Cambridge Library Collection - Mathematics

A thorough account of the roots and development of probability theory, published in 1865 by a distinguished Cambridge mathematician.

The influence of this 1859 work can still be traced in many modern treatments of differential equations and numerical analysis.

Published in 1802, the revised third edition of tables and instructions used by navigators at sea to determine their position.

Published in 1871, this collection comprises the influential first essay by mathematical physicist George Green (1793-1841) and nine further papers.

Reissued here in its 1815 sixth edition, this work gives a glimpse into the teaching of mathematics at Cambridge.

Published in 1896, this translation of a classic work of Greek geometry uses modern notation and includes considerable introductory material.

Originally published in 1921, this rigorous two-volume work traces ancient Greek mathematics from Thales of Miletus to Diophantus of Alexandria.

Originally published in 1921, this rigorous two-volume work traces ancient Greek mathematics from Thales of Miletus to Diophantus of Alexandria.

The collected works, in German, of the groundbreaking mathematician Bernhard Riemann (1826-66) first appeared in 1876.

By the end of the eighteenth century, British mathematics had been stuck in a rut for a hundred years. Calculus was still taught in the style of Newton, with no recognition of the great advances made in continental Europe. The examination system at Cambridge even mandated the use of Newtonian notation. As discontented undergraduates, Charles Babbage (1791–1871) and John Herschel (1792–1871) formed the Analytical Society in 1811. The group, including William Whewell and George Peacock, sought to promote the new continental mathematics. Babbage's preface to the present work, first published in 1813, may be considered the movement's manifesto. He provided the first paper here, and Herschel the two others. Although the group was relatively short-lived, its ideas took root as its erstwhile members rose to prominence. As the society's sole publication, this remains a significant text in the history of British mathematics.

Prefaced by a history of ancient Greek astronomy, this 1913 edition of Aristarchus' only surviving treatise includes a facing-page translation.

The 1839 English translation of an 1828 work on probability by Adolphe Quetelet (1796-1874), pioneer of social statistics.

This two-volume (1880-6) teaching aid for the Cambridge Mathematical Tripos greatly influenced the education of Srinivasa Ramanujan (1887-1920).

Published between 1896 and 1902, this revised two-volume textbook offers extensive coverage of statics, with formulae and examples throughout.

Published between 1896 and 1902, this revised two-volume textbook offers extensive coverage of statics, with formulae and examples throughout.

Prior to the advent of computers, no mathematician, physicist or engineer could do without a volume of tables of logarithmic and trigonometric functions. These tables made possible certain calculations which would otherwise be impossible. Unfortunately, carelessness and lazy plagiarism meant that the tables often contained serious errors. Those prepared by Charles Hutton (1737–1823) were notable for their reliability and remained the standard for a century. Hutton had risen, by mathematical ability, hard work and some luck, from humble beginnings to become a professor of mathematics at the Royal Military Academy. His mathematical work was distinguished by utility rather than originality, but his contributions to the teaching of the subject were substantial. This seventh edition was published in 1858 with additional material by Olinthus Gregory (1774–1841). The preliminary matter will be of interest to any modern-day reader who wishes to know how calculation was done before the electron

Niels Henrik Abel (1802–29) was one of the most prominent mathematicians in the first half of the nineteenth century. His pioneering work in diverse areas such as algebra, analysis, geometry and mechanics has made the adjective 'abelian' a commonplace in mathematical writing. These collected works, first published in two volumes in 1881 after careful preparation by the mathematicians Ludwig Sylow (1832–1918) and Sophus Lie (1842–99), contain some of the pillars of mathematical history. Volume 1 includes perhaps the most famous of Abel's results, namely his proof of the 'impossibility theorem', which states that the general fifth-degree polynomial is unsolvable by algebraic means. Also included in this volume is Abel's 'Paris memoir', which contains his many fundamental results on transcendental functions - in particular on elliptic integrals, elliptic functions, and what are known today as abelian integrals.

