Speaker 1: Chapter seventeen, Part three of A Short Account of the
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Speaker 1: Short Account of the History of Mathematics by W. W.
Speaker 1: Rowse Ball. Chapter eighteen Leibniz and the Mathematicians of the
Speaker 1: first half of the eighteenth century. Daniel Bernoulli. Daniel Bernoulli,
Speaker 1: whose name I mentioned above, and who was by far
Speaker 1: the ablest of the younger Bernoulli's, was a contemporary and
Speaker 1: intimate friend of Euler, whose works are mentioned in the
Speaker 1: next chapter. Daniel Bernoulli was born on February ninth, seventeen
Speaker 1: hundred and died at Bail, where he was professor of
Speaker 1: natural philosophy, on March seventeenth, seventeen eighty two. He went
Speaker 1: to Saint Petersburg in seventeen twenty four as professor of mathematics,
Speaker 1: but the roughness of the social life was distasteful to him,
Speaker 1: and he was not sorry when a temporary illness in
Speaker 1: seventeen thirty three allowed him to plead his health as
Speaker 1: an excuse for leaving. He then returned to bail, where
Speaker 1: he held successively chairs of medicine, metaphysics, and natural philosophy.
Speaker 1: There his earliest mathematical work was on the Excreciones, published
Speaker 1: in seventeen twenty four. These contained a theory of the
Speaker 1: oscillations of rigid bodies and a solution to the differential
Speaker 1: equations proposed by Riccatti. Two years later, he pointed out
Speaker 1: for the first time the frequent desirability of resolving a
Speaker 1: compound motion into motions of translation and motions of rotation.
Speaker 1: His chief work is his hydro Damonique, published in seventeen
Speaker 1: thirty eight. It resembled is Lagrange's Mechanique an arritique in
Speaker 1: being arranged so that all the results are consequences of
Speaker 1: a single principle, namely, in this case, the conservation of energy.
Speaker 1: This was followed by a memoir on the theory of
Speaker 1: the tides, to which, conjointly with memoirs by Euler and maclaurin,
Speaker 1: a prize was awarded by the French Academy. These three
Speaker 1: memoirs contain all that was done on the subject between
Speaker 1: publication of Newton's Principia and the investigations of Laplace. Bernoulli
Speaker 1: also wrote a large number of papers on various mechanical questions,
Speaker 1: especially on problems connected with vibrating strings and the solutions
Speaker 1: given by Taylor and d' lambert. He is the earliest
Speaker 1: writer who attempted to formulate a kinetic theory of gases,
Speaker 1: and he applied the idea to explain the law associated
Speaker 1: with the names of Boyle and Mariotte, the English mathematicians
Speaker 1: of the eighteenth century. I have reserved a notice of
Speaker 1: the English mathematicians who succeeded Newton, in order that the
Speaker 1: members of the English school may all be treated together.
Speaker 1: It was almost a matter of course that the English should,
Speaker 1: at least at first have adopted the notation of Newton
Speaker 1: in the infinitesimal calculus in preference to that of Libanates,
Speaker 1: and the English school would consequently, in any case have
Speaker 1: developed on somewhat different lines to that of the continent,
Speaker 1: where a knowledge of the infinitesimal calculus was derived solely
Speaker 1: from Lebants and the Bernoullis. But this separation into two
Speaker 1: distinct schools became very marked owing to the action of
Speaker 1: Libanates and John Bernoulli, which was naturally resented by Newton's friends,
Speaker 1: and so for forty or fifty years, to the mutual
Speaker 1: disadvantage of both sides, the quarrel raged. The leading members
Speaker 1: of the English School were Coats, des Mois, Detont, David Gregory,
Speaker 1: Halle McLaurin, Simpson and Taylor. I may, however, again remind
Speaker 1: my readers that as we approach the modern times, the
Speaker 1: number of capable mathematicians in Britain, France, Germany and Italy
Speaker 1: becomes very considerable. But that in a popular sketch like
Speaker 1: this book, it is only the leading men whom I
Speaker 1: propose to mention to David Gregory, Halley and Detonte. I
Speaker 1: need to devote but a few words. David Gregory. David Gregory,
Speaker 1: the nephew of James Gregory, mentioned above in page three
Speaker 1: point fifteen, born at Aberdeen on June twenty fourth, sixteen
Speaker 1: sixty one, and died at Maidenhead on October tenth, seventeen
Speaker 1: oh eight. Was appointed professor at Edinburgh in sixteen eighty four,
Speaker 1: and in sixteen ninety one was on Newton's recommendation elected
Speaker 1: Civilian Professor at Oxford. His chief works are one on geometry,
Speaker 1: issued in sixteen eighty four, one on optics published in
Speaker 1: sixteen ninety five, which contains the earliest suggestion of the
Speaker 1: possibility of making an achromatic combinations of lenses, and one
Speaker 1: on the Newtonian geometry, Physics and Astronomy, issued in seventeen
Speaker 1: o two. Halle Edmund Halley born in London in sixteen
Speaker 1: fifty six and died at Greenwich in seventeen forty two.
