STEWART, (DR) MATTHEW, an
eminent geometrician, and professor of mathematics in the university of
Edinburgh, was born at Rothsay, in the island of Bute,—of which his father,*
*the reverend Mr Dugald Stewart, was minister,—in the year 1717. [Memoir
by professor Playfair, Trans. R. Soc. Edin. I. 57.] On finishing his course
at the grammar school, he was entered at the university of Glasgow in 1734.
At college, he became acquainted with Dr Hutcheson and Dr Simson. In the
estimation of the latter, he rose, in after life*, *from the rank of a
favourite pupil, to that of an esteemed friend. They were long intimate
personal companions, admired the same branches of their common science, and
exhibited in their works symptoms of mutual assistance. It is said, indeed,
that we are indebted to the friendship and acuteness of Simson, for the
suggestion of mathematics as a study suited to the genius of Stewart. At all
events, there is every reason to suppose that the love of the latter for the
geometry of the ancients, was derived from his intercourse with his
instructor. While attending the lectures of Dr Gregory in Edinburgh, in
1741, the attractions of the new analysis were not sufficient to make him
neglect his favourite study; and he communicated to his friend his
discoveries in geometry, receiving similar communications in return. While
Simson was conducting the laborious investigations, which enabled him to
revive the porisms of the ancients, Stewart received the progressive benefit
of the discoveries, long before they were communicated to the world; and
while he probably assisted his friend in his investigations, he was enabled,
by investigating the subject in a new direction, to publish, in 1746, his
celebrated series of propositions, termed "General Theorems." "They are,"
says the author’s biographer, "among the most beautiful, as well as most
general propositions known in the whole compass of geometry, and are perhaps
only equalled by the remarkable *locus *to the circle in the second
book of Apollonius, or by the celebrated theorems of Mr Cotes. The first
demonstration of any considerable number of them, is that which was lately
communicated to this society [Communicated by Dr Small.] (the Royal Society
of Edinburgh); though I believe there are few mathematicians, into whose
hands they have fallen, whose skill they have not often exercised. The unity
which prevails among them, is a proof that a single, though extensive view,
guided Mr Stewart in the discovery of them all." Meanwhile, Mr Stewart had
become a licentiate of the church of Scotland; and through the joint
influence of the earl of Bute and the duke of Argyle, had obtained the
living of Roseneath. The "General Theorems" made their appearance at a time
when they were calculated to have a considerable effect on the prospects of
the author. In the summer of 1746, the mathematical chair of Edinburgh
became vacant, by the death of Mr Maclaurin. Stewart was not at that period
known to the learned world; and Mr Stirling, a gentleman of well known
reputation, was requested to become the new professor. This gentleman
declined the situation; and, towards the end of the year, when the patrons
of the university were looking for another candidate worthy of the important
duty, Stewart’s book was published. The author was readily offered the
situation, which he accepted. "The duties of this office," says his
biographer, "gave a turn somewhat different to his mathematical pursuits,
and led him to think of the most simple and elegant means of explaining
those difficult propositions, which were hitherto only accessible to men
deeply versed in the modern analysis. In doing this, he was pursuing the
object which, of all others, he most ardently wished to attain, viz., the
application of geometry to such problems as the algebraic calculus alone had
been thought able to resolve. His solution of Kepler’s problem was the first
specimen of this kind which he gave to the world; and it was impossible to
have produced one more to the credit of the method which he followed, or of
the abilities with which he applied it." This solution appeared in the
second volume of the Essays of the philosophical Society of Edinburgh, for
the year 1756. To quote again the words of the eminent biographer: "Whoever
examines it, will be astonished to find a problem brought down to the level
of elementary geometry, which had hitherto seemed to require the finding of
fluents, and the reversion of series; he will acknowledge the reasonableness
of whatever confidence Mr Stewart may be hereafter found to place in those
simple methods of investigation, which he could conduct with so much
ingenuity and success; and will be convinced, that the solution of a
problem, though the most elementary, may be the least obvious; and though
the easiest to be understood, may be the most difficult to be discovered."
In pursuance of his principle of introducing the forms of ancient
demonstration, as applicable to those more complicated parts of the science,
called the mixed mathematics, for which they had been considered
unqualified, he published, in 1761, his "Tracts, Physical and Mathematical,
containing an Explanation of several important Points in Physical Astronomy;
and a New Method of ascertaining the Sun’s distance from the Earth, by the
Theory of Gravitation." "In the first of these," says his biographer, "Mr
Stewart lays down the doctrine of centripetal forces, in a series of
propositions, demonstrated, (if we admit the quadrature of curves,) with the
utmost rigour, and requiring no previous knowledge of the mathematics,
except the elements of plain geometry, and conic sections. The good order of
these propositions, added to the clearness and simplicity of the
demonstrations, renders this tract the best elementary treatise of physical
astronomy that is anywhere to be found." It was the purpose of the three
remaining tracts to determine the effect of those forces which disturb the
motions of a secondary planet; and, in particular, to determine the distance
of the sun, from its effect in disturbing the motions of the moon. Owing to
the geometrical method which he adopted, and likewise to the extreme
distance of the sun, which makes all the disturbances he produces on the
motion of the moon, very near to that point at which increase of distance to
infinity would not change their force, he could only proceed on a system of
approximation; and in applying the principles of his plan to a practical
calculation of the sun’s distance, which he published in 1763, entitled,
"Distance of the Sun from the Earth, determined by the Theory of
Gravitation, together with several other things relative to the same
subject," he was found to have made a very considerable error. He found the
distance of the sun to be equal to 29,875 semi-diameters of the earth, or
about 118,541,428 English miles. About five years afterwards, there appeared
a pamphlet from the pen of Mr Dawson of Sudbury, called "Four Propositions,
intended to point out certain Errors in Dr Stewart’s Investigation, which
had given a result much greater than the truth." This was followed by a
second attack from Mr Lauden, who, like Price in arithmetic, accomplished
the difficult task of becComing an enthusiast in mathematics, and, by means
of exaggerating errors, and commenting on their atrocity, astonished the
world with a specimen of controversial mathematics. The biographer thus
states the sources of the mistakes which called forth these animadversions:
"As in arithmetic, we neglect those small fractions which, though of
inconsiderable amount, would exceedingly embarrass our computations; so, in
geometry, it is sometimes necessary to reject those small quantities, which
would add little to the accuracy, and much to the difficulty of the
investigation. In both cases, however, the same thing may happen; though
each quantity thrown out may be inconsiderable in itself, yet the amount of
them altogether, and their effect on the last result, may be greater than is
apprehended. This was just what had happened in the present case. The
problem to be resolved, is, in its nature, so complex, and involves the
estimation of so many causes, that, to avoid inextricable difficulties, it
is necessary to reject some quantities, as being small in comparison of the
rest, and to reason as if they had no existence." Soon after the publication
of this essay, Dr Stewart’s health began to decline; and in 1772, he retired
to the country, leaving the care of his class to his eminent son, Dugald
Stewart, who was elected joint professor with him in 1775. He died on the
23d January, 1785, at the age of sixty-eight. Besides the works above
mentioned, he published, "Propositiones Geometricae more veterum
Demonstratae ad Geometriam Antiquam Illustrandam et Promovendam Idoneae,"
1763. |