Niels Henrik Abel (1802–29) was one of the most prominent mathematicians in the first half of the nineteenth century. His pioneering work in diverse areas such as algebra, analysis, geometry and mechanics has made the adjective 'abelian' a commonplace in mathematical writing. These collected works, first published in two volumes in 1881 after careful preparation by the mathematicians Ludwig Sylow (1832–1918) and Sophus Lie (1842–99), contain some of the pillars of mathematical history. Volume 2 contains additional articles on elliptic functions and infinite series. It also includes extracts from Abel's letters, as well as detailed notes and commentary by Sylow and Lie on Abel's pioneering work.

Niels Henrik Abel (1802–29) was one of the most prominent mathematicians in the first half of the nineteenth century. His pioneering work in diverse areas such as algebra, analysis, geometry and mechanics has made the adjective 'abelian' a commonplace in mathematical writing. These collected works, first published in two volumes in 1881 after careful preparation by the mathematicians Ludwig Sylow (1832–1918) and Sophus Lie (1842–99), contain some of the pillars of mathematical history. Volume 1 includes perhaps the most famous of Abel's results, namely his proof of the 'impossibility theorem', as well as his 'Paris memoir', which contains his many fundamental results on transcendental functions. Volume 2 contains additional articles on elliptic functions and infinite series. It also includes extracts from Abel's letters, as well as detailed notes and commentary by Sylow and Lie on Abel's pioneering work.

The great nineteenth-century mathematician Peter Gustav Lejeune Dirichlet (1805–59) studied in Paris, coming under the influence of scholars including Fourier and Legendre. He then taught at Berlin and Göttingen universities, where he was the successor to Gauss and mentor to Riemann and Dedekind. His achievements include the first satisfactory proof of the convergence of Fourier series under appropriate conditions, and the theorem on primes in arithmetic progression which was, at the same time, the foundation of analytic number theory and one of its greatest achievements. He also did important work on Laplace's equation, the theory of series and many other topics. This two-volume collection of his works, published 1889–97, was compiled by Leopold Kronecker (1823–91). Volume 1 contains works published by Dirichlet up to 1843, together with a related 1846 essay.

The great nineteenth-century mathematician Peter Gustav Lejeune Dirichlet (1805–59) studied in Paris, coming under the influence of scholars including Fourier and Legendre. He then taught at Berlin and Göttingen universities, where he was the successor to Gauss and mentor to Riemann and Dedekind. His achievements include the first satisfactory proof of the convergence of Fourier series under appropriate conditions, and the theorem on primes in arithmetic progression which was, at the same time, the foundation of analytic number theory and one of its greatest achievements. He also did important work on Laplace's equation, the theory of series and many other topics. This two-volume collection of his works, published 1889–97, was compiled by Leopold Kronecker (1823–91). Volume 2 was completed by Lazarus Fuchs (1833–1902) and contains Dirichlet's publications from 1844 onwards, together with some unpublished papers and selected correspondence with Gauss, Alexander von Humboldt and Kronecke

The great nineteenth-century mathematician Peter Gustav Lejeune Dirichlet (1805–59) studied in Paris, coming under the influence of scholars including Fourier and Legendre. He then taught at Berlin and Göttingen universities, where he was the successor to Gauss and mentor to Riemann and Dedekind. His achievements include the first satisfactory proof of the convergence of Fourier series under appropriate conditions, and the theorem on primes in arithmetic progression which was, at the same time, the foundation of analytic number theory and one of its greatest achievements. He also did important work on Laplace's equation, the theory of series and many other topics. This two-volume collection of his works, published 1889–97, was compiled by Leopold Kronecker (1823–91). Volume 1 contains works published by Dirichlet up to 1843 and a related 1846 essay. Volume 2, completed by Lazarus Fuchs (1833–1902), contains Dirichlet's later publications, unpublished papers and selected correspondence.