Speaker 1: Was educated at Saint Paul's School, London and Queen's College, Oxford.
Speaker 1: In seventeen o three succeeded Wallace as civilian professor, and subsequently,
Speaker 1: in seventeen twenty was appointed Astronomer Royal in succession to Flamsteed,
Speaker 1: whose Historia Cerestis Britannica he edited in seventeen twelve first
Speaker 1: and imperfect edition. Halley's name will be recollected for the
Speaker 1: generous manner in which he secured the immediate publication of
Speaker 1: Newton's Principia in sixteen eighty seven. Most of his original
Speaker 1: work on was on astronomy and allied subjects, and lies
Speaker 1: outside the limits of this book. It may be, however,
Speaker 1: said that the work is of excellent quality, and both
Speaker 1: Lalande and Mehran speak of it in the highest terms.
Speaker 1: Halley conjecturally restored the eighth and lost Book of the
Speaker 1: Conics of Apollonius, and in seventeen ten brought out a
Speaker 1: magnificent edition of the whole work. He also edited the
Speaker 1: works of Serenus and those of Mennelos, and some of
Speaker 1: the minor works of Apollonius. He was, in his turn
Speaker 1: succeeded at Greenwich as an astronomer Royal by Bradley Diton.
Speaker 1: Humphrey Dieton born at Salisbury in May twenty ninth, sixteen
Speaker 1: seventy five and died in London in seventeen fifteen at
Speaker 1: Christ's Hospital, where he was mathematical master. He does not
Speaker 1: seem to have paid much attention to mathematics until he
Speaker 1: came to London about seventeen o five, and his early
Speaker 1: death was a distinct loss to English science. He published
Speaker 1: in seventeen o six a textbook on fluxions. This and
Speaker 1: another similar work by William Jones, which was issued in
Speaker 1: seventeen eleven, occupied in England much the same place as
Speaker 1: Laptel's treatise did in France. In seventeen oh nine, Detont
Speaker 1: issued an algebra and in seventeen twelve a treatise on perspective.
Speaker 1: He also wrote numerous papers on the philosophical transactions. He
Speaker 1: was the earliest writer to attempt to explain the phenomenon
Speaker 1: of capillary on mathematical principles, and he invented a method
Speaker 1: of finding the longitude which has been since used on
Speaker 1: various occasions. Taylor Brooke Taylor born at Edmonton on August eighteenth,
Speaker 1: sixteen eighty five and died in London on December twenty ninth,
Speaker 1: seventeen thirty one. Was educated at Saint John's College, Cambridge,
Speaker 1: and was among the most enthusiastic of Newton's admirers. From
Speaker 1: the year seventeen twelve onwards he wrote numerous papers on
Speaker 1: philosophical transactions, in which, among other things, he discussed the
Speaker 1: motion of projectiles, the center of oscillation, and the forms
Speaker 1: of liquids raised by capillarity. In seventeen nineteen he resigned
Speaker 1: the secretaryship of the Royal Society and abandoned the study
Speaker 1: of mathematics. His earliest work, that by which he is
Speaker 1: generally known, is his methodis incrematorum directa et inversa, published
Speaker 1: in London in seventeen fifteen. This contains a proof of
Speaker 1: the well known theorem f x plus h equals f
Speaker 1: of x plus h, f primed of x plus h
Speaker 1: squared over two factorial multiplied by f double primed x
Speaker 1: plus and so on, by which any function of a
Speaker 1: single variable can be expanded in powers of it. He
Speaker 1: does not consider the convergency of the series, and the proof,
Speaker 1: which involves numerous assumptions, is not worth reproducing. The work
Speaker 1: also includes several theorems on interpolation. Taylor was the earliest
Speaker 1: writer to deal with theorems on the change of the
Speaker 1: independent variable. He was perhaps the first to realize the
Speaker 1: possibility of a calculus of operation, and just as he
Speaker 1: denotes the n differential coefficient of why by why sub n,
Speaker 1: so he uses why subnegative one to represent the integral
