can hardly be

called the discoverer of the method since it is merely the extension of a

process for root extracting that appeared in the _Chiu-chang Suan-shu_ of

the second century B. C.

[144] He afterwards edited Loftus's _Inland Revenue Officers' Manual_

(London, 1865). The two equations mentioned were x^3 - 2x = 5 and y^3 -

90y^2 + 2500y - 16,000 = 0, in which y = 30 - 10x. Hence each place of y is

the complement of the following place of x with respect to 9.

[145] Probably the John Power Hicks who wrote a memoir on T. H. Key,

London, 1893.

[146] Possibly the one who wrote on the quadrature of the circle in 1881.

[147] As it is. But what a pity that we have not 12 fingers, with

duodecimal fractions instead of decimals! We should then have 0.6 for 1/2,

0.4 for 1/3, 0.8 for 2/3, 0.3 for 1/4, 0.9 for 3/4, and 0.16 for 1/8,

instead of 0.5, 0.333+, 0.666+, 0.25, 0.75, and 0.125 as we now have

with our decimal system. In other words, the most frequently used

fractions in business would be much more easily represented on the

duodecimal scale than on the decimal scale that we now use.

[148] He wrote Hints for an _Essay on Anemology and Ombrology_ (London,

1839-40) and _The Music of the Eye_ (London, 1831).

[149] Brigham Young (1801-1877) was born at Whitingham, Vermont, and

entered the Mormon church in 1832. In 1840 he was sent as a missionary to

England. After the death of Joseph Smith he became president of the Mormons

(1847), leading the church to Salt Lake City (1848).

[150] Joseph Smith (1805-1844) was also born in Vermont, and was four years

the junior of Brigham Young. The _Book of Mormon_ appeared in 1827, and the

church was founded in 1830. He was murdered in 1844.

[151] Orson Pratt (1811-1881) was one of the twelve apostles of the Mormon

Church (1835), and made several missionary journeys to England. He was

professor of mathematics in the University of Deseret (the Mormon name for

Utah). Besides the paper mentioned Pratt wrote the _Divine Authenticity of

the Book of Mormon_ (1849), _Cubic and Biquadratic Equations_ (1866), and a

_Key to the Universe_ (1866).

[152] "It does not follow."

[153] Dryden (1631-1700) published his _Religio Laici_ in 1682. The use of

the word "proportion" in the sense of ratio was common before his time, but

he uses it in the sense of having four terms; that is, that price is to

price as offence is to offence.

[154] Olinthus Gilbert Gregory (1774-1841) succeeded Hutton as professor of

mathematics at Woolwich. He was, with De Morgan, much interested in

founding the University of London. He wrote on astronomy (1793), mechanics

(1806), practical mathematics (1825), and Christian evidences (1811).

[155] See Vol. I, page 220, note 6 {482}. The _Pensees_ appeared

posthumously in 1670.

[156] "The right thing to do is not to wager at all." "Yes, but you ought

to wager; you have started out; and not to wager at all that God exists is

to wager that he does not exist."

[157] He lived about 300 A.D., in Africa, and wrote _Libri septem adversus

Gentes_. This was printed at Rome in 1542-3.

[158] Pierre Bayle (1647-1706) was professor of philosophy at the

Prostestant University at Sedan from 1675 until its dissolution in 1681. He

then became professor at Rotterdam (1681-1693). In 1684 he began the

publication of his journal of literary criticism _Nouvelles de la

Republique des Lettres_. He is best known for his erudite _Dictionnaire

historique et critique_ (1697).

[159] "But Christ himself does not prove what he promises. It is true. For,

as I have said, there cannot be any absolute proof of future events.

Therefore since it is a condition of future events that they cannot be

grasped or comprehended by any efforts of anticipation, is it not more

reasonable, out of two alternatives that are uncertain and that are hanging

in doubtful expectation, to give credence to the one that gives some hope

rather than to the one that offers none at all? For in the former case

there is no danger if, as is said to threaten, it becomes empty and void;

while in the latter case the danger is greatest, that is, the loss of

salvation, if when the time comes it is found that it was not a falsehood."

[160] Gregg wrote several other paradoxes, including the following: _The

Authentic Report of the extraordinary case of Tresham Dames Gregg ... his

committal to Bridewell for refusing to give his recognizance_ (Dublin,

1841), _An Appeal to Public Opinion upon a Case of Injury and Wrong ... in

the case of a question of prerogative that arose between_ [R. Whately] _...

Archbishop of Dublin and the author_ (London, 1861), _The Cosmology of Sir

Isaac Newton proved to be in accordance with the Bible_ (London, 1871),

_The Steam Locomotive as revealed in the Bible_ (London 1863) and _On the

Sacred Law of 1866, conferring perpetual life with immunity from decay and

disease. A cento of decisive scriptural oracles strangely discovered_

(London and Dublin, 1875). These titles will help the reader to understand

the man whom De Morgan so pleasantly satirizes.

[161] See Vol. I, page 261, note 2 {592}.

[162] "They have found it."

[163] The late Greeks used the letters of their alphabet as numerals,

adding three early alphabetic characters. The letter [chi] represented 600,

[xi] represented 60, and [digamma] stood for 6. This gives 666, the number

of the Beast given in the Revelation.

[164] "Allowing for necessary exceptions."

[165] Mr. Gregg is not alone in his efforts to use the calculus in original

lines, as any one who has read Herbart's application of the subject to

psychology will recall.

[166] See Vol. I, page 105, note 4 {188}; page 109, note 1 {197}.

[167] The full title shows the plan,--_The Decimal System as a whole, in

its relation to time, measure, weight, capacity, and money, in unison with

each other._ But why is this so much worse than the French plan of which we

have only the metric system and the decimal division of the angle left?

[168] One of the brothers of Sir Isaac Pitman (1813-1897), the inventor of

modern stenography. Of these brothers, Benjamin taught the art in America,

Jacob in Australia, and Joseph, Henry, and Frederick in England.

[169] For example, _The Phonographic Lecturer_ (London, 1871 etc.), _The

Phonographic Student_ (1867, etc.), and _The Shorthand Magazine_ (1866,

etc.).

[170] See Vol. II, page 68, note 148.

[171] It involves the theory of non-Euclidean geometry, Euclid's postulate

of parallels being used in proving this theorem.

[172] Referring to the fact that none of the works of Thales is extant.

[173] The author was one B. Bulstrode. Parts 4 and 5 were printed at

Calcutta.

[174] See Vol. II, page 5, note 18.

[175] See Vol. I, page 85, note 2 {129}.

[176] Alexander Vasilievich Suvaroff (1729-1800), a Russian general who

fought against the Turks, in the Polish wars, and in the early Napoleonic

campaigns. When he took Ismail in 1790 he sent this couplet to Empress

Catherine.

[177] "Newton hath determined rightly," "Newton hath not determined

rightly."

[178] See Vol. I, page 288, note 3 {621}.

[179] See Vol. I, page 326, note 1 {700}.

[180] "With great honor."

[181] Apparently unknown to biographers. He seems to have written nothing

else.

[182] Captain Marryat (1792-1848) published _Snarley-yow, or the Dog Fiend_

in 1837.

[183] He is not known to biographers, and published nothing else under this

name.

[184] See Vol. I, page 80, note 5 {119}.

[185] He published a _Family and Commercial Illustrated Almanack and Year

Book ... for 1861_ (Bath, 1860).

[186] Louis Dutens (1730-1812) was born at Tours, but went to England as a

young man. He made the first collection of the works of Leibnitz, against

the advice of Voltaire, who wrote to him: "Les ecrits de Leibnitz sont

epars comme les feuilles de la Sybille, et aussi obscurs que les ecrits de

cette vieille." The work appeared at Geneva, in six volumes, in 1769.

[187] Mungo Park (1771-1806), the first European to explore the Niger

(1795-6). His _Travels in the Interior of Africa_ appeared in 1799. He died

in Africa.

[188] Gerhard Mercator (1512-1594) the well-known map maker of Louvain. The

"Mercator's Projection" was probably made as early as 1550, but the

principle of its construction was first set forth by Edward Wright (London,

1599).

[189] Quirico Barilli Filopanti wrote a number of works and monographs. He

succeeded in getting his _Cesare al Rubicone_ and _Degli_ _usi idraulici

della Tela_ in the _Memoria letta ... all' Accademia delle Scienze in

Bologna_ (1847, 1866). He also wrote _Dio esiste_ (1881), _Dio Liberale_

(1880), and _Sunto della memoria sulle geuranie ossia di alcune singolari

relazioni cosmiche della terra e del cielo_ (1862).

[190] The periods of disembodiment may be interesting. They will be seen

from the following dates: Descartes (1596-1650), William III (1650-1702);

Roger Bacon (1214 to c. 1294), Boccaccio (1313-1375). Charles IX was born

in 1550 and died in 1574.

[191] His real name was Frederick Parker, and he wrote several works on the

Greek language and on religion. Among these were a translation of the New

Testament from the Vatican MS. (1864), _The Revealed History of Man_

(1854), _An Enquiry respecting the Punctuation of Ancient Greek_ (1841),

and _Rules for Ascertaining the sense conveyed in Ancient Greek

Manuscripts_ (1848, the seventh edition appearing in 1862).

[192] See Vol. I, page 352, second note 1 {736}.

The literature on the subject of the Great Pyramid, considered from the

standpoint of metrology, is extensive.

[193] See Vol. I, page 80, note 5 {119}.

[194] Sir Philip Francis (1740-1818) was a Whig politician. The evidence

that he was the author of the _Letters of Junius_ (1769-1772) is purely

circumstantial. He was clerk in the war office at the time of their

publication. In 1774 he was made a member of the Supreme Council of Bengal,

and was a vigorous opponent of Warren Hastings, the two fighting a duel in

1780. He entered parliament in 1784 and was among the leaders in the

agitation for parliamentary reform.

[195] Mrs. Cottle published a number of letters that attracted attention at

the time. Among these were letters to the emperor of France and king of

Sardinia (1859) relating to the prophecies of the war between France and

Austria; to G. C. Lavis and Her Majesty's Ministers (1859) relating to her

claims as a prophetess; and to the "Crowned Heads" at St. James, the King

of Prussia, and others (1860), relating to certain passages of Scripture.

She also wrote _The Lamb's Book of Life for the New Jerusalem Church and

Kingdom, interpreted for all nations_ (1861).

[196] See Vol. I, page 315, note 2 {685}, and Vol. II, page 58, note 109.

[197] A Congregational minister, who published a number of sermons, chiefly

obituaries, between 1804 and 1851. His _Frailty of Human Life_, two sermons

delivered on the occasion of the death of Princess Charlotte, went through

at least three editions.

[198] He was secretary of the Congregational Board and editor of the

_Congregational Year Book_ (from 1846) and the _Congregational Manual_.

[199] Frederick Denison Maurice (1805-1872) began his preaching as a

Unitarian but entered the Established Church in 1831, being ordained in

1834. He was professor of English and History at King's College, London,

from 1840 to 1853. He was one of the founders of Queen's College for women,

and was the first principal of the Working Men's College, London. The

subject referred to by De Morgan is his expression of opinion in his

_Theological Essays_ (1853) that future punishment is not eternal. As a

result of this expression he lost his professorship at King's College. In

1866 he was made Knightbridge Professor of Casuistry, Moral Theology, and

Moral Philosophy at Cambridge.