Few men in modern mathematics have had as great an impact as the Norwegian Niels Henrik Abel (1802–29), whose discoveries paved the way for several new branches of nineteenth-century mathematics. Tragically, Abel's short life was dominated by poverty and his scientific achievements were not fully recognised until after his death. This work, written by Carl Anton Bjerknes (1825–1903), was the first full biography of Abel. Originally published in 1880 and translated into French in 1885, it became a valuable resource for later Abel biographers and scholars of the history of mathematics. With insight and understanding, Bjerknes charts the progress of the talented young mathematician and gives a detailed account of Abel's work and his correspondence with other contemporary mathematicians. In particular, he examines in depth (from Abel's point of view) the dispute between Abel and his rival Jacobi relating to their discoveries of elliptic functions in the 1820s.

The British mathematician William Burnside (1852–1927) and Ferdinand Georg Frobenius (1849–1917), Professor at Zurich and Berlin universities, are considered to be the founders of the modern theory of finite groups. Not only did Burnside prove many important theorems, but he also laid down lines of research for the next hundred years: two Fields Medals have been awarded for work on problems suggested by him. The Theory of Groups of Finite Order, originally published in 1897, was the first major textbook on the subject. The 1911 second edition (reissued here) contains an account of Frobenius's character theory, and remained the standard reference for many years.

The French mathematician and engineer Gérard Desargues (1591–1661) was one of the founders of projective geometry. Desargues' theorem is named in the honour of this prolific writer of treatises on geometry and its application to the arts and architecture. His important writings, which had been lost, were published in 1864 by the mathematician and scientific historian Noël-Germinal Poudra (1794–1894). Poudra's two-volume edition, republished here, reveals the major role played by Desargues in the scientific debates of the seventeenth century. It includes a biography of Desargues, in which Poudra discusses his role as architect, as well as his influence on famous scientists of his time including Pascal and Descartes. Volume 1 contains the majority of Desargues' treatises, including 'Perspective' (1636), followed by an analysis by Poudra, and the 'Traité des Coniques' (1639), with a lexicon of the scientific terms used.

The French mathematician and engineer Gérard Desargues (1591–1661) was one of the founders of projective geometry. Desargues' theorem is named in the honour of this prolific writer of treatises on geometry and its application to the arts and architecture. His important writings, which had been lost, were published in 1864 by the mathematician and scientific historian Noël-Germinal Poudra (1794–1894). Poudra's two-volume edition, republished here, reveals the major role played by Desargues in the scientific debates of the seventeenth century. It includes a biography of Desargues, in which Poudra discusses his role as architect, as well as his influence on famous scientists of his time including Pascal and Descartes. Volume 2 contains Poudra's analysis of the works of the engraver Abraham Bosse (1603–76), which develop some of Desargues' ideas. It also reproduces some of the - often critical - responses to Desargues' work by his contemporaries.

The French mathematician and engineer Gérard Desargues (1591–1661) was one of the founders of projective geometry. Desargues' theorem is named in the honour of this prolific writer of treatises on geometry and its application to the arts and architecture. His important writings, which had been lost, were published in 1864 by the mathematician and scientific historian Noël-Germinal Poudra (1794–1894). Poudra's two-volume edition of his treatises, republished here, reveals the major role played by Desargues in the scientific debates of the seventeenth century. It includes a biography of Desargues, in which Poudra discusses his role as architect, as well as his influence on famous scientists of his time including Pascal and Descartes. Poudra also reproduces some of the - often critical - responses to Desargues' work by his contemporaries.

The genius of Carl Friedrich Gauss (1777–1855) and the novelty of his work (published in Latin, German, and occasionally French) in areas as diverse as number theory, probability and astronomy were already widely acknowledged during his lifetime. But it took another three generations of mathematicians to reveal the true extent of his output as they studied Gauss' extensive unpublished papers and his voluminous correspondence. This posthumous twelve-volume collection of Gauss' complete works, published between 1863 and 1933, marks the culmination of their efforts and provides a fascinating account of one of the great scientific minds of the nineteenth century. Volume 2, which appeared in 1863, supplements Volume 1 with additional articles on number theory. It also contains book reviews and posthumous papers, including an unfinished eighth chapter of the Disquisitiones arithmeticae.