Speaker 1: of why. Lastly, he is usually recognized as the creator
Speaker 1: of the theory of finite differences. The applications of the
Speaker 1: calculus to various questions given in the Methodists have hardly
Speaker 1: received that attention they deserve. The most important of them
Speaker 1: is the theory of the transverse vibration of strings, a
Speaker 1: problem which had baffled previous investigators. In this investigation, Taylor
Speaker 1: showes that the number of half vibrations executed in a
Speaker 1: second is by multi applied by the square root of
Speaker 1: the quantity dp divided by l n, Where l is
Speaker 1: the length of the string, n is its weight, p
Speaker 1: is the weight which stretches it, and D is the
Speaker 1: length of a second's pendulum. This is correct, but in
Speaker 1: arriving at it, he assumes that every point on the
Speaker 1: string will pass through its position of equilibrium at the
Speaker 1: same instant, a restriction which de la Bern subsequently shewed
Speaker 1: to be unnecessary. Taylor also found the form which the
Speaker 1: string assumes at any instant. This work also contains the
Speaker 1: earliest determination of the differential equation of the path of
Speaker 1: a ray of light when traversing a heterogeneous medium and
Speaker 1: assuming that the density of the air depends only on
Speaker 1: its distance from the Earth's surface tailor obtained by means
Speaker 1: of quadratures, The approximate form of the curve, the form
Speaker 1: of the caternary, and the deters termination of the centers
Speaker 1: of oscillation and percussion are also discussed. A treatise on Perspective,
Speaker 1: published in seventeen nineteen, contains the earliest general annunciation of
Speaker 1: the principle of vanishing points, though the idea of vanishing
Speaker 1: points for horizontal and parallel lines in a picture hung
Speaker 1: in a vertical plane had been enunciated by Guido Ubaldi
Speaker 1: in his perspective Libri Pisa sixteen hundred. Coats Roger Coates
Speaker 1: was born near Leicester on July tenth, sixteen eighty two,
Speaker 1: and died at Cambridge on June fifth, seventeen sixteen. He
Speaker 1: was educated at Trinity College, Cambridge, of which society he
Speaker 1: was a fellow, and in seventeen o six was elected
Speaker 1: to the newly created Plumian Chair of Astronomy in the
Speaker 1: University of Cambridge. From seventeen oh nine to seventeen thirteen,
Speaker 1: his time was mainly occupied in editing the second edition
Speaker 1: of the Principia. The remark of Newton that if only
Speaker 1: Coats had lived, we should have learnt something indicates the
Speaker 1: opinion of his abilities held by most of his contemporaries.
Speaker 1: Coates's writings were collected and published in seventeen twenty two
Speaker 1: under the titles Harmonia Mensurarum and Opera Miscellania. His lectures
Speaker 1: on hydrostatics were published in seventeen thirty eight. A large
Speaker 1: part of the Harmonium Mensuratum was given up to the
Speaker 1: decomposition and integration of rational algebraical expressions. That part, which
Speaker 1: deals with the theory of partial fractions, was left unfinished,
Speaker 1: but was completed by des Maire. Coates's theorem in trigonometry,
Speaker 1: which depends on forming the quadratic factors of x to
Speaker 1: the power n minus one, is well known. The proposition
Speaker 1: that if from a fixed point ozh a line be
Speaker 1: drawn cutting a curve in q one, q two, and
Speaker 1: so on to q n, and a point p b
Speaker 1: s taken on the line, so that the reciprocal of
Speaker 1: op is the arithmetic mean of the reciprocals of oq one,
Speaker 1: oq two, oq three, and so on all the way
Speaker 1: to oq n, then the locus of p will be
Speaker 1: a straight line. Is also due to Coats, the title
Speaker 1: of the book was derived from the latter theorem. The
Speaker 1: Opera Miscellania contains a paper on the method for determining
Speaker 1: the most probable result from a number of observations. This
Speaker 1: was the earliest attempt to frame a theory of errors.
