to Charles I., and the son was naturally brought up in royalist
principles. The date of his birth is variously assigned by his
biographers, but the more probable account fixes it to October, 1630. It
is recorded that his childhood was turbulent and quarrelsome; that he
was careless of his clothes, disinclined to study, and especially
addicted to fighting and promoting quarrels among his school-fellows;
and of a temper altogether so unpromising, that his father often
expressed a wish, that if any of his children should die, it might be
his son Isaac. He was first sent to school at the Charter House, and
removed thence to Felstead in Essex. Here his disposition seemed to
change: he made great progress in learning, and was entered at Trinity
College in 1645, in his fifteenth year, it being then usual to send boys
to college about that age. He passed his term as an under graduate with
much credit. The time and place were not favourable to the promotion of
Royalists; for a royalist master had been ejected to make room for one
placed there by the Parliament, and the fellows were chiefly of the same
political persuasion. But Barrow’s good conduct and attainments won the
favour of his superiors, and in 1649, the year after he took his degree,
he was elected fellow. It deserves to be known, for it is honourable to
both parties, that he never disguised or compromised his own principles.
[Illustration:
_Engraved by B. Holl._
BARROW.
_From the original Picture by Isaac Whood
at Trinity College, Cambridge._
Under the Superintendance of the Society for the Diffusion of Useful
Knowledge.
_London, Published by Charles Knight, Ludgate Street, & Pall Mall
East._
]
His earlier studies were especially turned towards natural philosophy;
and, rejecting the antiquated doctrines then taught in the schools, he
selected Bacon, Galileo, and Descartes as his favourite authors. He did
not commence the study of mathematics until after he had gained his
fellowship, and was led to it in a very circuitous way. He was induced
to read the Greek astronomers, with a view to solving the difficulties
of ancient chronology; and to understand their works a thorough
knowledge of geometry was indispensable. He therefore undertook the
study of that science; which suited the bent of his genius so well, that
he became one of the greatest proficients in it of his age. His first
intention was to become a physician, and he made considerable progress
in anatomy, chemistry, botany, and other sciences subservient to the
profession of medicine; but he changed his mind, and determined to make
divinity his chief pursuit. In 1655 he went abroad. His travels extended
through France, Italy, and the Levant, to Constantinople; and, after an
absence of four years, he returned to England through Germany and
Holland. During this period he lost no opportunity of prosecuting his
studies; and he sent home several descriptive poems, and some letters,
written in Latin, which are printed in his Opuscula, in the fourth
volume of the folio edition of his works. In the voyage to Smyrna he
gave a proof of the high spirit, which, purified from its childish
unruliness and violence, continued to form part of his character through
life. The vessel being attacked by an Algerine corsair, Barrow remained
on the deck, cheerfully and vigorously fighting, until the assailant
sheered off. Being asked afterwards why he did not go into the hold, and
leave the defence of the ship to those whom it concerned, he replied,
“It concerned no one more than myself. I would rather have died than
fallen into the hands of those merciless pirates.” He has described this
voyage, and its eventful circumstances, in a poem contained in his
Opuscula.
He entered into orders in 1659, and in the following year was made Greek
Professor at Cambridge. The numerous offices to which he was appointed
about this time, show that his merits were generally and highly
esteemed. He was chosen to be Professor of Geometry at Gresham College
in 1662; and was one of the first fellows elected into the Royal
Society, after the incorporation of that body by charter in 1663; in
which year he was also appointed the first mathematical lecturer on the
foundation of Mr. Lucas, at Cambridge. Not that he made sinecures of
these responsible employments, or thought himself qualified to discharge
the duties of all at once: for he resigned the Greek professorship, on
being appointed Lucasian Professor, for reasons explained in his
introductory oration, which is extant in the Opuscula. The Gresham
professorship he also gave up in 1664, intending thenceforth to reside
at Cambridge. Finally, in 1669, he resigned the Lucasian chair to his
great successor, Newton, intending to devote himself entirely to the
study of divinity. Barrow received the degree of D.D. by royal mandate,
in 1670; and, in 1672, was raised to the mastership of Trinity College
by the King, with the compliment, “that he had given it to the best
scholar in England.” In that high station he distinguished himself by
liberality: he remitted several allowances which his predecessors had
required from the college; he set on foot the scheme for a new library,
and contributed in purse, and still more by his personal exertions, to
its completion. It should be remarked that his patent of appointment
being drawn up, as usual, with a permission to marry, he caused that
part to be struck out, conceiving it to be at variance with the
statutes. He was cut off by a fever in the prime of life, May 4, 1679,
aged 49, during a visit to London. His remains were honourably deposited
in Westminster Abbey, among the worthies of the land; and in that noble
building a monument was erected to him by the contributions of his
friends.
