Born into a Newcastle coal mining family, Charles Hutton (1737-1823) displayed mathematical ability from an early age. He rose to become professor of mathematics at the Royal Military Academy and foreign secretary of the Royal Society. First published in 1795-6, this two-volume illustrated encyclopaedia aimed to supplement the great generalist reference works of the Enlightenment by focusing on philosophical and mathematical subjects; the coverage ranges across mathematics, astronomy, natural philosophy and engineering. Almost a century old, the last comparable reference work in English was John Harris' Lexicon Technicum. Hutton's work contains many historical and biographical entries, often with bibliographies, including many for continental analytical mathematicians who would have been relatively unfamiliar to British readers. These features make Hutton's Dictionary a particularly valuable record of eighteenth-century science and mathematics. Volume 1 ranges from abacist (a user of an abacus) to the English physician and Newtonian scientist James Jurin.

Born into a Newcastle coal mining family, Charles Hutton (1737-1823) displayed mathematical ability from an early age. He rose to become professor of mathematics at the Royal Military Academy and foreign secretary of the Royal Society. First published in 1795-6, this two-volume illustrated encyclopaedia aimed to supplement the great generalist reference works of the Enlightenment by focusing on philosophical and mathematical subjects; the coverage ranges across mathematics, astronomy, natural philosophy and engineering. Almost a century old, the last comparable reference work in English was John Harris' Lexicon Technicum. Hutton's work contains many historical and biographical entries, often with bibliographies, including many for continental analytical mathematicians who would have been relatively unfamiliar to British readers. These features make Hutton's Dictionary a particularly valuable record of eighteenth-century science and mathematics. Volume 2 ranges from kalendar to zone. Among the other topics covered are knots, Newton, magnets, and the Moon.

A member of the Academie francaise, Henri Poincare (1854 1912) was one of the greatest mathematicians and theoretical physicists of the late nineteenth and early twentieth centuries. His discovery of chaotic motion laid the foundations of modern chaos theory, and he was acknowledged by Einstein as a key contributor in the field of special relativity. He earned his enduring reputation as a philosopher of mathematics and science with this elegantly written work, which was first published in French as three separate essays: Science and Hypothesis (1902), The Value of Science (1905), and Science and Method (1908). Poincare asserts that much scientific work is a matter of convention, and that intuition and prediction play key roles. George Halsted's authorised 1913 English translation retains Poincare's lucid prose style, presenting complex ideas for both professional scientists and those readers interested in the history of mathematics and the philosophy of science."

A treasure for anyone interested in early modern India and the history of mathematics, this first English translation of the Siddhantasundara reveals the fascinating work of the scholar-astronomer Jnanaraja (circa 1500 C.E.). Toke Lindegaard Knudsen begins with an introduction to the traditions of ancient Hindu astronomy and describes what is known of Jnanaraja's life and family. He translates the Sanskrit verses into English and offers expert commentary on the style and substance of Jnanaraja's treatise.

The Siddhantasundara contains a comprehensive exposition of the system of Indian astronomy, including how to compute planetary positions and eclipses. It also explores deep, probing questions about the workings of the universe and sacred Hindu traditions. In a philosophical discussion, the treatise seeks a synthesis between the cosmological model used by the Indian astronomical tradition and the cosmology of a class of texts sacred in Hinduism. In his discourse, which includes a discussion of the direction of down and adhesive antipodeans, Jnanaraja rejects certain principles from the astronomical tradition and reinterprets principles from the sacred texts. He also constructs a complex poem on the seasons, many verses of which have two layers of meaning, one describing a season, the other a god's activities in that season.

The Siddhantasundara is the last major treatise of Indian astronomy and cosmology to receive serious scholarly attention, Knudsen's careful effort unveils the 500-year-old Sanskrit verses and shows the clever quirkiness of Jnanaraja's writing style, his keen use of mathematics, and his subtle philosophical arguments.