Speaker 1: It also contains essays on Newton's methodist differentiatis, the construction
Speaker 1: of tables by the method of differences, on the descent
Speaker 1: of a body under gravity, on the cycloidal pendulum, and
Speaker 1: on projectiles. Demoivre Abraham Demarra, more correctly written des Moirvre
Speaker 1: in two words, was born at Vitri in May twenty sixth,
Speaker 1: sixteen sixty seven, and died in Lund on November twenty seventh,
Speaker 1: seventeen fifty four. His parents came to England when he
Speaker 1: was a boy, and his education and friends were alike English.
Speaker 1: His interest in the higher mathematics is said to have originated,
Speaker 1: and is coming by chance across a copy of Newton's
Speaker 1: Principia from the Eleugee on Him, delivered in seventeen fifty
Speaker 1: four before the French Academy. It would seem that as
Speaker 1: a young fellow, his work as a teacher of mathematics
Speaker 1: had led him to the house of the Earl of
Speaker 1: Devonshire at the instant when Newton, who had asked permission
Speaker 1: to present a copy of his work to the Earl,
Speaker 1: was coming up taking up the book and charmed by
Speaker 1: the far reaching conclusions and the apparent simplicity of the reasoning,
Speaker 1: des Mauvre thought nothing would be easier than to master
Speaker 1: the subject, but to his surprise, found that to follow
Speaker 1: the argument overtaxed his powers. He however, bought a copy, and,
Speaker 1: as he had but little leisure, he tol or out
Speaker 1: the pages in order to carry one or two of
Speaker 1: them loose in his pocket, so that he could study
Speaker 1: them in the intervals of his work as a teacher. Subsequently,
Speaker 1: he joined the Royal Society, and he became intimately connected
Speaker 1: with Newton, Halley and other mathematicians of the English School.
Speaker 1: The manner of his death has a curious interest for psychologists.
Speaker 1: Shortly before it, he declared that it was necessary for
Speaker 1: him to sleep some ten minutes or a quarter of
Speaker 1: an hour longer each day than the preceding one. The
Speaker 1: day after he had thus reached a total of something
Speaker 1: over twenty three hours, he slept up to the limit
Speaker 1: of twenty four hours, and then died in his sleep.
Speaker 1: He is best known for having, together with Lambert, created
Speaker 1: that part of trigonometry which deals with imaginary quantities. Two
Speaker 1: theorems on this part of the subject are still connected
Speaker 1: with his name, namely that which asserts that sign n
Speaker 1: x plus ikos nx is one of the values of
Speaker 1: the quantity sin x plus KOs x all to the
Speaker 1: power n, and that which gives the various quadratic factors
Speaker 1: of x to the power two nus two times p
Speaker 1: x to the power n plus one. His chief works
Speaker 1: other than numerous papers in the Philosophical Transactions where the
Speaker 1: Doctrine of Chances published in seventeen eighteen and the Miscellania
Speaker 1: Analytica published in seventeen thirty. In the former, the theory
Speaker 1: of recurring series was first given, and the theory of
Speaker 1: partial fractions, which Coates's premature death had left unfinished, was completed,
Speaker 1: while the rule for finding the probability of a compound
Speaker 1: event was enunciated. The latter, besides the trigonometrical propositions mentioned above,
Speaker 1: contains some theorems in astronomy, but they are treated as
Speaker 1: problems in analysis. Maclaurin Colin maclaurin, who was born in
Speaker 1: Kilmoden in Argyllshire in February sixteen ninety eight and died
Speaker 1: at York on June fourteenth, seventeen forty six, was educated
Speaker 1: at the University of Glasgow. In seventeen seventeen, he was
Speaker 1: elected at the early age of nineteen Professor of Mathematics
Speaker 1: at Aberdeen, and in seventeen twenty five he was appointed
Speaker 1: the deputy of the mathematical Professor at Edinburgh, and ultimately
Speaker 1: succeeded him. There was some difficulty in securing a stipend
Speaker 1: for deputy, and Newton privately wrote offering to bear the
Speaker 1: cost so as to enable the university to secure the
Speaker 1: services of mclauren. McLaurin took an active part in opposing
Speaker 1: the advance of the young Pretender. In seventeen forty five,
Speaker 1: on the approach of the Highlanders, he fled to York,
Speaker 1: but the exposure in the trenches at Edinburgh and the
Speaker 1: privations he endured in his escape proved fatal to him.