[200] See Vol. I, page 46, note 1 {42}. Besides the books mentioned in

this list he wrote _The Ratio between Diameter and Circumference

demonstrated by angles, and Euclid's Theorem, Proposition 32, Book I,

proved to be fallacious_ (Liverpool, 1870). This is the theorem which

asserts that the exterior angle of a triangle is equal to the sum of the

two opposite interior angles, and that the sum of the interior angles

equals two right angles. He also published his _Curiosities of Mathematics_

in 1870, a work containing an extensive correspondence with every one who

would pay any attention to him. De Morgan was then too feeble to show any

interest in the final effort of the subject of some of his keenest satire.

[201] See Vol. I, page 332, note 4 {709}.

[202] See Vol. I, page 101, note 4 {174}.

[203] "The circle-squaring disease"; literally, "the circle-measuring

disease."

[204] See Vol. II, page 63, note 136.

[205] William Rutherford (c. 1798-1871), teacher of mathematics at

Woolwich, secretary of the Royal Astronomical Society, editor of _The

Mathematician_, and author of various textbooks. _The Extension of [pi] to

440 places_, appeared in the _Proceedings_ of the Royal Society in 1853 (p.

274).

[206] Charles Knight (1791-1873) was associated with De Morgan for many

years. After 1828 he superintended the publications of the Society for the

Diffusion of Useful Knowledge, to which De Morgan contributed, and he

edited the _Penny Cyclopedia_ (1833-1844) for which De Morgan wrote the

articles on mathematics.

[207] Sir William Hamilton. See Vol. I, page 112, note 7 {211}.

[208] Adam Smith (1723-1790) was not only known for his _Wealth of Nations_

(1776), but for his _Theory of Moral Sentiments_ (1759), published while he

was professor of moral philosophy at Glasgow (1752-1764). He was Lord

Rector of the university in 1787.

[209] See Vol. I, page 332, note 4 {709}.

[210] "Whip."

[211] "Terrible lash."

[212] "An accomplished fact [an accomplished fault]."

[213] See _Extracts from the Diary and Letters of Mrs. Mary Cobb_, London,

1805.

[214] "Gentle in manner."

[215] "Brave in action." The motto of Earl Newborough was "Suaviter in

modo, fortiter in re."

[216] "Reduction to an absurdity," a method of proof occasionally used in

geometry and in logic.

[217] "He has lost the right of being moved (struck) by evidence."

[218] For _radix quadratus_. The usual root sign is supposed to be derived

from _r_ (for radix), and at one time _q_ was commonly used for square, as

in Viete's style of writing Aq for A^2.

[219] The Garde Douloureuse was a castle in the marches of Wales and

received its name because of its exposure to attacks by the Welsh.

[220] "Out of the fight."

[221] "Hidden."

[222] John Cam Hobhouse (1786-1869), Baron Broughton, was committed to

Newgate for two months in 1819 for his anonymous pamphlet, _A Trifling

Mistake_. This was a great advertisement for him, and upon his release he

was at once elected to parliament for Westminster. He was a strong

supporter of all reform measures, and was Secretary for War in 1832. He was

created Baron Broughton de Gyfford in 1851.

[223] Thomas Erskine (1750-1823), the famous orator. He became Lord

Chancellor in 1806, but sat in the House of Commons most of his life.

[224] The above is explained in the MS. by a paragraph referring to some

anagrams, in one of which, by help of the orthography suggested, a

designation for this cyclometer was obtained from the letters of his

name.--S. E. De M.

[225] "A personal verb agrees with its subject."

[226] See Vol. I, page 326, note 1 {700}.

[227] See Vol. I, page 326, note 2 {701}.

[228] Apparently unknown to biographers.

[229] The _Bibliotheca Mathematica_ of Ludwig Adolph Sohncke (1807-1853),

professor of mathematics at Koenigsberg and Halle, covered the period from

1830 to 1854, being completed by W. Engelmann. It appeared in 1854.

[230] See Vol. I, page 392, note 2 {805}.

[231] See Vol. I, page 43, note 7 {32}.

[232] See Vol. II, page 91, note 187.

[233] Mason made a notable balloon trip from London to Weilburg, in the

Duchy of Nassau, in November, 1836, covering 500 miles in 18 hours. He

published an account of this trip in 1837, and a work entitled

_Aeronautica_ in 1838.

[234] William Harrison Ainsworth (1805-1885) the novelist.

[235] On this question see Vol. I, page 326, note 2 {701}.

[236] Major General Alfred Wilks Drayson, author of various works on

geology, astronomy, military surveying, and adventure.

[237] Hailes also wrote several other paradoxes on astronomy and circle

squaring during the period 1843-1872.

[238] See Vol. I, page 43, note 8 {33}.

[239] See Vol. I, page 43, note 7 {32}.

[240] "Very small errors are not to be condemned."

[241] He seems to have written nothing else.

[242] Besides the paradoxes here mentioned by De Morgan he wrote several

other works, including the following: _Abriss der Babylonisch-Assyrischen

Geschichte_ (Mannheim, 1854), _A Popular Inquiry into the Moon's rotation

on her axis_ (London, 1856), _Practical Tables for the reduction of the

Mahometan dates to the Christian kalendar_ (London, 1856), _Grundzuege einer

neuen Weltlehre_ (Munich, 1860), and _On the historical Antiquity of the

People of Egypt_ (London, 1863).

[243] Dircks (1806-1873) was a civil engineer of prominence, and a member

of the British Association and the Royal Society of Edinburgh. He wrote

(1863) on "Pepper's Ghost," an ingenious optical illusion invented by him.

There was a second edition of the _Perpetuum Mobile_ in 1870.

[244] George Stephenson (1781-1848), the inventor of the first successful

steam locomotive. His first engine was tried in 1814.

[245] Robert Stephenson (1803-1859), the only son of George. Most of the

early improvements in locomotive manufacture were due to him. He was also

well known for his construction of great bridges.

[246] "In its proper place."

[247] "A fool always finds a bigger fool to admire him."

[248] See Vol. I, page 43, note 7 {32}.

[249] See Vol. I, page 43, note 8 {33}.

[250] See Vol. I, page 85, note 2 {129}.

[251] See Vol. I, page 390, note 1 {390}.

[252] From 1823 to 1852 it was edited by I. C. Robertson; from 1852 to 1857

by R. A. Brooman; and from 1857 to 1863 by Brooman and E. J. Reed.

[253] Sir James Ivory (1765-1842) was, as a young man, manager of a flax

mill in Scotland. In 1804 he was made professor of mathematics at the Royal

Military College, then at Marlow and later at Sandhurst. He was deeply

interested in mathematical physics, and there is a theorem on the

attraction of ellipsoids that bears his name. He was awarded three medals

of the Royal Society, and was knighted together with Herschel and Brewster,

in 1831.

[254] See Vol. I, page 56, note 1 {64}.

[255] See Vol. I, page 153, note 5 {338}.

[256] See Vol. I, page 309, note 2 {670}.

[257] See Vol. I, page 87, note 4 {133}.

[258] George Canning (1770-1857), the Tory statesman and friend of Scott,

was much interested in founding the _Quarterly Review_ (1808) and was a

contributor to its pages.

[259] See Vol. I, page 186, note 14 {418}.

[260] See Vol. II, page 141, note 252.

[261] De Morgan had a number of excellent articles in this publication.

[262] See Vol. I, page 279, note 1 {611}.

[263] James Orchard Halliwell (1820-1889), afterwards Halliwell-Phillips,

came into prominence as a writer at an early age. When he was seventeen he

wrote a series of lives of mathematicians for the _Parthenon_. His _Rara

Mathematica_ appeared when he was but nineteen. He was a great bibliophile

and an enthusiastic student of Shakespeare.

[264] This was written at the age of twenty-two.

[265] The subject of this criticism is of long past date, and as it has

only been introduced by the author as an instance of faulty editorship, I

have omitted the name of the writer of the libel, and a few lines of

further detail.--S. E. De M.

[266] "Condemned souls."

[267] The editor of the _Mechanics' Magazine_ died soon after the above was

written.--S. E. De M.

[268] Thomas Stephens Davies (1795-1851) was mathematical master at

Woolwich and F. R. S. He contributed a series of "Geometrical Notes" to the

_Mechanics' Magazine_ and edited the _Mathematician_. He also published a

number of text-books.

[269] See Vol. II, page 66, note 143.

[270] The _Dictionary of Greek and Roman Biography_ (1849), edited by Sir

William Smith (1813-1893), whose other dictionaries on classical and

biblical matters are well known.

[271] "O J. S.! This is the worst! the greatest possible injury!"

[272] See Vol. I, page 44, note 9 {34} and page 110, note 5 {201}.

[273]

"If there's a man whom the judge's pitiless sentence awaiteth,

His head condemned to penalties and tribulations,

Let neither penitentiaries tire him with laborer's burdens

Nor let his stiffened hands be harrassed by work in the mines.

He must square the circle! For what else do I care?--all

Known punishments this one task hath surely included."

[274] Houlston was in the customs service. He also published _Inklings of

Areal Autometry_, London, 1874.

[275] This is Frederick C. Bakewell. He had already published _Natural

Evidence of a Future Life_ (London, 1835), _Philosophical Conversations_

(London, 1833, with other editions), and _Electric Science_ (London, 1853,

with other editions).

[276] Henry F. A. Pratt had already published _A Dissertation on the power

of the intercepted pressure of the Atmosphere_ (London, 1844) and _The

Genealogy of Creation_ (1861). Later he published a work _On Orbital

Motion_ (1863), and _Astronomical Investigations_ (1865).

[277] See Vol. I, page 260, note 1 {591}.

[278] Thomas Rawson Birks (1810-1883), a theologian and controversialist,

fellow of Trinity College, Cambridge, and (1872) professor of moral

philosophy in that university. He wrote _Modern Rationalism_ (1853), _The

Bible and Modern Thought_ (1861), _The First Principles of Moral Science_

(1873), and _Modern Physical Fatalism and the Doctrine of Evolution_

(1876), the last being an attack on Herbert Spencer's _First Principles_.

[279] Pseudonym for William Thorn. In the following year (1863) he

published a second work, _The Thorn-Tree: being a History of Thorn

Worship_, a reply to Bishop Colenso's work entitled _The Pentateuch and the

Book of Joshua critically examined_.

[280] Besides _The Pestilence_ (1866) he published _The True Church_

(1851), _The Church and her destinies_ (1855), _Religious reformation

imperatively demanded_ (1864), and _The Bible plan unfolded_ (second

edition, 1872).

[281] See Vol. II, page 97, note 195.

[282] Sir George Cornewall Lewis (1806-1863) also wrote an _Essay on the

Origin and Formation of the Romance Languages_ (1835), an _Essay on the

Government of Dependencies_ (1841), and an _Essay on Foreign Jurisdiction

and the Extradition of Criminals_ (1859). He was Chancellor of the

Exchequer in 1855 and Home Secretary in 1859.

