Originally published in 1946 as number thirty-nine in the Cambridge Tracts in Mathematics and Mathematical Physics series, this book provides a concise account regarding linear groups. Appendices are also included. This book will be of value to anyone with an interest in linear groups and the history of mathematics.

James Joseph Sylvester (1814-97) was an English mathematician who made key contributions to numerous areas of his field and was also of primary importance in the development of American mathematics, both as inaugural Professor of Mathematics at Johns Hopkins University and founder of the American Journal of Mathematics. Originally published in 1904, this book forms the first in four volumes of Sylvester's mathematical papers, covering the period from 1837 to 1853. Together these volumes provide a comprehensive resource that will be of value to anyone with an interest in Sylvester's theories and the history of mathematics.

James Joseph Sylvester (1814-97) was an English mathematician who made key contributions to numerous areas of his field and was also of primary importance in the development of American mathematics, both as inaugural Professor of Mathematics at Johns Hopkins University and founder of the American Journal of Mathematics. Originally published in 1908, this book forms the second in four volumes of Sylvester's mathematical papers, covering the period from 1854 to 1873. Together these volumes provide a comprehensive resource that will be of value to anyone with an interest in Sylvester's theories and the history of mathematics.

James Joseph Sylvester (1814-97) was an English mathematician who made key contributions to numerous areas of his field and was also of primary importance in the development of American mathematics, both as inaugural Professor of Mathematics at Johns Hopkins University and founder of the American Journal of Mathematics. Originally published in 1909, this book forms the third in four volumes of Sylvester's mathematical papers, covering the period from 1870 to 1883. Together these volumes provide a comprehensive resource that will be of value to anyone with an interest in Sylvester's theories and the history of mathematics.

James Joseph Sylvester (1814-97) was an English mathematician who made key contributions to numerous areas of his field and was also of primary importance in the development of American mathematics, both as inaugural Professor of Mathematics at Johns Hopkins University and founder of the American Journal of Mathematics. Originally published in 1912, this book forms the fourth in four volumes of Sylvester's mathematical papers, covering the period from 1882 to 1897. Together these volumes provide a comprehensive resource that will be of value to anyone with an interest in Sylvester's theories and the history of mathematics.

Henry Frederick Baker (1866 1956) was a renowned British mathematician specialising in algebraic geometry. He was elected a Fellow of the Royal Society in 1898 and appointed the Lowndean Professor of Astronomy and Geometry in the University of Cambridge in 1914. First published between 1922 and 1925, the six-volume Principles of Geometry was a synthesis of Baker's lecture series on geometry and was the first British work on geometry to use axiomatic methods without the use of co-ordinates. The first four volumes describe the projective geometry of space of between two and five dimensions, with the last two volumes reflecting Baker's later research interests in the birational theory of surfaces. The work as a whole provides a detailed insight into the geometry which was developing at the time of publication. This, the first volume, describes the foundations of projective geometry.

Henry Frederick Baker (1866 1956) was a renowned British mathematician specialising in algebraic geometry. He was elected a Fellow of the Royal Society in 1898 and appointed the Lowndean Professor of Astronomy and Geometry in the University of Cambridge in 1914. First published between 1922 and 1925, the six-volume Principles of Geometry was a synthesis of Baker's lecture series on geometry and was the first British work on geometry to use axiomatic methods without the use of co-ordinates. The first four volumes describe the projective geometry of space of between two and five dimensions, with the last two volumes reflecting Baker's later research interests in the birational theory of surfaces. The work as a whole provides a detailed insight into the geometry which was developing at the time of publication. This, the second volume, describes the principal configurations of space of two dimensions.

Henry Frederick Baker (1866 1956) was a renowned British mathematician specialising in algebraic geometry. He was elected a Fellow of the Royal Society in 1898 and appointed the Lowndean Professor of Astronomy and Geometry in the University of Cambridge in 1914. First published between 1922 and 1925, the six-volume Principles of Geometry was a synthesis of Baker's lecture series on geometry and was the first British work on geometry to use axiomatic methods without the use of co-ordinates. The first four volumes describe the projective geometry of space of between two and five dimensions, with the last two volumes reflecting Baker's later research interests in the birational theory of surfaces. The work as a whole provides a detailed insight into the geometry which was developing at the time of publication. This, the third volume, describes the principal configurations of space of three dimensions.

Henry Frederick Baker (1866 1956) was a renowned British mathematician specialising in algebraic geometry. He was elected a Fellow of the Royal Society in 1898 and appointed the Lowndean Professor of Astronomy and Geometry in the University of Cambridge in 1914. First published between 1922 and 1925, the six-volume Principles of Geometry was a synthesis of Baker's lecture series on geometry and was the first British work on geometry to use axiomatic methods without the use of co-ordinates. The first four volumes describe the projective geometry of space of between two and five dimensions, with the last two volumes reflecting Baker's later research interests in the birational theory of surfaces. The work as a whole provides a detailed insight into the geometry which was developing at the time of publication. This, the fourth volume, describes the principal configurations of space of four and five dimensions.