Speaker 1: His chief works are Geometrica Organica, London, seventeen teen nineteen,
Speaker 1: his Treatise on Fluxions, Edinburgh, seventeen forty two, His Algebra, London,
Speaker 1: seventeen forty eight, and his Account of Newton's Discoveries, London,
Speaker 1: seventeen forty eight. The Geometrica Organica is on the extension
Speaker 1: of a theorem given by Newton. Newton had shewn that
Speaker 1: if two angles bounded by straight lines turned round their
Speaker 1: respective summits, so that the point of intersection of two
Speaker 1: of these line moves along a straight line. The other
Speaker 1: point of intersection will describe a conic, and if the
Speaker 1: first point move along a conic, the second will describe
Speaker 1: a cortic. Maclaurin gave an analytical discussion on the general
Speaker 1: theorem and shewed by how this method various curves could
Speaker 1: be practically traced. This work contains an elaborate discussion on
Speaker 1: curves and their pedals, a branch of geometry which he
Speaker 1: had created in two papers published in the Philosophical Transactions
Speaker 1: for s. Seventeen eighteen n seventeen nineteen. In the following year,
Speaker 1: seventeen twenty, Maclaurin issued a supplement which is practically the
Speaker 1: same as his Delinearum Geometricarum Propritatibus. It is divided into
Speaker 1: three sections and an appendix. The first section contains a
Speaker 1: proof of Coats's theorem as alluded to, and also the
Speaker 1: analogous theorem discovered by himself that if a straight line
Speaker 1: O P one P two is drawn through a fixed point,
Speaker 1: oh cut a curve of the n degree in n
Speaker 1: points P one, P two, and so on. And if
Speaker 1: the tangents at P one, P two cut in a
Speaker 1: fixed line ox in points A one, A, two, and
Speaker 1: so on, then the sum of the receptacles of the
Speaker 1: distances A one, O, A two, and so forth is
Speaker 1: constant for all positions of the line O, P one,
Speaker 1: P two, and so on. These two theorems are generalizations
Speaker 1: of those given by Newton on diameters and asymptotes. Either
Speaker 1: is deducible from the other. In the second section, these
Speaker 1: theorems are applied to conics. Most of these harmonic properties
Speaker 1: connected with an inscribed quadrilateral are determined, and in particular,
Speaker 1: the theorem on an inscribed hexagon, which is known by
Speaker 1: the name of Pascal, is deduced. Pascal's essay was not
Speaker 1: published until seventeen seventy nine, and the earliest printed denunciation
Speaker 1: of his theorem was that given by maclaurin. In the
Speaker 1: third section, these theorems are applied to cubic curves. Amongst
Speaker 1: other propositions, he shews that if if a quadrilateral be
Speaker 1: inscribed in a cubic and if the points of intersection
Speaker 1: of the opposite sides also lie on the curve, then
Speaker 1: the tangents to the cubic at any two opposite angles
Speaker 1: of the quadrilateral will meet on the curve. The appendix
Speaker 1: contained some general theorems. One of these, which includes Pascal's
Speaker 1: as a particular case, is that if a polygon be
Speaker 1: deformed so that, while each of its sides passes through
Speaker 1: a fixed point, its angles save one describe respectively curves
Speaker 1: of the m F, N, P, F, and so forth degrees.
Speaker 1: Then shall the remaining angle describe a curve of the
Speaker 1: degree to mnp. But if the given points be collinear,
Speaker 1: the resulting curve will be only of the degree mnp.
Speaker 1: This essay was reprinted with editions on the Philosophical Transactions
Speaker 1: for seventeen thirty five. The Treatise of Fluxions, published in
Speaker 1: seventeen forty two, was the first logical and systematic exposition
Speaker 1: of the method of fluxions. The cause of its publication
Speaker 1: was an attack by Berkeley on the principles of the
Speaker 1: infinitesimal calculus. In it, article seven fifty one, page six
Speaker 1: hundred and ten, McLaurin gave a proof of the theorem
Speaker 1: that fivx equals f of zero plus five x f
Speaker 1: prime of zero plus x squared over two factorial f
Speaker 1: double prime of zero plus so on, and so forth.