Of Barrow’s mathematical works we must speak briefly. The earliest of
them was an edition of Euclid’s Elements, containing all the books,
published at Cambridge in 1655, followed by an edition of the Data in
1657. His Lectiones Opticæ, the first lectures delivered on the Lucasian
foundation, were printed in 1669, and attracted the following
commendation from the eminent mathematician, James Gregory. “Mr. Barrow,
in his Optics, shows himself a most subtle geometer, so that I think him
superior to any that ever I looked upon. I long exceedingly to see his
geometrical lectures, especially because I have some notions on that
subject by me.” In this work, (we speak on the authority of Montucla,
part iv. viii.), Barrow has applied himself principally to discuss
subjects unnoticed or insufficiently explained by preceding authors.
Among these was the general problem, to determine the focus of a lens;
which, except in a few cases, as where the opposite sides of the lens
are similar, and the incident rays of light parallel to the axis, had
hitherto been left to the practical skill and experience of the workman.
Barrow gave a complete solution of the problem, comprised in an elegant
formula which includes all cases, whether of parallel, convergent, or
divergent rays. This book, says Montucla, is a mine of curious and
interesting propositions in optics, to the solution of which geometry is
applied with peculiar elegance.
The Lectiones Geometricæ, full of profound researches into the
metaphysics of geometry, the method of tangents, and the properties of
curvilinear figures, appeared in the following year, 1670. The vast
improvements in our methods of investigation, arising out of the
invention of the fluxional or differential calculus, have cast into the
shade the labours, and in part the fame, of the early geometricians, and
have made that easy, which before was all but impossible. This work,
however, is remarkable as containing a way of determining the subtangent
of a curve, justly characterized by Montucla as being so intimately
connected with the above-named method of analysis, that it is needless
to seek in subsequent works the main principle of the differential
calculus. The inquiring reader will find a full account of it in
Montucla, or in Thomson’s History of the Royal Society, page 275. There
is an English translation of the Lectiones Geometricæ by Stone,
published in 1735. Barrow also edited the works of Archimedes, the
Conics of Apollonius, and the Spherics of Theodosius, in a very
compressed form, in 1 vol. 8vo. Lond. 1675. The treatise of Archimedes
on the Sphere and Cylinder, and the Mathematicæ Lectiones, a series of
Lucasian lectures, read in 1664 and subsequent years, were not printed
until 1683, after the author’s death. This work, or at least Kirby’s
translation, published about 1734, contains the Oration which he made
before the University on his election to the Lucasian chair. For further
detail see Ward’s Lives of the Gresham Professors.
It is however as a theologian that Barrow is best known to the present
age. Unlike his scientific writings, his theological works never can
grow obsolete, for they contain eternal truths set forth with a power of
argument, and force of eloquence, which must ever continue to command
the admiration of those who are capable of appreciating and relishing
the noblest qualities and products of the human mind. The light of
revelation shone clearly and steadily then as now; no modern discoveries
can increase or diminish its brightness; no new methods of reasoning, no
more convenient forms of notation or expression, can supersede the
sterling excellences which we have just ascribed to this great divine.
Others may rise up (they are yet to come) equal or superior to him in
these very excellences; still their fame can never detract from his; and
Barrow with his great predecessor, Hooker, will not fail to be classed
among the luminaries of the English church, and the standard authors of
the English language. Copious and majestic in his style, his sermons
were recommended by the great Lord Chatham to his great son, as
admirably adapted to imbue the public speaker with the coveted
“abundance of words” the knowledge and full command of his native
language. He himself neglected not to increase his stores from the
models of ancient eloquence; and his manuscripts, preserved in Trinity
College Library, bear testimony to the diligence with which he
transcribed the finest passages of the Greek and Latin authors,
especially Demosthenes and Chrysostom. His sermons were long, too long
it was thought by many of his hearers; but they were carefully composed,
written and rewritten again and again, and their method, argumentative
closeness, and abundant learning, show that he thought no pains too
great to bestow on the important duty of public teaching. Warburton said
that in reading Barrow’s sermons, he was obliged to think. They are
numerous, considering their nature and the comparatively short period of
the author’s clerical life. The first edition of his works, by
Archbishop Tillotson, to whom, in conjunction with his friend and
biographer Mr. Hill, Barrow left his manuscripts, contains seventy-seven
sermons on miscellaneous subjects, of which only two were printed, and
those not published, during the author’s life; together with a series of
thirty-four sermons on the Apostle’s Creed. Mr. Hughes, the late editor
of his works, has added to the former collection five more, printed for
the first time from the original MSS. in Trinity Library. We quote from
the life prefixed to that edition, the eloquent passage in which Mr.
Hughes speaks of these admirable works.