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1891 Excerpt: ...position of the face B E G F, it is easy to see that the two wedgeshaped figures Bee'b'oc and Pgg'p'ad are exactly equal; this follows from the equality of their corresponding faces. Hence the volume of the sheared figure must be equal to the volume of the right six-face. Now let us suppose in addition that the face B' E' G' P' is again moved in its own plane into the position B" E" G" F," So that B' and E' move along B' E' and p' G' respectively. Then the slant wedge-shaped figures B'b"f"p'ao and E'e"g"p'dc will again be equal, and the volume of the six-face B" E" G" P" A D C O obtained by this second shear will be equal to the volume of the figure obtained by the first shear, and therefore to the volume of the right six-face. But by n, ns of two shears we can move the face B E G P to any position in its plane, B" E" G" P," in which its sides remain parallel to their former position. Hence the volume of a six-face will remain unchanged if, one of its faces, o c D A, remaining fixed, the opposite face, B E G P, be moved anywhere parallel to itself in its own plane. We thus find that the volume of a six-face formed by three pairs of parallel planes is equal to the product of the area of one of its faces and the perpendicular distance between that face and its parallel. For this is the volume of the right six-face into which it may be sheared; and, as we have seen, shear does not alter volume. The knowledge thus gained of the volume of a sixface bounded by three pairs of parallel faces, or of a so-called parallelepiped, enables us to find the volume of an oblique cylinder. A right cylinder is the figure generated by any area moving parallel to itself in such wise that any point p ...

Throughout his early life, Isaac Todhunter (1820-84) excelled as a student of mathematics, gaining a scholarship at the University of London and numerous awards during his time at St John's College, Cambridge. Taking up fellowship of the college in 1849, he became widely known for both his educational texts and his historical accounts of various branches of mathematics. The present work, first published in 1865, describes the rise of probability theory as a recognised subject, beginning with a discussion of the famous 'problem of points', as considered by the likes of the Chevalier de Mere, Blaise Pascal and Pierre de Fermat during the latter half of the seventeenth century. Subsequently, the application of advanced methods that had been developed in classical areas of mathematics led to rapid progress in probability theory. Todhunter traces this growth, closing with a thorough account of Pierre-Simon Laplace's far-reaching work in the area.

From the end of antiquity to the middle of the nineteenth century it was generally believed that Aristotle had said all that there was to say concerning the rules of logic and inference. One of the ablest British mathematicians of his age, Augustus De Morgan (1806-71) played an important role in overturning that assumption with the publication of this book in 1847. He attempts to do several things with what we now see as varying degrees of success. The first is to treat logic as a branch of mathematics, more specifically as algebra. Here his contributions include his laws of complementation and the notion of a universe set. De Morgan also tries to tie together formal and probabilistic inference. Although he is never less than acute, the major advances in probability and statistics at the beginning of the twentieth century make this part of the book rather less prophetic.

In the preface to this work, mathematician Augustus De Morgan (1806 71) claims that 'The most worthless book of a bygone day is a record worthy of preservation.' His purpose in writing this catalogue, published in 1847, was to provide an accurate record of the early history of publishing on arithmetic, but describing only those books which he had examined himself. He surveyed the library of the Royal Society, works in the British Museum, the wares of specialist booksellers, and the private collections of himself and his friends to compile a chronological list of books from 1491 to 1846 (the final book being a work of his own), giving bibliographical details, a description of the contents, and sometimes comments on the mathematics on display. De Morgan's Formal Logic and a Memoir of Augustus De Morgan by his widow are also reissued in the Cambridge Library Collection."

This volume commemorates the life, work and foundational views of Kurt Goedel (1906-78), most famous for his hallmark works on the completeness of first-order logic, the incompleteness of number theory, and the consistency - with the other widely accepted axioms of set theory - of the axiom of choice and of the generalized continuum hypothesis. It explores current research, advances and ideas for future directions not only in the foundations of mathematics and logic, but also in the fields of computer science, artificial intelligence, physics, cosmology, philosophy, theology and the history of science. The discussion is supplemented by personal reflections from several scholars who knew Goedel personally, providing some interesting insights into his life. By putting his ideas and life's work into the context of current thinking and perceptions, this book will extend the impact of Goedel's fundamental work in mathematics, logic, philosophy and other disciplines for future generations of researchers.