Henry Frederick Baker (1866 1956) was a renowned British mathematician specialising in algebraic geometry. He was elected a Fellow of the Royal Society in 1898 and appointed the Lowndean Professor of Astronomy and Geometry in the University of Cambridge in 1914. First published between 1922 and 1925, the six-volume Principles of Geometry was a synthesis of Baker's lecture series on geometry and was the first British work on geometry to use axiomatic methods without the use of co-ordinates. The first four volumes describe the projective geometry of space of between two and five dimensions, with the last two volumes reflecting Baker's later research interests in the birational theory of surfaces. The work as a whole provides a detailed insight into the geometry which was developing at the time of publication. This, the fifth volume, describes the birational geometry of curves.

Henry Frederick Baker (1866 1956) was a renowned British mathematician specialising in algebraic geometry. He was elected a Fellow of the Royal Society in 1898 and appointed the Lowndean Professor of Astronomy and Geometry in the University of Cambridge in 1914. First published between 1922 and 1925, the six-volume Principles of Geometry was a synthesis of Baker's lecture series on geometry and was the first British work on geometry to use axiomatic methods without the use of co-ordinates. The first four volumes describe the projective geometry of space of between two and five dimensions, with the last two volumes reflecting Baker's later research interests in the birational theory of surfaces. The work as a whole provides a detailed insight into the geometry which was developing at the time of publication. This, the sixth and final volume, describes the birational geometric theory of surfaces.

Classical algebraic geometry, inseparably connected with the names of Abel, Riemann, Weierstrass, Poincaré, Clebsch, Jacobi and other outstanding mathematicians of the last century, was mainly an analytical theory. In our century the methods and ideas of topology, commutative algebra and Grothendieck's schemes enriched it and seemed to have replaced once and forever the somewhat naive language of classical algebraic geometry. This classic book, written in 1897, covers the whole of algebraic geometry and associated theories. Baker discusses the subject in terms of transcendental functions, and theta functions in particular. Many of the ideas put forward are of continuing relevance today, and some of the most exciting ideas from theoretical physics draw on work presented here.

The theory of surfaces has reached a certain stage of completeness and major efforts concentrate on solving concrete questions rather than developing further the formal theory. Many of these questions are touched upon in this classic volume: such as the classification of quartic surfaces, the description of moduli spaces for abelian surfaces, and the automorphism group of a Kummer surface. First printed in 1905 after the untimely death of the author, this work has stood for most of this century as one of the classic reference works in geometry.

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!

AN INTRODUCTION TO THE THEORY OF MULTIPLY PERIODIC FUNCTIONS BY H. F. BAKER, Sc. D., F. R. S., FELLOW OF ST JOHNS COLLEGE AND LECTURER IN MATHEMATICS IN THE UNIVERSITY OF CAMBRIDGE PROPERTY OF mum msrmiTE Of CAMBRIDGE at the University Press 1907 Sie erinnern Sich aber auch vielleicht zu gleieher Zeifc meiner Klagen, liber einen Satz, dor thoils schon an aich sehr interessdnt 1st, theils einem sehr betrachtlichen Theile jener Untersuchungen als Grundlage oder als Schlussstein dient, den ich damals schon liber 2 Jahr kannte, und der alle meine Bemiihungon, einen gcnligendon Bowels zu finden, vereitelt hatte, diesor Satz ist schon in meiner Theorie der Zahlcn angocloutct, und bctrifft die Bcstimmung eines Wurzelzeichens, sie hat rnich immer gequalt. Dieser Mangel hat rair allos Uebrige, was ich fand, verleidet und seit 4 Jahren wird selten eine Woche hingegangen seiu, wo ich nicht einen oder den anderon vergeblichen Versuch, diesen Knoten zu losen, gemacht hatte besonders lebhaft nun auch wieder in der letzten Zcit. Aber alles Bruten, allos Suchcn ist umsonst gowesen, traurig habe ich jedesmal die Feder wieder niederlegen mlissen. Endlich vor ein Paar Tagen ists gelungen GAUSS an OLBERS, September 1805 Sobering, Festrodo. PREFACE. present volume consists of two parts the first of these deals with the theory of hyperelliptic functions of two variables, the second with the reduction of the theory of general multiply-periodic functions to the theory of algebraic functions taken together they furnish what is intended to be an elementary and self-contained introduction to many of the leading ideas of the theory of multiply-periodic functions, with the incidental aim of aiding the comprehensionof the importance of this theory in analytical geometry. The first part is centred round some remarkable differential equations satisfied by the functions, which appear to be equally illuminative both of the analytical and geometrical aspects of the theory it was in fact to explain this that the book was originally entered upon. The account has no pretensions to completeness being anxious to explain the properties of the functions from the beginning, I have been debarred from following Humberts brilliant monograph, which assumes from the first Poincares theorem as to the number of zeros common to two theta functions this theorem is reached in this volume, certainly in a generalised form, only in the last chapter of Part n. being anxious to render the geometrical portions of the volume quite elementary, I have not been able to utilise the theory of quadratic complexes, which vi Preface. has proved so powerful in this connexion in the hands of Kummer and Klein and, for both these reasons, the account given here, and that given in the remarkable book from the pen of R. W. H. T. Hudson, will, I believe, only be regarded by readers as comple mentary. The theory of Kummers surface, and of the theta functions, has been much studied since the year 1847 or before in which Gopel first obtained the biquadratic relation connecting four theta functions and Wirtinger has shewn, in his Unter suchungen iiber Thetafunctionen, which has helped me in several ways in the second part of this volume, that the theory is capable of generalisation, in many of its results, to space of 2 1 dimensions but even in the case of two variables there is a certain inducement, not to come to too close quarters with thedetails, in the fact of the existence of sixteen theta functions connected together by many relations, at least in the minds of beginners. I hope therefore that the treatment here followed, which reduces the theory, in a very practical way, to that of one theta function and three periodic functions connected by an algebraic equation, may recommend itself to others, and, in a humble way, serve the purpose of the earlier books on elliptic functions, of encouraging a wider use of the functions in other branches of mathematics...