[283] Henry Malden (1800-1876), a classical scholar, fellow of Trinity

College, Cambridge, and professor of Greek at University College

(1831-1876), then (1831) the University of London. He wrote a _History of

Rome to 390 B. C._ (1830), and _On the Origin of Universities and

Academical Degrees_ (1835).

[284] Henry Longueville Mansel (1820-1871), theologian and metaphysician,

reader in theology at Magdalen College, Oxford (1855), and professor of

ecclesiastical history and Dean of St. Paul's (1866). He wrote on

metaphysics, and his Bampton Lectures (1858) were reprinted several times.

[285] "Hejus gave freely, gave freely. God is propitious, God is favorable

to him who gives freely. God is honored with a banquet of eggs at the cross

roads, the god of the world. God, with benignant spirit, desired in

sacrifice a goat, a bull to be carried within the precincts of the holy

place. God, twice propitiated, blesses the pit of the sacred libation."

[286] Eudoxus of Cnidus (408-355 B. C.) had much to do with the early

scientific astronomy of the Greeks. The fifth book of Euclid is generally

attributed to him. His astronomical works are known chiefly through the

poetical version of Aratus mentioned in note 13, page 167.

[287] Simplicius, a native of Cilicia, lived in the 6th century of our era.

He was driven from Athens by Justinian and went to Persia (531), but he

returned later and had some fame as a teacher.

[288] See Vol. I, page 160, note 3 {348}.

[289] See Vol. I, page 76, note 3 {112}.

[290] "Through right and wrong."

[291] "It is therefore to arrive at this parallelism, or to preserve it,

that Copernicus feared to be obliged to have recourse to this equal and

opposite movement which destroys the effect which he attributed so freely

to the first, of deranging the parallelism."

[292] A contemporary of Plato and a disciple of Aristotle.

[293] Meton's solstice, the beginning of the Metonic cycles, has been

placed at 432 B. C. Ptolemy states that he made the length of the year

365-1/4 + 1/72 days.

[294] Aratus lived about 270 B. C., at the court of Antigonus of Macedonia,

and probably practiced medicine there. He was the author of two

astronomical poems, the [Greek: Phainomena], apparently based on the lost

work of Eudoxus, and the [Greek: Dioseeia] based on Aristotle's

_Meteorologica_ and _De Signis Ventorum_ of Theophrastus.

[295] "The nineteen (-year) cycle of the shining sun."

[296] Claudius Salmasius (1588-1653), or Claude Saumaise, was a

distinguished classicist, and professor at the University of Leyden. The

word [Greek: eleioio] means Elian, thus making the phrase refer to the

brilliant one of Elis.

[297] Sir William Brown (1784-1864). In 1800 the family moved to Baltimore,

and there the father, Alexander Brown, became prominent in the linen trade.

William went to Liverpool where he acquired great wealth as a merchant and

banker. He was made a baronet in 1863.

[298] Robert Lowe (1811-1892), viscount Sherbrooke, was a fellow of

Magdalen College, Oxford (1835). He went to Australia in 1842 and was very

successful at the bar. He returned to England in 1850 and became leader

writer on the _Times_. He was many years in parliament, and in 1880 was

raised to the peerage.

[299] See Vol. I, page 42, note 4 {24}.

[300] Francis Walkingame (fl. about 1751-1785), whose _Tutor's Assistant_

went through many editions from 1751-1854.

[301] Davies Gilbert (1767-1839). His family name was Giddy, but he assumed

his wife's name. He sat in parliament from 1806 to 1832. In 1819 he secured

the establishment of the Cape of Good Hope observatory. He was Treasurer

(1820-1827) and President (1827-1830) of the Royal Society.

[302] See Vol. I, page 55, note 2 {63}.

[303] Sir Jonathan Frederick Pollock (1783-1870) entered parliament in 1831

and was knighted in 1834.

[304] Joseph Hume (1777-1855) entered parliament in 1812 and for thirty

years was leader of the Radical party.

[305] "What! when I say, 'Nicole, bring me my slippers,' is that prose?"

[306] Captain Basil Hall (1788-1844), a naval officer, carried on a series

of pendulum observations in 1820-1822, while on a cruise of the west coast

of North America. The results were published in 1823 in the _Philosophical

Transactions_. He also wrote two popular works on travel that went through

numerous editions.

[307] Anthony Ashley Cooper (1801-1885), Earl of Shaftesbury. His name is

connected with philanthropic work and factory legislation.

[308] See Vol. I, page 207, note 12 {469}.

[309] See Vol. I, page 80, note 5 {119}.

[310] Sir Thomas Maclear (1794-1879), an Irishman by birth, became

Astronomer Royal at the Cape of Good Hope in 1833. He was an indefatigable

observer. He was knighted in 1860.

[311] Thomas Romney Robinson (1792-1882), another Irish astronomer of

prominence. He was a deputy professor at Trinity College, Dublin, but took

charge of the Armagh observatory in 1823 and remained there until his

death.

[312] Sir James South (1785-1867) was in early life a surgeon, but gave up

his practice in 1816 and fitted up a private observatory. He contributed to

the science of astronomy, particularly with respect to the study of double

stars.

[313] Sir John Wrottesley (1798-1867), second Baron Wrottesley. Like Sir

James South, he took up the study of astronomy after a professional

career,--in his case in law. He built a private observatory in 1829 and

made a long series of observations, publishing three star catalogues. He

was president of the Astronomical Society from 1841 to 1843, and of the

Royal Society from 1854 to 1857.

[314] He seems to have written nothing else.

[315] See Vol. II, page 68, note 147.

[316] "The wills are free, and I wish neither the one nor the other."

[317] "The force of inertia conquered."

[318] Reddie also wrote _The Mechanics of the Heavens_, referred to later

in this work. He must not be confused with Judge James Reddie (1773-1852),

of Glasgow, who wrote on international law, although this is done in the

printed edition of the British Museum catalogue, for he is mentioned by De

Morgan somewhat later as alive in 1862.

[319] Henry Dunning Macleod (1821-1902), a lawyer and writer on political

economy, was a Scotchman by birth. He wrote on economical questions, and

lectured on banking at Cambridge (1877) and at King's College, London

(1878). He was a free lance in his field, and was not considered orthodox

by the majority of economists of his time. He was an unsuccessful candidate

for the chairs of political economy at Cambridge (1863), Edinburgh (1871),

and Oxford (1888).

[320] See Vol. I, page 252, note 2 {576}.

[321] Francis Henry Laing (1816-1889) was a graduate of Queen's College,

Cambridge, and a clergyman in the Church of England until 1846, when he

entered the Church of Rome. He taught in various Jesuit colleges until

1862, when his eccentricity was too marked to warrant the Church in

allowing him to continue. He published various controversial writings

during his later years. Of course if he had known the works of Wessel,

Gaus, Buee, Argand, and others, he would not have made such a sorry

exhibition of his ignorance of mathematics.

[322] See Vol. I, page 329, note 1 {705}. The book went into a second

edition in 1864.

[323] Thomas Weddle (1817-1853) was, at the time of publishing this paper,

a teacher in a private school. In 1851 he became professor of mathematics

at Sandhurst. He contributed several papers to the _Cambridge and Dublin

Mathematical Journal_, chiefly on geometry.

[324] See Vol. II, page 109, note 205.

[325] See Vol. II, page 66, note 143.

[326] See Vol. II, page 151, note 268.

[327] George Barrett (1752-1821) worked from 1786 to 1811 on a set of life

insurance and annuity tables. He invented a plan known as the "columnar

method" for the construction of such tables, and as De Morgan states, this

was published by Francis Baily, appearing in the appendix to his work on

annuities, in the edition of 1813. Some of his tables were used in

Babbage's _Comparative View of the various Institutions for the Assurance

of Lives_ (1826).

[328] See Vol. I, page 309, note 2 {670}.

[329] This was his _Practical short and direct Method of Calculating the

Logarithm of any given Number, and the Number corresponding to any given

Logarithm_ (1849).

[330] This is William Neile (1637-1670), grandson of Richard Neile (not

Neal), Archbishop of York. At the age of 19, in 1657, he gave the first

rectification of the semicubical parabola. Although he communicated it to

Brouncker, Wren, and others, it was not published until 1639, when it

appeared in John Wallis's _De Cycloide_.

[331] I myself "was a considerable part."

[332] He also wrote _A Glance at the Universe_ ("2d thousand" in 1862), and

_The Resurrection Body_ (1869).

[333] See Vol. I, page 63, note 1 {74}.

[334] As Swift gave it in his _Poetry. A Rhapsody_, it is as follows:

"So, naturalists observe, a flea

Has smaller fleas that on him prey;

And these have smaller still to bite 'em.

And so proceed _ad infinitum_."

[335] Perhaps 1,600,000,000 years, if Boltwood's recent computations based

on radium disintegration stand the test. This would mean, according to

MacCurdy's estimate, 60,000,000 years since life first appeared on the

earth.

[336] De Morgan wrote better than he knew, for this work, the _Allgemeine

Encyclopaedie der Wissenschaften und Kuenste_, begun at Leipsic in 1818, is

still (1913) unfinished. Section I, A-G, consists of 99 parts in 56

volumes; Section II, H-N, consists of 43 volumes and is not yet completed;

and Section III, O-Z, consists of 25 volumes thus far, with most of the

work still to be done. Johann Samuel Ersch (1766-1828), the founder, was

head librarian at Halle. Johann Gottfried Gruber (1774-1851), his

associate, was professor of philosophy at the same university.

[337] William Howitt (1792-1879) was a poet, a spiritualist, and a

miscellaneous writer. He and his wife became spiritualists about 1850. He

wrote numerous popular works on travel, nature and history.

[338] See Vol. II, page 55, note 108.

[339] As will be inferred from the text, C. D. was Mrs. De Morgan, and

A. B. was De Morgan.

[340] Jean Meslier (1678-1733), cure of Estrepigny, in Champagne, was a

skeptic, but preached only strict orthodoxy to his people. It was only in

his manuscript, _Mon Testament_, that was published after his death, and

that caused a great sensation in France, that his antagonism to

Christianity became known.

[341] Baron Zach relates that a friend of his, in a writing intended for

publication, said _Un esprit doit se frotter contre un autre_. The censors

struck it out. The Austrian police have a keen eye for consequences.--A. De

M.

"One mind must rub against another." On Baron Zach, see Vol. II, page 45,

note 4.

[342] Referring to the first Lord Eldon (1751-1838), who was Lord

Chancellor from 1799 to 1827, with the exception of one year.

[343] "Sleeping power."

[344] "Causes sleep."

[345] Richard Hooker (c. 1554-1600), a theologian, "the ablest living

advocate of the Church of England as by law established."

[346] See Vol. I, page 76, note 3 {112}.

[347] "Other I,"--other self.

[348] This "utter rejection" has been repeated (1872) by the same

writer.--S. E. De M.

[349] Edward Jenner (1749-1823) was a physician and biologist. His first

experiments in vaccination were made in 1796, and his discovery was

published in 1798.

[350] See Vol. II, page 38, note 80.

[351] "You will go most safely in the middle (way)."