The genius of Carl Friedrich Gauss (1777–1855) and the novelty of his work (published in Latin, German, and occasionally French) in areas as diverse as number theory, probability and astronomy were already widely acknowledged during his lifetime. But it took another three generations of mathematicians to reveal the true extent of his output as they studied Gauss' extensive unpublished papers and his voluminous correspondence. This posthumous twelve-volume collection of Gauss' complete works, published between 1863 and 1933, marks the culmination of their efforts and provides a fascinating account of one of the great scientific minds of the nineteenth century. Volume 3, which appeared in 1866, focuses on analysis. It includes Gauss' work on elliptic functions and on power series, for which he gave the first convergence criteria, as well as his first (1799) proof of the fundamental theorem of algebra, and reviews of works by contemporaries including Fourier.

The genius of Carl Friedrich Gauss (1777–1855) and the novelty of his work (published in Latin, German, and occasionally French) in areas as diverse as number theory, probability and astronomy were already widely acknowledged during his lifetime. But it took another three generations of mathematicians to reveal the true extent of his output as they studied Gauss' extensive unpublished papers and his voluminous correspondence. This posthumous twelve-volume collection of Gauss' complete works, published between 1863 and 1933, marks the culmination of their efforts and provides a fascinating account of one of the great scientific minds of the nineteenth century. Volume 4, published in 1873, contains Gauss' theoretical work on differential geometry and probability, reviews of work by contemporaries including Herschel, and notes relating to geodesic surveys of the Kingdom of Hanover from the 1820s to the 1840s, together with a description of the heliotrope Gauss invented for the surveys.

The genius of Carl Friedrich Gauss (1777–1855) and the novelty of his work (published in Latin, German, and occasionally French) in areas as diverse as number theory, probability and astronomy were already widely acknowledged during his lifetime. But it took another three generations of mathematicians to reveal the true extent of his output as they studied Gauss' extensive unpublished papers and his voluminous correspondence. This posthumous twelve-volume collection of Gauss' complete works, published between 1863 and 1933, marks the culmination of their efforts and provides a fascinating account of one of the great scientific minds of the nineteenth century. Volume 5, published in 1867, covers Gauss' work on mechanics and geomagnetism. It includes expositions of his principle of least constraint and the theory of capillarity. It also contains book reviews, and a description of the aurora borealis observed in January 1831.

The genius of Carl Friedrich Gauss (1777–1855) and the novelty of his work (published in Latin, German, and occasionally French) in areas as diverse as number theory, probability and astronomy were already widely acknowledged during his lifetime. But it took another three generations of mathematicians to reveal the true extent of his output as they studied Gauss' extensive unpublished papers and his voluminous correspondence. This posthumous twelve-volume collection of Gauss' complete works, published between 1863 and 1933, marks the culmination of their efforts and provides a fascinating account of one of the great scientific minds of the nineteenth century. One of Gauss' key successes in astronomy was the prediction of the path of Ceres, leading to its rediscovery in 1801. The original reports about this dramatic course of events appear in Volume 6, published in 1874, which includes all of Gauss' publications on astronomy, book reviews and letters.

The genius of Carl Friedrich Gauss (1777–1855) and the novelty of his work (published in Latin, German, and occasionally French) in areas as diverse as number theory, probability and astronomy were already widely acknowledged during his lifetime. But it took another three generations of mathematicians to reveal the true extent of his output as they studied Gauss' extensive unpublished papers and his voluminous correspondence. This posthumous twelve-volume collection of Gauss' complete works, published between 1863 and 1933, marks the culmination of their efforts and provides a fascinating account of one of the great scientific minds of the nineteenth century. Volume 7, published in 1906, contains some of the most surprising material discovered among Gauss' papers: extensive calculations concerning the motion of Pallas. The volume also includes a reprint of Gauss' 1809 book on orbits, Theoria motus corporum coelestium, followed by his later updates and corrections.