“Never, probably, was religion at a lower ebb in the British dominions,
than when that profligate Prince Charles II., who sat unawed on a throne
formed as it were out of his father’s scaffold, found the people so
wearied of puritanical hypocrisy, presbyterian mortifications, and a
thousand forms of unintelligible mysticism, that they were ready to
plunge into the opposite vices of scepticism or infidelity, and to
regard with complacency the dissolute morals of himself and his vile
associates. To denounce this wickedness in the most awful terms; to
strike at guilt with fearless aim, whether exalted in high places, or
lurking in obscure retreats; to delineate the native horrors and sad
effects of vice, to develope the charms of virtue, and inspire a love of
it in the human heart; in short, to assist in building up the fallen
buttresses and broken pillars of God’s church upon earth, was the high
and holy duty to which Barrow was called.”
Besides his sermons, Barrow wrote a shorter Exposition of the Creed, an
Exposition of the Decalogue, an Exposition of the Lord’s Prayer, and a
short account of the doctrine of the Sacraments. These were composed in
1669, the year in which the Lectiones Opticæ were published, in
obedience to some college regulation, and, Mr. Hughes conjectures, as
exercises for a college preachership. Barrow says, in a letter, that
they so took up his thoughts, that he could not easily apply them to any
other matter. His great work on the Pope’s Supremacy was not composed
till 1676. The pains which he took with it were immense; and we are told
by the same authority that “the state of his MS. in Trinity Library
shows that probably no piece was ever composed more studiously, digested
more carefully, or supported by more numerous and powerful authorities.”
Barrow states in this work the several positions, on which the Romanists
ground their claim on behalf of the Bishop of Rome, for universal
supremacy over the Christian church. These he divides into seven heads,
which he proceeds severally and successively to refute. “This treatise,”
says Dr. Tillotson, in his preface to it, “he gave to me on his
death-bed, with the character that he hoped it was indifferent perfect,
though not altogether as he had intended it, if God had granted him
longer life. He designed indeed to have transcribed it again, and to
have filled up those many spaces which were purposely left in it for the
farther confirmation and illustration of several things, by more
testimonies and instances which he had in his thoughts. And it would
certainly have added much to the beauty and perfection of this work, had
it pleased God that he had lived to finish it to his mind, and to have
given it his last hand. However, as it is, it is not only a just, but an
admirable discourse on this subject, which many others have handled
before, but he hath exhausted it; insomuch that no argument of moment,
nay, hardly any consideration properly belonging to it, hath escaped his
large and comprehensive mind. He hath said enough to silence the
controversy for ever, and to deter all wise men of both sides from
meddling any further with it.” Appended to this treatise on the
Supremacy of the Pope, is a discourse on the Unity of the Church.
We conclude with a few scattered notices of the character and person of
this excellent man. His habits, it will readily be supposed, were very
laborious. Dr. Pope, in his Life of Bishop Ward, says that during winter
Barrow would rise before light, being never without a tinder-box, and
that he has known him frequently rise after his first sleep, light and
burn out his candle, and then return to bed before day. In pecuniary
affairs he was generous in the extreme. Of his liberality to his college
we have already spoken. We may add that, being appointed to two
ecclesiastical preferments, he bestowed the profits of both in charity,
and resigned them as soon as he became master of Trinity. He left no
property but books and unpublished manuscripts. Pure in his morals, he
was the farthest possible from moroseness; amiable, lively, and witty in
his temper and conversation, he was impatient of any looseness,
irreverence, or censoriousness of speech, “being of all men,” says Dr.
Tillotson, in his Address to the Reader, “I ever had the happiness to
know, the clearest of this common guilt, and most free from offending in
word; coming as near as it is possible for human frailty to do, to the
perfect idea of St. James, his _perfect man_.”
His figure was low and spare, but of uncommon strength; and his courage,
devoid of all alloy of quarrelsomeness, was approved in more than one
instance related by the biographers of his peaceful life. It was among
his peculiarities that he never would sit for his portrait; but some of
his friends found means to have it taken without his knowledge, while
they engaged his attention in discourse. There is a full length of him
in the hall of Trinity, in fit conjunction with those of Newton and
Bacon.
The earliest authority for Barrow’s life is a short memoir by his friend
and executor, Mr. Hill, prefixed to the first edition of his works. Mr.
Ward added some particulars, in his Lives of the Gresham Professors. The
fullest accounts are to be found in the second edition of the Biographia
Britannica, and in the life prefixed to Mr. Hughes’s edition of his
theological works. In this the editor has given an analysis of the
contents of each piece, calculated to assist the student to a thorough
understanding of the author’s train of argument.
[Illustration: Monument of Barrow in Westminster Abbey.]
[Illustration:
_Engraved by W. Hopwood._
D’ALEMBERT.
_From the original Picture by De la Tour
in the Collection of the Institute of France._
Under the Superintendance of the Society for the Diffusion of Useful
Knowledge.