[352] Pierre Joseph Arson was known early in the 19th century for his

controversy with Hoene Wronski the mathematician, whom he attacked in his

_Document pour l'histoire des grands fourbes qui ont figure sur la terre_

(1817-1818).

[353] "We enter the course by night and are consumed by fire."

[354] See Vol. I, page 51, note 3 {51}.

[355] See Vol. I, page 336, note 8 {713}.

[356] See Vol. I, page 137, note 8 {286}.

[357] See Vol. I, page 229, note 2 {515}.

[358] Richard Cobden (1804-1865), the cotton manufacturer and statesman who

was prominent in his advocacy of the repeal of the Corn Laws.

[359] James Smith (1775-1839), solicitor to the Board of Ordnance. With his

brother Horatio he wrote numerous satires. His _Horace in London_ (1813)

imitated the Roman poet. His works were collected and published in 1840.

[360] Samuel Butler (1612-1680), the poet and satirist, author of

_Hudibras_ (1663-1678).

[361] "Is it not fine to be sure of one's action when entering in a combat

with another? There, push me a little in order to see. NICOLE. Well! what's

the matter? M. JOURDAIN. Slowly. Ho there! Ho! gently. Deuce take the

rascal! NICOLE. You told me to push. M. JOURDAIN. Yes, but you pushed me

_en tierce_, before you pushed _en quarte_, and you did not give me time to

parry."

[362] John Abernethy (1764-1831), the famous physician and surgeon.

[363] See Vol. I, page 102, note 5 {175}.

[364] "With what measure ye mete, it shall be measured to you again."

[365] Eusebius of Caesarea (c. 260-340), leader of the moderate party at the

Council of Nicaea, and author of a _History of the Christian Church_ in ten

books (c. 324 A. D.).

[366] Nathaniel Lardner (1684-1768), a non-conformist minister and one of

the first to advocate the scientific study of early Christian literature.

[367] Henry Alford (1810-1871) Dean of Canterbury (1857-1871) and editor of

the Greek Testament (1849-1861).

[368] The work was _The Number and Names of the Apocalyptic Beasts: with an

explanation and application. Part I._ London, 1848, as mentioned below.

Thom also wrote _The Assurance of Faith, or Calvinism identified with

Universalism_ (London, 1833), and various other religious works.

[369] See Vol. I, page 222, note 14 {490}.

[370] John Hamilton Thom (1808-1894) was converted to Unitarianism and was

long a minister in that church, preaching in the Renshaw Street Chapel from

1831 to 1866. De Morgan refers to the Liverpool Unitarian controversy

conducted by James Martineau and Henry Giles in response to a challenge by

thirteen Anglican Clergy. In 1839 Thom contributed four lectures and a

letter to this controversy. Among his religious works were a _Life of

Blanco White_ (1845) and _Hymns, Chants, and Anthems_ (1854).

[371] The spelling of these names is occasionally changed to meet the

condition that the numerical value of the letters shall be 666, "the number

of the beast" of Revelations. The names include Julius Caesar; Valerius

Jovius Diocletianus (249-313), emperor from 287 to 305, persecutor of the

Christians; Louis, presumably Louis XIV; Gerbert (940-1003), who reigned as

Pope Sylvester II from 999 to 1003, known to mathematicians for his abacus

and his interest in geometry, and accused by his opponents as being in

league with the devil; Linus, the second Bishop of Rome, the successor of

Peter; Camillo Borghese (1552-1621), who reigned as Pope Paul V from 1605

to 1621, and who excommunicated all Venice in 1606 for its claim to try

ecclesiastics before lay tribunals, thus taking a position which he was

forced to abandon; Luther, Calvin; Laud (see Vol. I, page 145, note 7

{307}); Genseric (c. 406-477), king of the Vandals, who sacked Rome in 455

and persecuted the orthodox Christians in Africa; Boniface III, who was

pope for nine months in 606; Beza (see Vol. I, page 66, note 6 {83});

Mohammed; [Greek: braski], who was Giovanni Angelo Braschi (1717-1799), and

who reigned as Pope Pius VI from 1775 to 1799, dying in captivity because

he declined to resign his temporal power to Napoleon; Bonaparte; and, under

[Greek: Ion Paune], possibly Pope John XIV, who reigned in 983 and 984

during the absence of Boniface VII in Constantinople.

[372] The Greek words and names are also occasionally misspelled so as to

fit them to the number 666. They are [Greek: Lateinos] (Latin), [Greek: he

latine basileia] (the Latin kingdom), [Greek: ekklesia italika] (the

Italian Church), [Greek: euanthas] (blooming), [Greek: teitan] (Titan),

[Greek: arnoume] (renounce), [Greek: lampetis] (the lustrous), [Greek: ho

niketes] (conqueror), [Greek: kakos hodegos] (bad guide), [Greek: alethes

blaberos] (truthful harmful one), [Greek: palai baskanos] (a slanderer of

old), [Greek: amnos adikos] (unmanageable lamb), [Greek: antemos]

(Antemos), [Greek: genserikos] (Genseric), [Greek: euinas] (with stout

fibers), [Greek: Benediktos] (Benedict), [Greek: Bonibazios g. papa x. e.

e. e. a.] (Boniface III, pope 68, bishop of bishops I), [Greek: oulpios]

(baneful), [Greek: dios eimi he heras] (I, a god, am the), [Greek: he missa

he papike] (the papal brief), [Greek: loutherana] (Lutheran), [Greek:

saxoneios] (Saxon), [Greek: Bezza antitheos] (Beza antigod), [Greek: he

alazoneia biou] (the illusion of life), [Greek: Maometis] (Mahomet);

[Greek: Maometes b.] (Mahomet II), [Greek: theos eimi epi gaies] (I am lord

over the earth), [Greek: iapetos] (Iapetos, father of Atlas), [Greek:

papeiskos] (Papeiskos), [Greek: dioklasianos] (Diocletian), [Greek: cheina]

(Cheina = Cain? China?), [Greek: braski] (Braschi, as explained in note

10), [Greek: Ion Paune] (Paunian violet, but see note 10), [Greek: koupoks]

(cowpox), [Greek: Bonneparte] (Bonneparte), [Greek: N. Boneparte] (N.

Boneparte), [Greek: euporia] (facility), [Greek: paradosis] (surrender),

[Greek: to megatherion] (the megathereum, the beast).

[373] James Wapshare, whose _Harmony of the Word of God in Spirit and in

Truth_ appeared in 1849.

[374] The literature relating to the _Swastika_ is too extended to permit

of any adequate summary in these notes.

[375] Henry Edward Manning (1808-1892), at first an Anglican clergyman, he

became a Roman Catholic priest in 1851, and became Cardinal in 1875. He

succeeded Cardinal Wiseman as Archbishop of Westminster in 1865. He wrote a

number of religious works.

[376] John Bright (1811-1889), Quaker, cotton manufacturer, and statesman.

He worked with Cobden for free trade, peace, and reform of the electorate.

[377] "The fallacy of many questions."

[378] William Wilberforce (1759-1833), best known for his long fight for

the abolition of the slave trade.

[379] Richard Martin (1754-1834), high sheriff of County Galway and owner

of a large estate in Connemara. Curiously enough, he was known both for his

readiness in duelling and for his love for animals. He was known as

"Humanity Martin," and in 1822 secured the passage of an act "to prevent

the cruel and improper treatment of cattle." He was one of the founders

(1824) of the Royal Society for the Prevention of Cruelty to Animals. He is

usually considered the original of Godfrey O'Malley in Lever's novel,

_Charles O'Malley_.

[380] See Vol. I, page 149, note 1 {323}, also text on same page.

[381] See Vol. I, page 44, note 9 {34}, also text, Vol. I, page 110.

[382] "Penitential seat."

[383] "Well placed upon the cushion."

[384] See Vol. II, page 58, note 109.

[385] "He has lost the right of being influenced by evidence."

[386] "Hung up."

[387] "A few things to the wise, nothing to the unlettered."

[388] The fallacy results from dividing both members of an equation by 0, x

- 1 being the same as 1 - 1, and calling the quotients finite.

[389] "If you order him to the sky he will go."

[390] _Similia similibus curanter_, "Like cures like," the homeopathic

motto.

[391] "Without harm to the proprieties."

[392] "What are you doing? I am standing here."

[393] Lors feist l'Anglois tel signe. La main gausche toute ouverte il leva

hault en l'aer, puis ferma au poing les quatres doigtz d'icelle et le

poulce estendu assit sus la pinne du nez. Soubdain apres leva la dextre

toute ouverte, et toute ouverte la baissa, joignant la poulce au lieu que

fermait le petit doigt de la gausche, et les quatre doigtz d'icelle mouvoit

lentement en l'aer. Puis au rebours feit de la dextre ce qu'il avoit faict

de la gausche, et de la gausche ce que avoit faict de la dextre.--A. De M.

[394] _Suaviter in modo, fortiter in re_, "Gentle in manners, firm in

action."

[395] See Vol. I, page 101, note 4 {174}.

[396] See Vol. I, page 315, note 3 {686}.

[397] Henry Fawcett (1833-1884) became totally blind in 1858, but in spite

of this handicap he became professor of political economy at Cambridge and

sat in parliament for a number of years. He championed the cause of reform

and in particular he was prominent in the protection of the native

interests of India. The establishing of the parcels post (1882) took place

while he was postmaster general (1880-1884).

[398] Of course the whole thing depends upon what definition of division is

taken. We can multiply 2 ft. by 3 ft. if we define multiplication so as to

allow it, or 2 ft. by 3 lb, getting foot-pounds, as is done in physics.

[399] Richard Milward (1609-1680), for so the name is usually given, was

rector of Great Braxted (Essex) and canon of Windsor. He was long the

amanuensis of John Selden, and the _Table Talk_ was published nine years

after Milward's death, from notes that he left. Some doubt has been cast

upon the authenticity of the work owing to many of the opinions that it

ascribes to Selden.

[400] John Selden (1584-1654) was a jurist, legal antiquary, and Oriental

scholar. He sat in the Long Parliament, and while an advocate of reform he

was not an extremist. He was sent to the Tower for his support of the

resolution against "tonnage and poundage," in 1629. His _History of Tythes_

(1618) was suppressed at the demand of the bishops. His _De Diis Syriis_

(1617) is still esteemed a classic on Semitic mythology.

[401] See Vol. I, page 42, note 4 {24}.

[402] See Vol. II, page 249, note 398.

[403] John Palmer (1742-1818) was a theatrical manager. In 1782 he set

forth a plan for forwarding the mails by stage coaches instead of by

postmen. Pitt adopted the plan in 1784. Palmer was made comptroller-general

of the post office in 1786 and was dismissed six years later for

arbitrarily suspending a deputy. He had been verbally promised 2-1/2% on

the increased revenue, but Pitt gave him only a pension of L3000. In 1813

he was awarded L50,000 in addition to his pension.

[404] Dionysius Lardner (1793-1859), professor of natural philosophy in

London University (now University College). His _Cabinet Cyclopaedia_

(1829-1849) contained 133 volumes. De Morgan wrote on probabilities, and

Lardner on various branches of mathematics, and there were many other

well-known contributors. Lardner is said to have made $200,000 on a lecture

tour in America.