Successful long-distance navigation depends on knowing latitude and longitude, and the determination of longitude depends on knowing the exact time at some fixed point on the earth's surface. Since Newton it had been hoped that a method based on accurate prediction of the moon's orbit would give such a time. Building on the work of Euler, Thomas Mayer and others, the astronomer and mathematician Nevil Maskelyne (1732-1811) was able to devise such a method and yearly publication of the Nautical Almanac and Astronomical Ephemeris placed it in the hands of every ship's captain. First published in 1767 and reissued here in the revised third edition of 1802, the present work provided the necessary tables and instructions. The development of rugged and accurate chronometers eventually displaced Maskelyne's method, but navigators continued to make use of it for many decades. This edition of the tables notably formed part of the library of the Beagle on Darwin's famous voyage.

A distinguished mathematician and notable university teacher, Isaac Todhunter (1820 84) became known for the successful textbooks he produced as well as for a work ethic that was extraordinary, even by Victorian standards. A scholar who read all the major European languages, Todhunter was an open-minded man who admired George Boole and helped introduce the moral science examination at Cambridge. His many gifts enabled him to produce the histories of mathematical subjects which form his lasting memorial. First published between 1886 and 1893, the present work was the last of these. Edited and completed after Todhunter's death by Karl Pearson (1857 1936), another extraordinary man who pioneered modern statistics, these volumes trace the mathematical understanding of elasticity from the seventeenth to the late nineteenth century. Volume 1 (1886) begins with Galileo Galilei and extends to the researches of Saint-Venant up to 1850."

A distinguished mathematician and notable university teacher, Isaac Todhunter (1820 84) became known for the successful textbooks he produced as well as for a work ethic that was extraordinary, even by Victorian standards. A scholar who read all the major European languages, Todhunter was an open-minded man who admired George Boole and helped introduce the moral science examination at Cambridge. His many gifts enabled him to produce the histories of mathematical subjects which form his lasting memorial. First published between 1886 and 1893, the present work was the last of these. Edited and completed after Todhunter's death by Karl Pearson (1857 1936), another extraordinary man who pioneered modern statistics, these volumes trace the mathematical understanding of elasticity from the seventeenth to the late nineteenth century. Volume 2 (1893) was split into two parts. Part 1 includes the work of Saint-Venant from 1850 to 1886."

A distinguished mathematician and notable university teacher, Isaac Todhunter (1820 84) became known for the successful textbooks he produced as well as for a work ethic that was extraordinary, even by Victorian standards. A scholar who read all the major European languages, Todhunter was an open-minded man who admired George Boole and helped introduce the moral science examination at Cambridge. His many gifts enabled him to produce the histories of mathematical subjects which form his lasting memorial. First published between 1886 and 1893, the present work was the last of these. Edited and completed after Todhunter's death by Karl Pearson (1857 1936), another extraordinary man who pioneered modern statistics, these volumes trace the mathematical understanding of elasticity from the seventeenth to the late nineteenth century. Volume 2 (1893) was split into two parts. Part 2 covers the work of Neumann, Kirchhoff, Clebsch, Boussinesq, and Lord Kelvin."

A miller's son, George Green (1793 1841) received little formal schooling yet managed to acquire significant knowledge of modern mathematics, especially French work. In 1828 he published his Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism, the work for which he is now celebrated. Admitted to Cambridge in 1833 as a mature student, Green went on to become a fellow of Gonville and Caius College. His early death, however, cut short a promising career as a mathematical physicist. While English contemporaries saw what he might have achieved, they did not understand what he had actually achieved. Only when William Thomson (later Lord Kelvin) rediscovered Green's first publication and shared it with the French mathematical elite was his greatness truly appreciated. Edited by the Cambridge mathematician Norman Macleod Ferrers (1829 1903) and published in 1871, this collection comprises Green's influential essay and nine further papers."