_London, Published by Charles Knight, Ludgate Street, & Pall Mall
East._
]
[Illustration]
D’ALEMBERT.
Jean le Rond D’alembert, one of the most distinguished mathematicians of
the last century, owed none of his eminence to the accidents of birth or
fortune. Even to a name he had no legal title; he derived the one half
of that which he bore from the church of St. Jean le Rond in Paris, near
which he was exposed; and the other probably from his foster-mother, a
glazier’s wife, to whose care he was intrusted by a commissary of
police, who found him. It is conjectured that both the exposure and the
adoption of the infant were preconcerted; for a short time the father
appeared, and settled on him a yearly pension of twelve hundred francs,
equivalent to about £50.
Owing to these circumstances the date of D’Alembert’s birth is not
exactly known; it is said to have been the 16th or 17th of November,
1717. He commenced his studies at the Collège des Quatre Nations when
twelve years old. Mathematics and poetry seem to have been his favourite
pursuits, since his instructors, he says, endeavoured to turn him from
them; making it a charge against the former, that they dried up the
heart, and recommending that his study of the latter should be confined
to the poem of St. Prosper upon Grace. He was permitted, however, to
study the rudiments of mathematics: and we may infer that he was little
indebted either to books or teachers, from the mortification which he
felt somewhat later in life, at finding that he had been anticipated in
many things which he had believed to be discoveries of his own. He
meant, at one time, to follow the profession of the law, and proceeded
so far as to be admitted an advocate. Finding this not to his taste, he
tried medicine; and, resolute in good intentions, sent his mathematical
books to a friend, to be retained till he had taken his doctor’s degree.
But he reclaimed book after book on various pretexts, and finally
determined to content himself with his annuity of fifty pounds, and
liberty to devote his whole time to the scientific pursuits which he
loved so much. His mode of life at this period has been described by
himself:—“He awoke,” he says, “every morning, thinking with pleasure on
the studies of the preceding evening, and on the prospect of continuing
them during the day. When his thoughts were called off for a moment,
they turned to the satisfaction he should have at the play in the
evening, and between the acts of the piece he meditated on the pleasures
of the next morning’s study.”
The history of D’Alembert’s life is soon told. Some memoirs written in
1739 and 1740, and some corrections which he made in the Analyse
Démontrée of Reynau, a work then much esteemed in France, obtained for
him an entrance into the Académie des Sciences in 1741, at the early age
of twenty-four. Simple in his habits, careless of his own advancement,
or of the favours of great men, he refused several advantageous offers,
which would have withdrawn him from the society of Paris, and from the
libraries and other literary advantages of that great metropolis.
Frederic II. of Prussia sought to tempt him to Berlin in 1752, and again
in 1759. The invitation was again repeated and urged upon him in 1759
and 1763; and on the last occasion the King assured D’Alembert that, in
rejecting it, he had made the only false calculation of his whole life.
In 1762 Catharine of Russia wished him to undertake the education of her
son, and endeavoured to overcome his reluctance to leave Paris, by
promising him an income of ten thousand francs, and a kind reception to
as many of his friends as would accompany him. “I know,” she said, “that
your refusal arises from your desire to cultivate your studies and your
friendships in quiet. But this is of no consequence: bring all your
friends with you, and I promise you that both you and they shall have
every accommodation in my power.” But his income had been rendered
sufficient for his wants by a pension of twelve hundred francs from the
King of Prussia, and an equal sum from the French Government; and he
declined to profit by any of these liberal offers.
It is to D’Alembert’s honour that, until the end of her life, he repaid
the services of his foster-mother with filial attention and love. It is
said that when his name became famous, his mother, Mademoiselle de
Tencin, a lady of rank and wit, and known in the literary circles of the
day, sent for him, and acquainted him with the relationship which
existed between them. His well-merited reply was, “You are only my
step-mother, the glazier’s wife is my mother.” He lived unmarried, but
the latter years of his life were overcast in consequence of a singular
and unfortunate attachment to a M^{lle.} de l’Espinasse, a young lady of
talent, whose society was much courted by the literary men of Paris. She
professed to return this attachment; insomuch that when D’Alembert was
attacked by a severe illness in 1765, she insisted on becoming his
nurse, and after his recovery took up her abode under his roof. The
connexion is said to have been purely Platonic; and this, it has been
observed, _may_ be believed, because, had the fact been different, there
was little reason for concealing it, according to the code of morals
which then regulated Parisian society. But the lady proved fickle; and
worse than fickle, for she treated D’Alembert, who still retained his
affection for her, with contempt and unkindness. Yet this ill usage did
not alienate his regard. Upon her death he fell into a state of profound
melancholy, from which he never entirely recovered. He died October 29,
1783. Not having conformed, on his death-bed, to the requisitions of the
Roman church, some difficulty was experienced in procuring the rites of
burial; and in consequence his interment was strictly private.