[405] Thomas Fysche Palmer (1747-1802) joined the Unitarians in 1783, and

in 1785 took a charge in Dundee. He was arrested for sedition because of an

address that it was falsely alleged that he gave before a society known as

the "Friends of Liberty." As a matter of fact the address was given by an

uneducated weaver, and Palmer was merely asked to revise it, declining to

do even this. Nevertheless he was sentenced to Botany Bay (1794) for seven

years. The trial aroused great indignation.

[406] See Vol. I, page 80, note 5 {119}.

[407] See Vol. II, page 244, note 394.

[408] See Vol. I, page 352, note 1 {731}.

[409] See Vol. I, page 332, note 4 {709}.

[410] "The lawyers are brought into court; let them accuse each other."

[411] Samuel Rogers (1763-1855), the poet and art connoisseur. He declined

the laureateship on the death of Wordsworth (1850). Byron, his pretended

friend, wrote a lampoon (1818) ridiculing his cadaverous appearance.

[412] Theodore Edward Hook (1788-1841), the well-known wit. He is satirized

as Mr. Wagg in _Vanity Fair_. The _John Bull_ was founded in 1820 and Hook

was made editor.

[413] "On pitying the heretic."

[414] A term of medieval logic. Barbara: All M is P, all S is M, hence all

S is P. Celarent: No M is P, all S is M, hence no S is P.

[415] "Simply," "According to which," "It does not follow."

[416]

"O sweet soul, what good shall I declare

That heretofore was thine, since such are thy remains!"

[417] "Stupid fellow!"

[418] Christopher Barker (c. 1529-1599), also called Barkar, was the

Queen's printer. He began to publish books in 1569, but did no actual

printing until 1576. In 1575 the Geneva Bible was first printed in England,

the work being done for Barker. He published 38 partial or complete

editions of the Bible from 1575 to 1588, and 34 were published by his

deputies (1588-1599).

[419] James Franklin (1697-1735) was born in Boston, Mass., and was sent to

London to learn the printer's trade. He returned in 1717 and started a

printing house. Benjamin, his brother, was apprenticed to him but ran away

(1723). James published the _New England Courant_ (1721-1727), and Benjamin

is said to have begun his literary career by writing for it.

[420] James Hodder was a writing master in Tokenhouse Yard, Lothbury, in

1661, and later kept a boarding school in Bromley-by-Bow. His famous

arithmetic appeared at London in 1661 and went through many editions. It

was the basis of Cocker's work. (See Vol. I, page 42, note 4 {24}.) It was

long thought to have been the first arithmetic published in America, and it

was the first English one. There was, however, an arithmetic published much

earlier than this, in Mexico, the _Sumario compendioso ... con algunas

reglas tocantes al Aritmetica_, by "Juan Diaz Freyle," in 1556.

[421] Henry Mose, Hodder's successor, kept a school in Sherborne Lane,

London.

[422] Rear Admiral Sir Francis Beaufort (1774-1857), F.R.S., was

hydrographer to the Navy from 1829 to 1855. He prepared an atlas that was

printed by the Society for the Diffusion of Useful Knowledge.

[423] Antoine Sabatier (1742-1817), born at Castres, was known as the Abbe

but was really nothing more than a "clerc tonsure." He lived at Court and

was pensioned to write against the philosophers of the Voltaire group. He

posed as the defender of morality, a commodity of which he seems to have

possessed not the slightest trace.

[424] Maffeo Barberini was pope, as Urban VIII, from 1623 to 1644. It was

during his ambitious reign that Galileo was summoned to Rome to make his

recantation (1633), the exact nature of which is still a matter of dispute.

[425] This Baden Powell (1796-1860) was the Savilian professor of geometry

(1827-1860) at Oxford.

[426] "Memoirs of the famous bishop of Chiapa, by which it appears that he

had butchered or burned or drowned ten million infidels in America in order

to convert them. I believe that this bishop exaggerated; but if we should

reduce these sacrifices to five million victims, this would still be

admirable."

[427] Alfonso X (1221-1284), known as El Sabio (the Wise), was interested

in astronomy and caused the Alphonsine Tables to be prepared. These table

were used by astronomers for a long time. It is said that when the

Ptolemaic system of the universe was explained to him he remarked that if

he had been present at the Creation he could have shown how to arrange

things in a much simpler fashion.

[428] George Richards (c. 1767-1837), fellow of Oriel (1790-1796), Bampton

lecturer (1800), Vicar of St. Martin's-in-the-Fields, Westminster (1824),

and a poet of no mean ability.

[429] The "Aboriginal Britons," an excellent poem, by Richards. (Note by

Byron.)--A. De M.

[430] John Watkins (d. after 1831), a teacher and miscellaneous writer.

[431] Frederic Shoberl (1775-1853), a miscellaneous writer.

[432] He wrote, besides the _Aboriginal Britons_, _Songs of the Aboriginal

Bards_ (1792), _Modern France: a Poem_ (1793), _Odin, a drama_ (1804),

_Emma, a drama on the model of the Greek theatre_ (1804), _Poems_ (2

volumes, 1804), and a _Monody on the Death of Lord Nelson_ (1806).

[433] Henry Kirke White (1785-1806), published his first volume of poems at

the age of 18. Southey and William Wilberforce became interested in him and

procured for him a sizarship at St. John's College, Cambridge. He at once

showed great brilliancy, but he died of tuberculosis at the age of 21.

[434] John Wolcot, known as Peter Pindar (1738-1819), was a London

physician. He wrote numerous satirical poems. His _Bozzy and Piozzi, or the

British Biographers_, appeared in 1786, and reached the 9th edition in

1788.

[435] See Vol. I, page 235, note 8 {532}.

[436] Richard Payne Knight (1750-1824) was a collector of bronzes, gems,

and coins, many of his pieces being now in the British Museum. He sat in

parliament for twenty-six years (1780-1806), but took no active part in

legislation. He opposed the acquisition of the Elgin Marbles, holding them

to be of little importance. His _Analytical Inquiry into the Principles of

Taste_ appeared in 1808.

[437] Mario Nizzoli (1498-1566), a well-known student of Cicero, was for a

time professor at the University of Parma. His _Observationes in M. Tullium

Ciceronem_ appeared at Pratalboino in 1535. It was revised by his nephew

under the title _Thesaurus Ciceronianus_ (Venice, 1570).

[438] See Vol. I, page 314, note 4 {681}.

[439]

"Like the geometer, who bends all his powers

To measure the circle, and does not succeed,

Thinking what principle he needs."

[440] Francis Quarles (1592-1644), a religious poet. He wrote paraphrases

of the Bible and numerous elegies. In the early days of the revolutionary

struggle he sided with the Royalists. One of his most popular works was the

_Emblems_ (1635), with illustrations by William Marshall.

[441] Regnault de Becourt wrote _La Creation du monde, ou Systeme

d'organisation primitive suivi de l'interpretation des principaux

phenomenes et accidents que se sont operes dans la nature depuis l'origine

de univers jusqu'a nos jours_ (1816). This may be the work translated by

Dalmas.

[442] "Because it lacks a holy prophet."

[443] Anghera. See Vol. II, page 60, note 127.

[444] Edmund Curll (1675-1747), a well-known bookseller, publisher, and

pamphleteer. He was for a time at "The Peacock without Temple Bar," and

later at "The Dial and Bible against St. Dunstan's Church." He was fined

repeatedly for publishing immoral works, and once stood in the pillory for

it. He is ridiculed in the _Dunciad_ for having been tossed in a blanket by

the boys of Westminster School because of an oration that displeased them.

[445] See Vol. II, page 109, note 206.

[446] Encyclopaedia.

[447] Author of the _Historia Naturalis_ (77 A.D.)

[448] Author of the _De Institutione Oratorio Libri_ XII (c. 91 A.D.)

[449] His _De Architectures Libri_ X was not merely a work on architecture

and building, but on the education of the architect.

[450] Cyclophoria.

[451] William Caxton (c. 1422-c.1492), sometime Governor of the Company of

Merchant Adventurers in Bruges (between 1449 and 1470). He learned the art

of printing either at Bruges or Cologne, and between 1471 and 1477 set up a

press at Westminster. Tradition says that the first book printed in England

was his _Game and Playe of Chesse_ (1474). The _Myrrour of the Worlde and

th'ymage of the same_ appeared in 1480. It contains a brief statement on

arithmetic, the first mathematics to appear in print in England.

[452] See Vol. I, page 45, note 6 {40}. De Morgan is wrong as to the date

of the _Margarita Philosophica_. The first edition appeared at Freiburg in

1503.

[453] Reisch was confessor to Maximilian I (1459-1519), King of the Romans

(1486) and Emperor (1493-1519).

[454] Joachim Sterck Ringelbergh (c. 1499-c. 1536), teacher of philosophy

and mathematics in various cities of France and Germany. His _Institutionum

astronomicarum libri III_ appeared at Basel in 1528, his _Cosmographia_ at

Paris in 1529, and his _Opera_ at Leyden in 1531.

[455] Johannes Heinrich Alsted (1588-1638) was professor of philosophy and

theology at his birthplace, Herborn, in Nassau, and later at Weissenberg.

He published several works, including the _Elementale mathematicum_ (1611),

_Systema physicae harmonicae_ (1612), _Methodus admirandorum

mathematicorum_ (1613), _Encyclopaedia septem tomis distincta_ (1630), and

the work mentioned above.

[456] Johann Jakob Hoffmann (1635-1706), professor of Greek and history at

his birthplace, Basel. He also wrote the _Epitome metrica historiae

universalis civilis et sacrae ab orbe condito_ (1686).

[457] Ephraim Chambers (c. 1680-1740), a crotchety, penurious, but

kind-hearted freethinker. His _Cyclopaedia, or an Universal Dictionary_ was

translated into French and is said to have suggested the great

_Encyclopedie_.

[458] _Encyclopedie, ou Dictionnaire raisonne des sciences, des arts et des

metiers, par un societe de gens de lettres. Mis en ordre et publie par M.

Diderot, et quant a la partie mathematique, par M. d'Alembert._ Paris,

1751-1780, 35 volumes.

[459] "From the egg" (state).

[460] See Vol. I, page 382, note 12 {785}.

[461] See Vol. II, page 4, note 15.

[462] "In morals nothing should serve man as a model but God; in the arts,

nothing but nature."

[463] _Encyclopedie Methodique, ou par ordre de matieres._ Paris,

1782-1832, 166-1/2 volumes.

[464] See Vol. II, page 193, note 336.

[465] _Encyclopaedia Metropolitana; or, Universal Dictionary of Knowledge._

London, 1845, 29 volumes. A second edition came out in 1848-1858 in 40

volumes.

[466] See Vol. I, page 137, note 8 {286}.

[467] See Vol. I, page 80, note 5 {119}.

[468] De Morgan should be alive to satirize some of the statements on the

history of mathematics in the eleventh edition.

[469] John Pringle Nichol (1804-1859), Regius professor of astronomy at

Glasgow and a popular lecturer on the subject. He lectured in the United

States in 1848-1849. His _Views of the Architecture of the Heavens_ (1838)

was a very popular work, and his _Planetary System_ (1848, 1850) contains

the first suggestion for the study of sun spots by the aid of photography.