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!

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

This scarce antiquarian book is included in our special Legacy Reprint Series. In the interest of creating a more extensive selection of rare historical book reprints, we have chosen to reproduce this title even though it may possibly have occasional imperfections such as missing and blurred pages, missing text, poor pictures, markings, dark backgrounds and other reproduction issues beyond our control. Because this work is culturally important, we have made it available as a part of our commitment to protecting, preserving and promoting the world's literature.

This book is a facsimile reprint and may contain imperfections such as marks, notations, marginalia and flawed pages.

AN INTRODUCTION TO THE THEORY OF MULTIPLY PERIODIC FUNCTIONS BY H. F. BAKER, Sc. D., F. R. S., FELLOW OF ST JOHNS COLLEGE AND LECTURER IN MATHEMATICS IN THE UNIVERSITY OF CAMBRIDGE PROPERTY OF mum msrmiTE Of CAMBRIDGE at the University Press 1907 Sie erinnern Sich aber auch vielleicht zu gleieher Zeifc meiner Klagen, liber einen Satz, dor thoils schon an aich sehr interessdnt 1st, theils einem sehr betrachtlichen Theile jener Untersuchungen als Grundlage oder als Schlussstein dient, den ich damals schon liber 2 Jahr kannte, und der alle meine Bemiihungon, einen gcnligendon Bowels zu finden, vereitelt hatte, diesor Satz ist schon in meiner Theorie der Zahlcn angocloutct, und bctrifft die Bcstimmung eines Wurzelzeichens, sie hat rnich immer gequalt. Dieser Mangel hat rair allos Uebrige, was ich fand, verleidet und seit 4 Jahren wird selten eine Woche hingegangen seiu, wo ich nicht einen oder den anderon vergeblichen Versuch, diesen Knoten zu losen, gemacht hatte besonders lebhaft nun auch wieder in der letzten Zcit. Aber alles Bruten, allos Suchcn ist umsonst gowesen, traurig habe ich jedesmal die Feder wieder niederlegen mlissen. Endlich vor ein Paar Tagen ists gelungen GAUSS an OLBERS, September 1805 Sobering, Festrodo. PREFACE. present volume consists of two parts the first of these deals with the theory of hyperelliptic functions of two variables, the second with the reduction of the theory of general multiply-periodic functions to the theory of algebraic functions taken together they furnish what is intended to be an elementary and self-contained introduction to many of the leading ideas of the theory of multiply-periodic functions, with the incidental aim of aiding the comprehensionof the importance of this theory in analytical geometry. The first part is centred round some remarkable differential equations satisfied by the functions, which appear to be equally illuminative both of the analytical and geometrical aspects of the theory it was in fact to explain this that the book was originally entered upon. The account has no pretensions to completeness being anxious to explain the properties of the functions from the beginning, I have been debarred from following Humberts brilliant monograph, which assumes from the first Poincares theorem as to the number of zeros common to two theta functions this theorem is reached in this volume, certainly in a generalised form, only in the last chapter of Part n. being anxious to render the geometrical portions of the volume quite elementary, I have not been able to utilise the theory of quadratic complexes, which vi Preface. has proved so powerful in this connexion in the hands of Kummer and Klein and, for both these reasons, the account given here, and that given in the remarkable book from the pen of R. W. H. T. Hudson, will, I believe, only be regarded by readers as comple mentary. The theory of Kummers surface, and of the theta functions, has been much studied since the year 1847 or before in which Gopel first obtained the biquadratic relation connecting four theta functions and Wirtinger has shewn, in his Unter suchungen iiber Thetafunctionen, which has helped me in several ways in the second part of this volume, that the theory is capable of generalisation, in many of its results, to space of 2 1 dimensions but even in the case of two variables there is a certain inducement, not to come to too close quarters with thedetails, in the fact of the existence of sixteen theta functions connected together by many relations, at least in the minds of beginners. I hope therefore that the treatment here followed, which reduces the theory, in a very practical way, to that of one theta function and three periodic functions connected by an algebraic equation, may recommend itself to others, and, in a humble way, serve the purpose of the earlier books on elliptic functions, of encouraging a wider use of the functions in other branches of mathematics...