Pascal and P. de Fermat had initiated he brought very nearly to perfection; but the demonstrations are so involved, and the omissions in the chain of reasoning so frequent, that the Theorie analytique (1812) is to the best mathematicians a work requiring most arduous study.
Lessing' in 1773, which purports to have been sent by Archimedes to the mathematicians at Alexandria in a letter to Eratosthenes.
The time thus spent seems to have been on the whole happy, even allowing for warm discussions with the mathematicians and metaphysicians of France, and for harassing controversies in the Netherlands.
A work so widely circulated by the author naturally attracted attention, but in France it was principally the mathematicians who took it up, and their criticisms were more pungent than complimentary.
Modern mathematicians may find on reading this brilliant summary a good many dicta which they will call in question, but, whatever its defects may be, Peacock's report remains a work of permanent value.
Thus early commenced the separation between what were long called mathematical and political geography, the one subject appealing mainly to mathematicians, the other to historians.
Roberval was one of those mathematicians who, just before the invention of the infinitesimal calculus, occupied their attention with problems which are only soluble, or can be most easily solved, by some method involving limits or infinitesimals, and in the solution of which accordingly the calculus is always now employed.
In the second, which took place in the Church of St John and St Paul, and lasted three days, he undertook to refute innumerable errors in Aristotelians, mathematicians and schoolmen, to conduct his dispute either logically or by the secret doctrine of numbers, &c. According to Aldus, who attended the debate and published an account of it in his dedication to Crichton prefixed to Cicero's "Paradoxa" (1581), the young Scotsman was completely successful.
This knowledge, joined to what he had gathered by historical reading of equally unusual extent, he carefully digested and gave to the world in his Biographisch-literarisches Handworterbuch zur Geschichte der exacten Wissenschaften, containing notices of the lives and labours of mathematicians, astronomers, physicists, and chemists, of all peoples and all ages.
Of the more immediate successors of Newton in Great Britain Maclaurin is probably the only one who can be placed in competition with the great mathematicians of the continent of Europe at the time.
The method of preparing these gores was originally found empirically, but since the days of Albert Darer it has also engaged the minds of many mathematicians, foremost among whom was Professor A.
Map projections were dealt with by two eminent mathematicians, J.
But the desire to obtain general enunciations of theorems without exceptional cases has led mathematicians to employ entities of ever-ascending types of elaboration.
These entities are not created by mathematicians, they are employed by them, and their definitions should point out the construction of the new entities in terms of those already on hand.
Except for the immediate purposes of an explanation, such as the above, it is unnecessary for mathematicians to have separate symbols, such as 2, 2r and 2 R, or 2/3 and (2/3) R.
This is exactly the same reason as that which has led mathematicians to work with signed real numbers in preference to real numbers, and with real numbers in preference to rational numbers.
In the course of this process, undertaken for the first time with the rigour of mathematicians, some contradictions have become apparent.
Indeed, mathematicians now reserve "continuity" as the term for the latter kind of continuity; the mere property of having an infinite number of terms between any two terms is called "compactness."
The classification in question was drawn up by an international committee of eminent mathematicians, and thus has the highest authority.
It was remarkable both for the brilliance of its achievements and for the large number of French mathematicians of the first rank who flourished during it.
Between them the general theory of the complex variable, and of the various "infinite" processes of mathematical analysis, was established, while other mathematicians, such as Poncelet, Steiner, Lobatschewsky and von Staudt, were founding modern geometry, and Gauss inaugurated the differential geometry of surfaces.
In the next and last period the progress of pure mathematics has been dominated by the critical spirit introduced by the German mathematicians under the guidance of Weierstrass, though foreshadowed by earlier analysts, such as Abel.
Leonardo's works are mainly developments of the results obtained by his predecessors; the influences of Greek, Arabian, and Indian mathematicians may be clearly discerned in his methods.
His standard work on algebra, written in Arabic, and other treatises of a similar character raised him at once to the foremost rank among the mathematicians of that age, and induced Sultgn Malik-Shgh to summon him in A.H.
Maxwell explained electric and magnetic forces, not by the action at a distance assumed by the earlier mathematicians, but by stresses in a medium filling all space, and possessing qualities like those attributed to the old luminiferous ether.
Amongst the brilliant group of mathematicians whose magnanimous rivalry contributed to accomplish the task of generalization and deduction reserved for the 18th century, Lagrange occupies an eminent place.
Recognized as among the first mathematicians of his day, he was also widely known for the universality and depth of his philological and philosophical knowledge.
The time had come when the results obtained in the development and application of the law of gravitation by three generations of illustrious mathematicians might be presented from a single point of view.
Although the term " algebra " is now in universal use, various other appellations were used by the Italian mathematicians during the Renaissance.
Investigation of the writings of Indian mathematicians has exhibited a fundamental distinction between the Greek and Indian mind, the former being pre-eminently geometrical and speculative, the latter arithmetical and mainly practical.
The Arabians more closely resembled the Hindus than the Greeks in the choice of studies; their philosophers blended speculative dissertations with the more progressive study of medicine; their mathematicians neglected the subtleties of the conic sections and Diophantine analysis, and applied themselves more particularly to perfect the system of numerals, arithmetic and astronomy.