[470] See Vol. II, page 109, note 206.

[471] George Long (1800-1879), a native of Poulton, in Lancashire, was

called to the University of Virginia when he was only twenty-four years old

as professor of ancient languages. He returned to England in 1828 to become

professor of Greek at London University. From 1833 to 1849 he edited the

twenty-nine volumes of the _Penny Cyclopaedia_. He was an authority on Roman

law.

[472] A legal phrase, "Qui tam pro domina regina, quam pro se ipso

sequitur,"--"Who sues as much on the Queen's account as on his own."

[473] Arthur Cayley (1821-1895) was a fellow of Trinity College, Cambridge

(1842-1846) and was afterwards a lawyer (1849-1863). During his fourteen

years at the bar he published some two hundred mathematical papers. In 1863

he became professor of mathematics at Cambridge, and so remained until his

death. His collected papers, nine hundred in number, were published by the

Cambridge Press in 13 volumes (1889-1898). He contributed extensively to

the theory of invariants and covariants. De Morgan's reference to his

coining of new names is justified, although his contemporary, Professor

Sylvester, so far surpassed him in this respect as to have been dubbed "the

mathematical Adam."

[474] See Vol. II, page 26, note 56.

[475] See Vol. I, page 111, note 3 {207}.

[476] See Vol. I, page 87, note 6 {135}.

[477] Pierre Dupuy (1582-1651) was a friend and relative of De Thou. With

the collaboration of his brother and Nicolas Rigault he published the 1620

and 1626 editions of De Thou's History. He also wrote on law and history.

His younger brother, Jacques (died in 1656), edited his works. The two had

a valuable collection of books and manuscripts which they bequeathed to the

Royal Library at Paris.

[478] See Vol. I, page 51, note 3 {51}.

[479] It was Cosmo de' Medici (1590-1621) who was the patron of Galileo.

[480] See Vol. I, page 40, note 4 {20}.

[481] See Vol. I, page 106, note 4 {188}.

[482] Sir Edward Sherburne (1618-1702), a scholar of considerable

reputation. The reference by De Morgan is to _The Sphere of Marcus

Manilius_, in the appendix to which is a _Catalogue of Astronomers, ancient

and modern_.

[483] George Parker, second Earl of Macclesfield (1697-1764). He erected an

observatory at Shirburn Castle, Oxfordshire, in 1739, and fitted it out

with the best equipment then available. He was President of the Royal

Society in 1752.

[484] See Vol. II, page 148, note 263.

[485] See Vol. I, page 140, note 7 {296}.

[486] See Vol. I, page 106, note 4 {188}.

[487] Edward Bernard (1638-1696), although Savilian professor of astronomy

at Oxford, was chiefly interested in archeology.

[488] See Vol. I, page 107, note 1 {190}.

[489] See Vol. I, page 107, note 1 {190}.

[490] See Vol. I, page 135, note 3 {281}.

[491] Philip Dormer Stanhope, fourth Earl of Chesterfield (1694-1773), well

known for the letters written to his son which were published posthumously

(1774).

[492] Peter Daval (died in 1763), Vice-President of the Royal Society, and

an astronomer of some ability.

[493] See Vol. I, page 376, note 1 {766}.

[494] William Oughtred (c. 1573-1660), a fellow of King's College,

Cambridge, and afterwards vicar of Aldbury, Surrey, wrote the best-known

arithmetic and trigonometry of his time. His _Arithmeticae in Numero &

Speciebus Institutio ... quasi Clavis Mathematicae est_ (1631) went through

many editions and appeared in English as _The Key to the Mathematicks new

forged and filed_ in 1647.

[495] See Vol. I, page 140, note 5 {294}.

[496] Stephen Jordan Rigaud (1816-1859) was senior assistant master of

Westminster School (1846) and head master of Queen Elizabeth's School at

Ipswich (1850). He was made Bishop of Antigua in 1858 and died of yellow

fever the following year.

[497] He also wrote a memoir of his father, privately printed at Oxford in

1883.

[498] See Vol. I, page 69, note 3 {96}.

[499] See Vol. I, page 106, note 4 {188}.

[500] William Gascoigne was born at Middleton before 1612 and was killed in

the battle of Marston Moor in 1644. He was an astronomer and invented the

micrometer with movable threads (before 1639).

[501] Seth Ward (1617-1689) was deprived of his fellowship at Cambridge for

refusing to sign the covenant. He became professor of astronomy at Oxford

(1649), Bishop of Exeter (1662), Bishop of Salisbury (1667), and Chancellor

of the Garter (1671). He is best known for his solution of Kepler's problem

to approximate a planet's orbit, which appeared in his _Astronomia

geometrica_ in 1656.

[502] See Vol. I, page 110, note 2 {198}.

[503] See Vol. I, page 100, note 2 {172}.

[504] See Vol. I, page 107, note 1 {190}.

[505] See Vol. I page 114, note 6 {220}.

[506] See Vol. I, page 77, note 4 {118}.

[507] See Vol. I, page 125, note 3 {253}.

[508] See Vol. I, page 105, note 2 {186}.

[509] Heinrich Oldenburgh (1626-1678) was consul in England for the City

of Bremen, his birthplace, and afterwards became a private teacher in

London. He became secretary of the Royal Society and contributed on

physics and astronomy to the _Philosophical Transactions_.

[510] Thomas Brancker, or Branker (1636-1676) wrote the _Doctrinae

sphaericae adumbratio et usus globorum artificialium_ (1662) and

translated the algebra of Rhonius with the help of Pell. The latter work

appeared under the title of _An Introduction to Algebra_ (1668), and

is noteworthy as having brought before English mathematicians the

symbol / for division. The symbol never had any standing on the

Continent for this purpose, but thereafter became so popular in England

that it is still used in all the English-speaking world.

[511] See Vol. I, page 118, note 1 {230}.

[512] Pierre Bertius (1565-1629) was a native of Flanders and was educated

at London and Leyden. He became a professor at Leyden, and later held the

chair of mathematics at the College de France. He wrote chiefly on

geography.

[513] See Vol. II, page 297, note 487.

[514] Giovanni Alphonso Borelli (1608-1679) was professor of mathematics at

Messina (1646-1656) and at Pisa (1656-1657), after which he taught in Rome

at the Convent of St. Panteleon. He wrote several works on geometry,

astronomy, and physics.

[515] See Vol. I, page 172, note 2 {381}.

[516] Ignace Gaston Pardies (c. 1636-1673), a Jesuit, professor of ancient

languages and later of mathematics and physics at the College of Pau, and

afterwards professor of rhetoric at the College Louis-le-Grand at Paris. He

wrote on geometry, astronomy and physics.

[517] Pierre Fermat was born in 1608 (or possibly in 1595) near Toulouse,

and died in 1665. Although connected with the parliament of Toulouse, his

significant work was in mathematics. He was one of the world's geniuses in

the theory of numbers, and was one of the founders of the theory of

probabilities and of analytic geometry. After his death his son published

his edition of Diophantus (1670) and his _Varia opera mathematica_ (1679).

[518] This may be Christopher Townley (1603-1674) the antiquary, or his

nephew, Richard, who improved the micrometer already invented by Gascoigne.

[519] Adrien Auzout a native of Rouen, who died at Rome in 1691. He

invented a screw micrometer with movable threads (1666) and made many

improvements in astronomical instruments.

[520] See Vol. I, page 66, note 9 {86}.

[521] See Vol. I, page 124, note 7 {248}.

[522] John Machin (d. 1751) was professor of astronomy at Gresham College

(1713-1751) and secretary of the Royal Society. He translated Newton's

_Principia_ into English. His computation of [pi] to 100 places is given in

William Jones's _Synopsis palmariorum matheseos_ (1706).

[523] Pierre Remond de Montmort (1678-1719) was canon of Notre Dame until

his marriage. He was a gentleman of leisure and devoted himself to the

study of mathematics, especially of probabilities.

[524] Roger Cotes (1682-1716), first Plumian professor of astronomy and

physics at Cambridge, and editor of the second edition of Newton's

_Principia_. His posthumous _Harmonia Mensurarum_ (1722) contains "Cotes's

Theorem" on the binomial equation. Newton said of him, "If Mr. Cotes had

lived we had known something."

[525] See Vol. I, page 135, note 3 {281}.

[526] See Vol. I, page 377, note 4 {769}.

[527] Charles Rene Reyneau (1656-1728) was professor of mathematics at

Angers. His _Analyse demontree, ou Maniere de resoudre les problemes de

mathematiques_ (1708) was a successful attempt to popularize the theories

of men like Descartes, Newton, Leibnitz, and the Bernoullis.

[528] Brook Taylor (1685-1731), secretary of the Royal Society, and student

of mathematics and physics. His _Methodus incrementorum directa et inversa_

(1715) was the first treatise on the calculus of finite differences. It

contained the well-known theorem that bears his name.

[529] Pierre Louis Moreau de Maupertuis (1698-1759) was sent with Clairaut

(1735) to measure an arc of a meridian in Lapland. He was head of the

physics department in the Berlin Academy from 1745 until 1753. He wrote

_Sur la figure de la terre_ (1738) and on geography and astronomy.

[530] Pierre Bouguer (1698-1758) was professor of hydrography at Paris, and

was one of those sent by the Academy of Sciences to measure an arc of a

meridian in Peru (1735). The object of this and the work of Maupertuis was

to determine the shape of the earth and see if Newton's theory was

supported.

[531] Charles Marie de la Condamine (1701-1774) was a member of the Paris

Academy of Sciences and was sent with Bouguer to Peru, for the purpose

mentioned in the preceding note. He wrote on the figure of the earth, but

was not a scientist of high rank.

[532] See Vol. I, page 136, note 5 {283}.

[533] See Vol. II, page 296, note 483.

[534] Thomas Baker (c. 1625-1689) gave a geometric solution of the

biquadratic in his _Geometrical Key, or Gate of Equations unlocked_ (1684).

[535] See Vol. I, page 160, note 5 {350}.

[536] See Vol. I, page 87, note 4 {133}.

[537] See Vol. I, page 132, note 2 {272}.

[538] See Vol. I, page 118, second note 1 {231}.

[539] The name of Newton is so well known that no note seems necessary. He

was born at Woolsthorpe, Lincolnshire, in 1642, and died at Kensington in

1727.

[540] John Keill (1671-1721), professor of astronomy at Oxford from 1710,

is said to have been the first to teach the Newtonian physics by direct

experiment, the apparatus being invented by him for the purpose. He wrote

on astronomy and physics. His _Epistola de legibus virium centripetarum_,

in the Philosophical Transactions for 1708, accused Leibnitz of having

obtained his ideas of the calculus from Newton, thus starting the priority

controversy.

[541] Thomas Digges (d. in 1595) wrote _An Arithmeticall Militare Treatise,

named Stratioticos_ (1579), and completed _A geometrical practise, named

Pantometria_ (1571) that had been begun by his father, Leonard Digges.

[542] John Dee (1527-1608), the most famous astrologer of his day, and

something of a mathematician, wrote a preface to Billingsley's translation

of Euclid into English (1570).