In his autobiography, Charles Darwin wrote of his time at Cambridge: 'I attempted mathematics ... but I got on very slowly. The work was repugnant to me, chiefly from my not being able to see any meaning in the early steps in algebra. This impatience was very foolish, and in after years I have deeply regretted that I did not proceed far enough at least to understand something of the great leading principles of mathematics, for men thus endowed seem to have an extra sense.' First published in 1795 and reissued here in its 1815 sixth edition, The Elements of Algebra by James Wood (1760-1839) was one of the standard Cambridge texts for decades, so its presence in Darwin's library aboard the Beagle is readily understandable. Then, as now, Cambridge had a high opinion of itself as a mathematical university. The contents of Wood's book give an interesting glimpse of the standards expected of the less able students.

As senior wrangler in 1854, Edward John Routh (1831-1907) was the man who beat James Clerk Maxwell in the Cambridge mathematics tripos. He went on to become a highly successful coach in mathematics at Cambridge, producing a total of twenty-seven senior wranglers during his career - an unrivalled achievement. In addition to his considerable teaching commitments, Routh was also a very able and productive researcher who contributed to the foundations of control theory and to the modern treatment of mechanics. This two-volume textbook, which first appeared in 1891-2 and is reissued here in the revised edition that was published between 1896 and 1902, offers extensive coverage of statics, providing formulae and examples throughout for the benefit of students. While the growth of modern physics and mathematics may have forced out the problem-based mechanics of Routh's textbooks from the undergraduate syllabus, the utility and importance of his work is undiminished.

Thomas Harriot (1560-1621) was a pioneer in both the figurative and literal sense. Navigational adviser and loyal friend to Sir Walter Ralegh, Harriot took part in the first expedition to colonize Virginia. Not only was he responsible for getting Ralegh's ships safely to harbor in the New World, once there he became the first European to acquire a working knowledge of an indigenous language (he also began a lifelong love of tobacco, which may have been his undoing). Harriot's abilities were seemingly unlimited and nearly awe-inspiring. He was the first to use a telescope to map the moon's craters, and, independently of Galileo, discovered and recorded sunspots. He preceded Newton (whose fame eclipsed his) in his discovery of the properties of the prism. He was arguably the best mathematician of his age, and one of the finest experimental scientists of all time. Yet Harriot has traditionally remained a tantalizingly elusive character. He had no close family to pass down records, and few of his letters survive. Most importantly, he never published his scientific discoveries, and half a century after his death he had all but been forgotten. In recent decades, many (self-styled "Harrioteers") have become obsessed with restoring to Harriot his right place, but Robyn Arianrhod's biography is the first actually to do this, and she has done it the only way it can be done: through his science. Using Harriot's re-discovered manuscripts, Arianrhod illuminates the full extent of his achievements in science and physics, expertly guiding us through what makes them original and important, and the story behind them. Because he hadn't yet polished them for publication, Harriot's papers also proffer unique insight into the scientific process itself. Though his thinking depended on a more natural, intuitive approach than those who followed him, Harriot laid the foundations of what in Newton's time would become modern physics. Arianrhod's biography offers the human face of scientific discovery, a lived example of the way in which science actually progresses. Set against the backdrop of the Elizabethan world with all of its dramas and creative tensions-Harriot's years almost exactly overlap those of Shakespeare's-this biography gives proper due to one of history's most remarkable minds.

This scarce antiquarian book is a selection from Kessinger Publishing's Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the world's literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone

Active in Alexandria in the third century BCE, Apollonius of Perga ranks as one of the greatest Greek geometers. Building on foundations laid by Euclid, he is famous for defining the parabola, hyperbola and ellipse in his major treatise on conic sections. The dense nature of its text, however, made it inaccessible to most readers. When it was originally published in 1896 by the civil servant and classical scholar Thomas Little Heath (1861 1940), the present work was the first English translation and, more importantly, the first serious effort to standardise the terminology and notation. Along with clear diagrams, Heath includes a thorough introduction to the work and the history of the subject. Seeing the treatise as more than an esoteric artefact, Heath presents it as a valuable tool for modern mathematicians. His works on Diophantos of Alexandria (1885) and Aristarchus of Samos (1913) are also reissued in this series.