Speaker 1: This was obtained in the manner given in many modern textbooks,
Speaker 1: by assuming that fivx can be expanded in a form
Speaker 1: like fivx equals a not plus a one x plus
Speaker 1: a two x squared plus and so on and so on.
Speaker 1: Then on differentiating and putting x equals zero in the
Speaker 1: successive results, the values of a zero, a, one, and
Speaker 1: so on are obtained. But he did not investigate the
Speaker 1: convergency of the series. The result had been previously given
Speaker 1: in seventeen thirty by James Sterling in his methodis differentialis,
Speaker 1: and of course is at once deducible from Taylor's theorem,
Speaker 1: on which the proofs by Sterling and McLaurin are admittedly founded.
Speaker 1: McLaurin also here enunciated article three fifty, page two nine,
Speaker 1: the important theorem that if pix be positive and decreases
Speaker 1: x increases from x equels a to x equals infinity,
Speaker 1: then the series five A plus five, A plus one
Speaker 1: plus five, a plus two and so on is convergent
Speaker 1: or divergent, as the integral going from a to infinity
Speaker 1: of five x dx is finite or infinite. He also
Speaker 1: gives the correct theory of maxima and minima, and rules
Speaker 1: for finding and discriminating multiple points. This treatise is, however,
Speaker 1: especially valuable for the solutions that contains of numerous problems
Speaker 1: in geometry, statics, the theory of attractions, and astronomy. To
Speaker 1: solve these, he reverted to classical methods, and so powerful
Speaker 1: did these processes seem when used by him that Claat,
Speaker 1: after reading the work, abend an analysis and attack the
Speaker 1: problem of the figure of the Earth again by pure
Speaker 1: geometry at a later time. This part of the book
Speaker 1: was described by Lagrange as the chef de ro de
Speaker 1: giometri compeu capere atus qiachimde nousalasse de plubo e des
Speaker 1: plus angeneux. McLaurin also determined the attraction of a homogeneous
Speaker 1: ellipsoid at an internal point and gave some theorems on
Speaker 1: its attraction at an external point. In effecting this, he
Speaker 1: introduced the conception of level surfaces, i e. Surfaces at
Speaker 1: every point of which the resultant attraction is perpendicular to
Speaker 1: the surface. No further advances in the theory of attractions
Speaker 1: was made until lagrange. In seventeen seventy three introduced the
Speaker 1: idea of the potential sea below. McLaurin also shewed that
Speaker 1: a spheroid was a possible form of equilibrium of a
Speaker 1: mass of homogeneous liquid rotating about an axis passing through
Speaker 1: its center of mass. Finally, he discussed the tides. This
Speaker 1: part had been previously published in seventeen forty and had
Speaker 1: received a prize from the French Academy. Among maclaurin's minor
Speaker 1: works is his Algebra, published in seventeen forty eight and
Speaker 1: founded on Newton's universal arithmetic. It contains the results of
Speaker 1: some early papers of maclaurin, notably of two written in
Speaker 1: seventeen twenty six and seventeen twenty nine on the number
Speaker 1: of imaginary roots of an equation suggested by Newton's theorems
Speaker 1: see above, and of one written in seventeen twenty nine,
Speaker 1: containing the well known rule for finding equal roots by
Speaker 1: means of the derived equation. To this, a treatise entitled
Speaker 1: Delinearum Geometricarum propeitatibus generalibus was added as an appendix. Besides
Speaker 1: the paper of seventeen twenty above alluded to, it contained
Speaker 1: some additional and elegant theorems. McLaurin also produced in Stea
Speaker 1: seventeen twenty eight, an exposition of the Newtonian philosophy, in
Speaker 1: which is incorporated in the posthumous work printed in seventeen
Speaker 1: forty eight. Almost the last paper he wrote was one
Speaker 1: printed in the Philosophical Transactions in seventeen forty three, in
Speaker 1: which he discussed, from a mathematical point of view, the
Speaker 1: form of abees cell. McLaurin was succeeded in his chair
Speaker 1: at Edinburgh by pupil Matthew Stewart born at Rothsay in
Speaker 1: seventeen seventeen and died in Edinburgh on January twenty third,
Speaker 1: seventeen eighty five. A mathematician of considerable power, to whom
Speaker 1: I allude in passing for his theorems on the problem
Speaker 1: of three bodies, and for his discussion treated by transversals
Speaker 1: and involution of the properties of the circle and straight line.