[543] See Vol. I, page 76, note 3 {112}.

[544] Thomas Harriot (1560-1621) was tutor in mathematics to Sir Walter

Raleigh, who sent him to survey Virginia (1585). He was one of the best

English algebraists of his time, but his _Artis Analyticae Praxis ad

Aequationes Algebraicas resolvendas_ (1631) did not appear until ten years

after his death.

[545] Thomas Lydiat (1572-1626), rector of Alkerton, devoted his life

chiefly to the study of chronology, writing upon the subject and taking

issue with Scaliger (1601).

[546] See Vol. I, page 69, note 3 {96}.

[547] Walter Warner edited Harriot's _Artis Analyticae Praxis_ (1631).

Tarporley is not known in mathematics.

[548] See Vol. I, page 105, note 2 {186}.

[549] See Vol. I, page 115, note 3 {224}.

[550] See Vol. II, page 300, note 509.

[551] See Vol. I, page 107, note 1 {190}.

[552] Sir Samuel Morland (1625-1695) was a diplomat and inventor. For some

years he was assistant to John Pell, then ambassador to Switzerland. He

wrote on arithmetical instruments invented by him (1673), on hydrostatics

(1697) and on church history (1658).

[553] See Vol. I, page 153, note 4 {337}.

[554] See Vol. I, page 85, note 2 {129}.

[555] See Vol. I, page 43, note 8 {33}.

[556] See Vol. I, page 43, note 7 {32}.

[557] See Vol. I, page 382, note 13 {786}. The history of the subject may

be followed in Braunmuehl's _Geschichte der Trigonometrie_.

[558] See Vol. I, page 377, note 3 {768}.

[559] See Vol. I, page 108, note 2 {192}.

[560] Michael Dary wrote _Dary's Miscellanies_ (1669), _Gauging epitomised_

(1669), and _The general Doctrine of Equation_ (1664).

[561] John Newton (1622-1678), canon of Hereford (1673), educational

reformer, and writer on elementary mathematics and astronomy.

[562] See Vol. I, page 87, note 4 {133}.

[563] "The average of the two equal altitudes of the sun before and after

dinner."

[564] See Vol. I, page 42, note 4 {24}.

[565] London, 1678. It went though many editions.

[566] "This I who once ..."

[567] Arthur Murphy (1727-1805) worked in a banking house until 1754. He

then went on the stage and met with some success at Covent Garden. His

first comedy, _The Apprentice_ (1756) was so successful that he left the

stage and took to play writing. His translation of Tacitus appeared in

1793, in four volumes.

[568] Edmund Wingate (1596-1656) went to Paris in 1624 as tutor to Princess

Henrietta Maria and remained there several years. He wrote _L'usage de la

regle de proportion_ (Paris, 1624, with an English translation in 1626),

_Arithmetique Logarithmetique_ (Paris, 1626, with an English translation in

1635), and _Of Natural and Artificial Arithmetick_ (London, 1630, revised

in 1650-1652), part I of which was one of the most popular textbooks ever

produced in England.

[569] John Lambert (1619-1694) was Major-General during the Revolution and

helped to draw up the request for Cromwell to assume the protectorate. He

was imprisoned in the Tower by the Rump Parliament. He was confined in

Guernsey until the clandestine marriage of his daughter Mary to Charles

Hatton, son of the governor, after which he was removed (1667) to St.

Nicholas in Plymouth Sound.

[570] Samuel Foster (d. in 1652) was made professor of astronomy at Gresham

College in March, 1636, but resigned in November of that year, being

succeeded by Mungo Murray. Murray vacated his chair by marriage in 1641 and

Foster succeeded him. He wrote on dialling and made a number of

improvements in geometric instruments.

[571] "Twice of the word a minister," that is, twice a minister of the

Gospel.

[572] This is _The Lives of the Professors of Gresham College to which is

prefixed the Life of the Founder, Sir Thomas Gresham_, London, 1740. It was

written by John Ward (c. 1679-1758), professor of rhetoric (1720) at

Gresham College and vice-president (1752) of the Royal Society.

[573] Charles Montagu (1661-1715), first Earl of Halifax, was Lord of the

Treasury in 1692, and was created Baron Halifax in 1700 and Viscount

Sunbury and Earl of Halifax in 1714. He introduced the bill establishing

the Bank of England, the bill becoming a law in 1694. He had troubles of

his own, without considering Newton, for he was impeached in 1701, and was

the subject of a damaging resolution of censure as auditor of the exchequer

in 1703. Although nothing came of either of these attacks, he was out of

office during much of Queen Anne's reign.

[574] See Vol. II, page 302, note 547.

[575] See Vol. I, page 105, note 2 {186}.

[576] James Dodson (d. 1757) was master of the Royal Mathematical School,

Christ's Hospital. He was De Morgan's great-grandfather. The

_Anti-Logarithmic Canon_ was published in 1742.

[577] See Vol. I, page 106, note 4 {188}.

[578] See Vol. I, page 110, note 2 {198}.

[579] Richard Busby, (1606-1695), master of Westminster School (1640) had

among his pupils Dryden and Locke.

[580] See Vol. I, page 107, note 1 {190}.

[581] Herbert Thorndike (1598-1672), fellow of Trinity College, Cambridge

(1620-1646), and Prebend of Westminster (1661), was a well-known

theological writer of the time.

[582] See Vol. I, page 140, note 5 {294}.

[583] See Vol. I, page 108, note 2 {192}.

[584] "Labor performed returns in a circle."

[585] See Vol. II, page 208.

[586] "Whatever objections one may make to the above arguments, one always

falls into an absurdity."

[587] See Vol. II. page 11, note 29. _The Circle Squared; and the solution

of the problem adapted to explain the difference between square and

superficial measurement_ appeared at Brighton in 1865.

[588] "And beyond that nothing."

[589] Gillott (1759-1873) was the pioneer maker of steel pens by machinery,

reducing the price from 1s. each to 4d. a gross. He was a great collector

of paintings and old violins.

[590] William Edward Walker wrote five works on circle squaring (1853,

1854, 1857, 1862, 1864), mostly and perhaps all published at Birmingham.

[591] Solomon M. Drach wrote _An easy Rule for formulizing all Epicyclical

Curves_ (London, 1849), _On the Circle area and Heptagon-chord_ (London,

1864), _An easy general Rule for filling up all Magic Squares_ (London,

1873), and _Hebrew Almanack-Signs_ (London, 1877), besides numerous

articles in journals.

[592] See Vol. I, page 168, note 3 {371}.

[593] See Vol. I, page 254, note 2 {580}.

[594] See Vol. I, page 98, note 6 {163}.

[595] Robert Fludd or Flud (1574-1637) was a physician with a large London

practice. He denied the diurnal rotation of the earth, and was attacked by

Kepler and Mersenne, and accused of magic by Gassendi. His _Apologia

Compendiania, Fraternitatem de Rosea Cruce suspicionis ... maculis

aspersam, veritatis quasi Fluctibus abluens_ (Leyden, 1616) is one of a

large number of works of the mystic type.

[596] Consult _To the Christianity of the Age. Notes ... comprising an

elucidation of the scope and contents of the writings ... of Dionysius

Andreas Freher_ (1854).

[597] Sir William Robert Grove (1811-1896), although called to the bar

(1835) and to the bench (1853), is best known for his work as a physicist.

He was professor of experimental philosophy (1840-1847) at the London

Institution, and invented a battery (1839) known by his name. His

_Correlation of Physical Forces_ (1846) went through six editions and was

translated into French.

[598] Johann Tauler (c. 1300-1361), a Dominican monk of Strassburg, a

mystic, closely in touch with the Gottesfreunde of Basel. His _Sermons_

first appeared in print at Leipsic in 1498.

[599] Paracelsus (c. 1490-1541). His real name was Theophrastes Bombast von

Hohenheim, and he took the name by which he is generally known because he

held himself superior to Celsus. He was a famous physician and pharmacist,

but was also a mystic and neo-Platonist. He lectured in German on medicine

at Basel, but lost his position through the opposition of the orthodox

physicians and apothecaries.

[600] See Vol. I, page 256, note 2 {588}.

[601] Philip Schwarzerd (1497-1560) was professor of Greek at Wittenberg.

He helped Luther with his translation of the Bible.

[602] Johann Reuchlin (1455-1522), the first great German humanist, was

very influential in establishing the study of Greek and Hebrew in Germany.

His lectures were mostly delivered privately in Heidelberg and Stuttgart.

Unlike Melanchthon, he remained in the Catholic Church.

[603] Joseph Chitty (1776-1841) published his _Precedents of Pleading_ in

1808 and his _Reports of Cases on Practice and Pleading_ in 1820-23 (2

volumes).

[604] See Vol. I, page 44, note 1 {35}.

[605] See Vol. I, page 44, note 4 {38}.

[606] Jean Pelerin, also known as Viator, who wrote on perspective. His

work appeared in 1505, with editions in 1509 and 1521.

[607] Henry Stephens. See Vol. I, page 44, note 3 {37}.

[608] The well-known grammarian (1745-1826). He was born at Swatara, in

Pennsylvania, and practised law in New York until 1784, after which he

resided in England. His grammar (1795) went through 50 editions, and the

abridgment (1818) through 120 editions. Murray's friend Dalton, the

chemist, said that "of all the contrivances invented by human ingenuity for

puzzling the brains of the young, Lindley Murray's grammar was the worst."

[609] Robert Recorde (c. 1510-1558) read and probably taught mathematics

and medicine at Cambridge up to 1545. After that he taught mathematics at

Oxford and practised medicine in London. His _Grounde of Artes_, published

about 1540, was the first arithmetic published in English that had any

influence. It went through many editions. The _Castle of Knowledge_

appeared in 1551. It was a textbook on astronomy and the first to set forth

the Copernican theory in England. Like Recorde's other works it was written

on the catechism plan. His _Whetstone of Witte ... containying thextraction

of Rootes: The Cosike practise, with the rule of Equation: and the woorkes

of Surde Nombres_ appeared in 1557, and it is in this work that the modern

sign of equality first appears in print. The word "Cosike" is an adjective

that was used for a long time in Germany as equivalent to algebraic, being

derived from the Italian _cosa_, which stood for the unknown quantity.

[610] Robert Cecil (c. 1563-1612), first Earl of Salisbury, Secretary of

State under Elizabeth (1596-1603) and under James I (1603-1612).

[611] In America the German pronunciation is at present universal among

mathematicians, as in the case of most other German names. This is due, no

doubt, to the great influence that Germany has had on American education in

the last fifty years.

[612] The latest transliteration is substantially K'ung-fu-tz[vu].

[613] The tendency seems to be, however, to adopt the forms used of

individuals or places as rapidly as the mass of people comes to be prepared

for it. Thus the spelling Leipzig, instead of Leipsic, is coming to be very

common in America.

[614] Sir Edward Coke (1552-1634), the celebrated jurist.