'If one would understand the Greek genius fully, it would be a good plan to begin with their geometry.' As early as the sixth century BCE, Thales of Miletus used geometrical principles to calculate distance and height. Within a few hundred years, Euclid had produced his seminal Elements, which was still used as a textbook when this two-volume work was first published in 1921. A distinguished civil servant as well as an expert on ancient Greek mathematics, Sir Thomas Little Heath (1861 1940) includes here sufficient detail for a modern mathematician to grasp ancient methodology, alongside explanatory sections aimed at classicists. This remains a rigorous and essential exposition of a vast topic. Volume 1 includes an introduction that touches on the conditions which made possible the rapid development of philosophy and science in ancient Greece. The coverage begins with Thales and ends with Euclid."

'If one would understand the Greek genius fully, it would be a good plan to begin with their geometry.' As early as the sixth century BCE, Thales of Miletus used geometrical principles to calculate distance and height. Within a few hundred years, Euclid had produced his seminal Elements, which was still used as a textbook when this two-volume work was first published in 1921. A distinguished civil servant as well as an expert on ancient Greek mathematics, Sir Thomas Little Heath (1861 1940) includes here sufficient detail for a modern mathematician to grasp ancient methodology, alongside explanatory sections aimed at classicists. This remains a rigorous and essential exposition of a vast topic. Volume 2 focuses on post-Euclidian mathematics, beginning with the work of Aristarchus of Samos and extending to that of Diophantus of Alexandria. Heath had previously published separate studies on these two thinkers (also reissued in this series)."

In 1844, the Prussian schoolmaster Hermann Grassmann (1809-77) published Die Lineale Ausdehnungslehre (also reissued in the Cambridge Library Collection). This revolutionary work anticipated the modern theory of vector spaces and exterior algebras. It was little understood at the time and the few sympathetic mathematicians, rather than trying harder to comprehend it, urged Grassmann to write an extended version of his theories. The present work is that version, first published in 1862. However, this also proved too far ahead of its time and Grassmann turned to historical linguistics, in which field his contributions are still remembered. His mathematical work eventually found champions such as Hankel, Peano, Whitehead and Elie Cartan, and it is now recognised for the brilliant achievement that it was in the history of mathematics.

The Swiss mathematician Jakob Steiner (1796-1863) came from a poor background with an incomplete education, yet such was his mathematical talent that eventually the Prussian university system adapted itself to him rather than he to it. A geometer in an age dominated by analysts, he pursued his own interests in his own way. The elegant results which bear his name - including Steiner circles, systems and symmetrisation - are known to most mathematicians today. Considered by many to be the greatest geometer since Apollonius of Perga, Steiner did important work on systemising geometry, laying the foundation for much later work on projective geometry. Edited by the eminent mathematician Karl Weierstrass (1815-97), this two-volume edition of Steiner's collected works offers scholars access to his influential writings in the original German. Volume 1 was published in 1881.

The Greek astronomer Aristarchus of Samos was active in the third century BCE, more than a thousand years before Copernicus presented his model of a heliocentric solar system. It was Aristarchus, however, who first suggested - in a work that is now lost - that the planets revolve around the sun. Edited by Sir Thomas Little Heath (1861 1940), this 1913 publication contains the ancient astronomer's only surviving treatise, which does not propound the heliocentric hypothesis. The Greek text is based principally on the tenth-century manuscript Vaticanus Graecus 204. Heath also provides a facing-page English translation and explanatory notes. The treatise is prefaced by a substantial history of ancient Greek astronomy, ranging from Homer's first mention of constellations to work by Heraclides of Pontus in the fourth century BCE relating to the Earth's rotation. Heath's collection of translated ancient texts, Greek Astronomy (1932), is also reissued in this series.

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.