Contemporaneously with the remarkable discoveries of the Italian mathematicians, algebra was increasing in popularity in Germany, France and England.
In recent times many mathematicians have formulated other kinds of algebras, in which the operators do not obey the laws of ordinary algebra.
This study was inaugurated by George Peacock, who was one of the earliest mathematicians to recognize the symbolic character of the fundamental principles of algebra.
"It is very evident," he says, "that all other means of improving medicine have been found ineffectual, by the stand it was at for two thousand years, and that, since mathematicians have sot themselves to the study of it, men already begin to talk so intelligibly and comprehensibly, even about abstruse matters, that it is to be hoped that mathematical learning will be the distinguishing mark of a physician and a quack."
Liouville, Caspary, Jukovsky, Liapounoff, Kolosoff and others, chiefly Russian mathematicians; and the general solution requires the double-theta hyperelliptic function.
In 1826 he moved to Paris, and during a ten months' stay he met the leading mathematicians of France; but he was little appreciated, for his work was scarcely known; and his modesty restrained him from proclaiming his researches.
Under Abel's guidance, the prevailing obscurities of analysis began to be cleared, new fields were entered upon and the study of functions so advanced as to provide mathematicians with numerous ramifications along which progress could be made.
In 1724 he was offered the chair of mathematics in the university of Upsala, which he declined, on the ground that it was a mistake for mathematicians to be limited to theory.
This problem engaged the attention of British as well as continental mathematicians; and its proposal gave rise to a painful quarrel with his brother Jean.
In his dispute with his brother, in his controversies with the English and Scottish mathematicians, and in his harsh and jealous bearing to his son Daniel, he showed a mean, unfair and violent temper.
He was a member of almost every learned society in Europe, and one of the first mathematicians of a mathematical age.
His two sons, Jean and Jacques, are the last noted mathematicians of the family.
That principle had been made use of by the Greek authors of the classic age; but of later mathematicians only Hero, Diophantus, &c., ventured to regard lines and surfaces as mere numbers that could be joined to give a new number, their sum.
During the three centuries that have elapsed between Vieta's day and our own several changes of opinion have taken place on this subject, till the principle has at last proved so far victorious that modern mathematicians like to make homogeneous such equations as are not so from the beginning, in order to get values of a symmetrical shape.
In like manner, after the French mathematicians had attempted, with more or less ingenuity, to construct a theory of elastic solids from the hypothesis that they consist of atoms in equilibrium under the action of their mutual forces, Stokes and others showed that all the results of this hypothesis, so far at least as they agreed with facts, might be deduced from the postulate that elastic bodies exist, and from the hypothesis that the smallest portions into which we can divide them are sensibly homogeneous.
He was well acquainted with the works of the mathematicians of his own time, and has been called the "English d'Alembert."
Many of Pell's manuscripts fell into the hands of Dr Busby, master of Westminster School, and afterwards came into the possession of the Royal Society; they are still preserved in something like forty folio volumes, which contain, not only Pell's own memoirs, but much of his correspondence with the mathematicians of his time.
These problems were also attacked by the Arabian mathematicians; Tobit ben Korra (836-901) is credited with a solution, while Abul Gud solved it by means of a parabola and an equilateral hyperbola.
Legendre had pursued the subject which would now be called elliptic integrals alone from 1786 to 1827, the results of his labours having been almost entirely neglected by his contemporaries, but his work had scarcely appeared in 1827 when the discoveries which were independently made by the two young and as yet unknown mathematicians Abel and Jacobi placed the subject on a new basis, and revolutionized it completely.
Pfaff's researches bore chiefly on the theory of series, to which he applied the methods of the so-called combinatorial school of German mathematicians, and on the solution of differential equations.
If 1 denotes the logarithm to base e (that is, the so-called "Napierian " or hyperbolic logarithm) and L denotes, as above, " Napier's " logarithm, the connexion between 1 and L is expressed by L = r o 7 loge 10 7 - 10 7 / or e t = I 07e-L/Ia7 Napier's work (which will henceforth in this article be referred to as the Descriptio) immediately on its appearance in 1614 attracted the attention of perhaps the two most eminent English mathematicians then living - Edward Wright and Henry Briggs.
In the preface Robert Napier says that he has been assured from undoubted authority that the new invention is much thought of by the ablest mathematicians, and that nothing would delight them more than the publication of the mode of construction of the canon.
Those engaged upon the work were divided into three sections: the first consisted of five or six mathematicians, including Legendre, who were engaged in the purely analytical work, or the calculation of the fundamental numbers; the second section consisted of seven or eight calculators possessing some mathematical knowledge; and the third comprised seventy or eighty ordinary computers.
7r72, which, in reality, is equivalent tol determining a square equal in area to a circle, engaged the attention of mathematicians for many centuries.
The Premature Death Of Regiomontanus Caused The Design To Be Suspended For The Time; But In The Following Century Numerous Memoirs Appeared On The Subject, Among The Authors Of Which Were Staler, Albert Pighius, Johann Schbner, Lucas Gauricus, And Other Mathematicians Of Celebrity.
The Milanese sculptor, Ambrogio, who worked so much for Federigo, married a lady of Urbino, and was the progenitor of the Baroccio family, among whom were many able mathematicians and painters.