[615] Dethlef Cluvier or Cluever (d. 1708 at Hamburg) was a nephew, not a

grandson, of Philippe Cluvier, or Philipp Cluever (1580-c. 1623). Dethlef

traveled in France and Italy and then taught mathematics in London. He

wrote on astronomy and philosophy and also published in the _Acta

Eruditorum_ (1686) his _Schediasma geometricum de nova infinitorum

scientia_. _Quadratura circuli infinitis modis demonstrata_, and his

_Monitum ad geometras_ (1687). Philippe was geographer of the Academy of

Leyden. His _Introductionis in universam geographiam tam veterem quam novam

libri sex_ appeared at Leyden in 1624, about the time of his death.

[616] See Vol. I, page 124, note 7 {248}.

[617] Bernard Nieuwentijt (1654-1718), a physician and burgomaster at

Purmerend. His _Considerationes circa Analyseos ad quantitates infinite

parvas applicatae Principia et Calculi Differentialis usum_ (Amsterdam,

1694) was attacked by Leibnitz. He replied in his _Considerationes secundae_

(1694), and also wrote the _Analysis Infinitorum, seu Curvilineorum

Proprietates ex Polygonorum Natura deductae_ (1695). His most famous work

was on the existence of God, _Het Regt Gebruik der Werelt Beschouwingen_

(1718).

[618] "From a given line to construct" etc.

[619] "Pirates do not fight one another."

[620] Claude Mallemens (Mallement) de Messanges (1653-1723) was professor

of philosophy at the College du Plessis, in Paris, for 34 years. The work

to which De Morgan refers is probably the _Fameux Probleme de la quadrature

du cercle, resolu geometriquement par le cercle et a ligne droite_ that

appeared in 1683.

[621] On Tycho Brahe see Vol. I, page 76, note 3 {112}.

[622] Wilhelm Frederik von Zytphen also published the _Tidens Stroem_, a

chronological table, in 1840. The work to which De Morgan refers, the

_Solens Bevaegelse i Verdensrummet_, appeared first in 1861. De Morgan seems

to have missed his _Nogl Ord om Cirkelens Quadratur_ which appeared in

1865, at Copenhagen.

[623] James Joseph Sylvester (1814-1897), professor of natural philosophy

at University College, London (1837-1841), professor of mathematics at the

University of Virginia (1841-1845), actuary in London (1845-1855),

professor of mathematics at Woolwich (1877-1884) and at Johns Hopkins

University, Baltimore (1877-1884), and Savilian professor of geometry at

Oxford (1884-1894).

[624] See Vol. I, page 76, note 3 {112}.

[625] See Vol. II, page 205, note 349.

[626] See Vol. I, page 76, note 3 {112}.

[627] See Vol. I, page 46, note 1 {42}.

[628] See Vol. II, page 183, note 318.

[629] See Vol. I, page 321, note 2 {691}.

[630] James Mill, born 1773, died 1836.

[631] See Vol. II, page 3, note 11.

[632] See Vol. II, page 3, note 13.

[633] See Vol. II, page 3, note 14.

[634] This anecdote is printed at page 4 (Vol. II); but as it is used in

illustration here, and is given more in detail, I have not omitted

it.--S.E. De M.

[635] See Vol. II, page 4, note 15.

[636] See Vol. I, page 382, note 13 {786}.

[637] "Monsieur, (a + b^{n})/n = x, whence God exists; answer that!"

[638] "Monsieur, you know very well that your argument requires the

development of x according to integral powers of n."

[639] See Vol. I, page 153, note 4 {337}.

[640] Thomas Love Peacock (1785-1866) an English novelist and poet.

[641] Perhaps Dr. Samuel Warren (1807-1877), the author of _Ten Thousand a

Year_ (serially in Blackwood's in 1839; London, 1841).

[642] See Vol. I, page 255, note 6 {584}.

[643] "From many, one; much in little; Ultima Thule (the most remote

region); without which not."

[644] Spurius Maelius (fl. 440 B. C.), who distributed corn freely among the

poor in the famine of 440 B. C. and was assassinated by the patricians.

[645] Spurius Cassius Viscellinus, Roman consul in 502, 493, and 486 B. C.

Put to death in 485.

[646] "O what a fine bearing, he said, that has no brain."

[647] Sir William Rowan Hamilton. See Vol. I, page 332, note 4 {709}.

[648] William Allen Whitworth, the author of the well-known _Choice and

Chance_ (Cambridge, 1867), and other works.

[649] James Maurice Wilson, whose _Elementary Geometry_ appeared in 1868

and went through several editions.

[650] See Vol. II, page 183, note 315.

[651] "Force of inertia conquered," and "Victory in the whole heavens."

[652] "With all his might."

[653] George Berkeley (1685-1753), Bishop of Cloyne, the idealistic

philosopher and author of the _Principles of Human Knowledge_ (1710), _The

Analyst, or a Discourse addressed to an Infidel Mathematician_ (1734), and

_A Defense of Freethinking in Mathematics_ (1735). He asserted that space

involves the idea of movement without the sensation of resistance. Space

sensation less than the "minima sensibilia" is, therefore, impossible. From

this he argues that infinitesimals are impossible concepts.

[654] See Vol. I, page 85, note 2 {129}.

[655] See Vol. I, page 81, note 6 {120}.

[656] Edwin Dunkin revised Lardner's _Handbook of Astronomy_ (1869) and

Milner's _The Heavens and the Earth_ (1873) and wrote _The Midnight Sky_

(1869).

[657] Michael Faraday (1791-1867) the celebrated physicist and chemist. He

was an assistant to Sir Humphrey Davy (1813) and became professor of

chemistry at the Royal Institution, London, in 1827.

[658] "If you teach a fool he shows no joyous countenance; he cordially

hates you; he wishes you buried."

[659] "Every man is an animal, Sortes is a man, therefore Sortes is an

animal."

[660]

"May some choice patron bless each grey goose quill;

May every Bavius have his Bufo still."--POPE, _Prologue to the Satires._

Bavius has become proverbial as a bad poet from the lines in Vergil's

_Eclogues_ (III, 90):

"Qui Bavium non odit, amet tua carmina, Maevi,

Atque idem jungat vulpes, et mulgeat hircos."

"He who does not hate Bavius shall love thy verses, O Maevius; and the same

shall yoke foxes and shall milk he-goats."

Bavius and Maevius were the worst of Latin poets, condemned by Horace as

well as Vergil.

[661] See Vol. II, page 158, note 279.

[662] "Honest," "useful," "handsome," "sweet."

[663] "Let not the fourth man attempt to speak."

[664]

"In those old times,--ah

'Twas just like this, ah!"

[665] See Vol. I, page 382, note 12 {785}.

[666] These remarks were never written.--S. E. De M.

[667]

"Fleas, flies, and friars, are masters who sadly the people abuse,

And thistles and briars are sure growing grains to abuse.

O Christ, who hatest strife and slayst all things in peace,

Destroy where'er are rife, briars, friars, flies and fleas.

Fleas, flies, and friars foul fall them these fifteen years

For none that there is loveth fleas, flies, nor freres."

[668] "It is my plan to restore to an unskilled race the worthy arts of a

better life."

[669] The first sentences of the first oration of Cicero against Catiline:

"Quo usque tandem abutere, Catilina, patientia nostra?" (How long, O

Catiline, will you abuse our patience?) "Quamdiu etiam furor iste tuus nos

eludet?" (How long will this your madness baffle us?) "Nihilne te nocturnum

praesidium Palati, ... nihil horum ora voltusque moverunt?" (Does the night

watch of the Palatium, ... do the faces and expressions of all these men

fail to move you?) "In te conferri ..." (This plague should have been

inflicted upon you long ago, which you have plotted against us so long.)

[670] "Beware of the things that are marked."

[671] "Farewell, ye teachers without learning! See to it that at our next

meeting we may find you strong in body and sound in mind."

[672] See Vol. I, page 336, note 8 {713}.

[673] See Vol. I, page 229, note 2 {515}.

[674] This proof, although capable of improvement, is left as in the

original. Those who may be interested in the mathematics of the question,

may consult F. Enriques, _Fragen der Elementargeometrie_ (German by

Fleischer), Leipsic, 1907, Part II, p. 267; F. Rudio, _Archimedes_,

_Huygens_, _Lambert_, _Legendre_. _Vier Abhandlungen ueber die

Kreismessung_, Leipsic, 1892; F. Klein, _Famous Problems of Elementary

Geometry_ (English by Beman and Smith), Boston, 1895; J. W. A. Young,

_Monographs on Modern Mathematics_, New York, 1911, Chap. IX (by the editor

of the present edition of De Morgan.)

[675] See Vol. I, page 69, note 2 {95}.

[676] See Vol. I, page 137, note 8 {286}.

[677] Joseph Allen Galbraith who, with Samuel Haughton, wrote the Galbraith

and Haughton's _Scientific Manuals_. (Euclid, 1856; Algebra, 1860;

Trigonometry, 1854; Optics, 1854, and others.)

[678] This note on Carlyle (1795-1881) is interesting. The translation of

Legendre appeared in the same year (1824) as his translation of Goethe's

_Wilhelm Meister_.

[679] Michael Stifel (1487-1567), also known as Stiefel, Styfel, and

Stifelius, was an Augustine monk but became a convert to Lutheranism. He

was professor of mathematics at Jena (1559-1567). His edition of the _Coss_

appeared at Koenigsberg in 1553, the first edition having been published in

1525. The + and - signs first appeared in print in Widman's arithmetic of

1489, but for purposes of algebra this book was one of the first to make

them known.

[680] Christoff Rudolff was born about 1500 and died between 1540 and 1552.

_Die Coss_ appeared in 1525 and his arithmetic in 1526.

* * * * *

Corrections made to printed original.

Page 9, "long-fostered prejudice": 'perjudice' in original.

Page 73, "Pensees, ch. 7": 'Pansees' in original.

Page 127, "and pulled out a plum": 'und' in original.

Page 147, "did not come forward": 'forword' in original.

Page 172, "come into general circulation": 'circulalation' in original.

Ibid., "the more difficult fractions which we have got": 'he have got' in

original.

Page 192, "it has been stated": 'started' in original.

Page 216, "the obsolete word tetch of the same meaning": 'meaing' in

original.

Page 228, "[Greek: dioklasianos]": 'dioklalasianos' in original.

Page 233. After `Henry E. Manning' were printed two paragraphs `Shilling

versus Franc.' and `Teutonic Long Hundred 120 versus 100 or the Decimal

question.' These appear to have been set in error, there is no applicable

context.

Page 316, "in a manner depending upon the difference": 'maner' in original.

Page 322, "neither what Newton did, nor what was done before him.": 'not'

(for 'nor') in original.

Page 344, "Victoria toto coelo": 'tolo' in original.

Page 368, "cannot be brought up to 1": 'up to +-' in original.

Page 371, "Q_2=b_2 Q_1+a_2": 'Q_2=b_2 Q_1-a_2' in original.

Note 50, "all who were not in the road to Heaven were excommunicated":

'excomunicated' in original.

Note 372, "[Greek: he alazoneia biou]": 'alaxoneia' in original.

Ibid., "Iapetos": 'Ispetos' in original.

Ibid., "Papeiskos": 'Paspeisoks' in original.

Ibid., "[Greek: dioklasianos]": 'dioklalasianos' in original.