Speaker 1: McLaurin was one of the most able mathematicians of the
Speaker 1: eighteenth century, but his influence on the progress of British
Speaker 1: mathod thematics was on the whole unfortunate, by himself abandoning
Speaker 1: the use of both analysis and of the infinitesimal calculus.
Speaker 1: He induced Newton's countrymen to confine themselves to Newton's methods,
Speaker 1: and I remarked before it was not until about eighteen twenty,
Speaker 1: when the differential calculus was introduced into the Cambridge curriculum,
Speaker 1: that English mathematicians made any general use of the more
Speaker 1: powerful methods of modern analysis. Simpson, the last member of
Speaker 1: the English school whom I need mention here is Thomas Simpson,
Speaker 1: who was born in Leicestershire on August twentieth, seventeen ten
Speaker 1: and died on May fourteenth, seventeen sixty one. His father
Speaker 1: was a weaver, and he owed his education to his
Speaker 1: own efforts. His mathematical interests were first aroused by the
Speaker 1: solar eclipse which took place in seventeen twenty four, and
Speaker 1: with the aid of the of a fortune telling peddler,
Speaker 1: he mastered the Cocker's arithmetic and the elements of algebra.
Speaker 1: He then gave up his weaving and became an usher
Speaker 1: at a school, and by constant and laborious efforts, improved
Speaker 1: his mathematical education, so that by seventeen thirty five he
Speaker 1: was able to solve several questions involving the infinitesimal calculus,
Speaker 1: which had been recently proposed. He next moved to London,
Speaker 1: and in seventeen forty three was appointed professor of mathematics
Speaker 1: at Woolwich, a post which he continued to occupy till
Speaker 1: his death. The works published by Simpson prove him to
Speaker 1: have been a man of extraordinary natural genius and extreme industry.
Speaker 1: The most important of them are his Fluxions seventeen thirty
Speaker 1: seven and seventeen fifty, with numerous applications to physics and astronomy,
Speaker 1: His Laws of Chance and his Essays seventeen forty and
Speaker 1: his theory of annuities and reversions, a branch of mathematics
Speaker 1: that is due to James Dodson fifteen ninety seven to
Speaker 1: sixteen fifty seven, who was a master at Christ's Hospital, London,
Speaker 1: with Tables of the Value of Lives seventeen forty two,
Speaker 1: his Dissertations seventeen forty three, in which the figure of
Speaker 1: the Earth, the force of attraction at the surface of
Speaker 1: a nearly spherical body, the theory of the tides, and
Speaker 1: the law of astronomical refraction are discussed. His Algebra seventeen
Speaker 1: forty five, His geometry seventeen forty seven, his Trigonometry seventeen
Speaker 1: forty eight, in which he introduced the current abbreviations for
Speaker 1: the trigonometrical functions, His Select Exercises seventeen fifty two, containing
Speaker 1: the solutions of numerous problems and a theory of gunnery,
Speaker 1: and lastly his Miscellaneous Tracts seventeen fifty four. The last
Speaker 1: consists of eight memoirs, and these contain his best known
Speaker 1: investigations the The first three papers are on various problems
Speaker 1: in astronomy. The fourth is on the theory of mean observations,
Speaker 1: the fifth and sixth on problems influctions and algebra. The
Speaker 1: seventh contain a general solution of the isoparametrical problem. The
Speaker 1: eighth contains a discussion of the third and ninth sections
Speaker 1: of the Principia and their application to the lunar orbit.
Speaker 1: In this last memoir, Simpson attained a differential equation for
Speaker 1: the motion of the apse of the lunar orbit similar
Speaker 1: to that arrived at by Claiat, but instead of solving
Speaker 1: it by successive approximations, he deduced a general solution by
Speaker 1: indeterminate coefficients. The result agrees with that given by Clairot.
Speaker 1: Simpson first solved this problem in seventeen forty seven, two
Speaker 1: years later than the publication of Clairot's memoir, but the
Speaker 1: solution was discovered independently of Clirot's researches, of which Simpson
Speaker 1: first heard in seventeen forty six. End of section twenty nine,
Speaker 1: recording by Paul King, Oakville, Ontario, p J K DOT
Speaker 1: scripts on MI I T dot E du forward slash
Speaker 1: p K J