The genius of Carl Friedrich Gauss (1777–1855) and the novelty of his work (published in Latin, German, and occasionally French) in areas as diverse as number theory, probability and astronomy were already widely acknowledged during his lifetime. But it took another three generations of mathematicians to reveal the true extent of his output as they studied Gauss' extensive unpublished papers and his voluminous correspondence. This posthumous twelve-volume collection of Gauss' complete works, published between 1863 and 1933, marks the culmination of their efforts and provides a fascinating account of one of the great scientific minds of the nineteenth century. Volume 8, published in 1900, supplements the first four volumes with further work on number theory, probability and differential geometry that was discovered posthumously among Gauss' papers. Gauss here engages with work by scholars including Lagrange, Legendre, Lobatschewsky and Möbius, and paves the way for non-Euclidean geometr

The genius of Carl Friedrich Gauss (1777–1855) and the novelty of his work (published in Latin, German, and occasionally French) in areas as diverse as number theory, probability and astronomy were already widely acknowledged during his lifetime. But it took another three generations of mathematicians to reveal the true extent of his output as they studied Gauss' extensive unpublished papers and his voluminous correspondence. This posthumous twelve-volume collection of Gauss' complete works, published between 1863 and 1933, marks the culmination of their efforts and provides a fascinating account of one of the great scientific minds of the nineteenth century. Volume 9, which appeared in 1903, supplements the account in Volume 4 of geodesy, triangulation, and the geodesic survey of the Kingdom of Hanover. It includes both published work and previously unpublished notes found among Gauss' papers.

The genius of Carl Friedrich Gauss (1777–1855) and the novelty of his work (published in Latin, German, and occasionally French) in areas as diverse as number theory, probability and astronomy were already widely acknowledged during his lifetime. But it took another three generations of mathematicians to reveal the true extent of his output as they studied Gauss' extensive unpublished papers and his voluminous correspondence. This posthumous twelve-volume collection of Gauss' complete works, published between 1863 and 1933, marks the culmination of their efforts and provides a fascinating account of one of the great scientific minds of the nineteenth century. An invaluable source in tracing Gauss' development is his scientific diary, which was only discovered in 1898. Volume 10 Part I, published in 1917, contains a photographic reproduction of this manuscript and a detailed commentary, together with many letters about pure mathematics, and shorter works including a preface to Piazzi.

The genius of Carl Friedrich Gauss (1777–1855) and the novelty of his work (published in Latin, German, and occasionally French) in areas as diverse as number theory, probability and astronomy were already widely acknowledged during his lifetime. But it took another three generations of mathematicians to reveal the true extent of his output as they studied Gauss' extensive unpublished papers and his voluminous correspondence. This posthumous twelve-volume collection of Gauss' complete works, published between 1863 and 1933, marks the culmination of their efforts and provides a fascinating account of one of the great scientific minds of the nineteenth century. At the suggestion of Felix Klein, Gauss' twentieth-century successors planned a scientific biography consisting of essays covering the various areas in which he worked. Volume 10, Part II, (dated 1922–33) contains seven contributions, individually paginated and originally sold separately, relating to pure mathematics, probability

The genius of Carl Friedrich Gauss (1777–1855) and the novelty of his work (published in Latin, German, and occasionally French) in areas as diverse as number theory, probability and astronomy were already widely acknowledged during his lifetime. But it took another three generations of mathematicians to reveal the true extent of his output as they studied Gauss' extensive unpublished papers and his voluminous correspondence. This posthumous twelve-volume collection of Gauss' complete works, published between 1863 and 1933, marks the culmination of their efforts and provides a fascinating account of one of the great scientific minds of the nineteenth century. Volume 11 Part I, which appeared in 1927, supplements volumes 5 to 7 with additional material on physics (particularly magnetism) and both theoretical and practical astronomy. It also contains a substantial amount of scientific correspondence with scholars including Schumacher, Olbers and Bessel.