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[PDF page 359] 343 Once more the author of aShort History of Mathematics and a History of the Study of Mathematics at Cambridgegives evidence of the width of his reading and of his skill in compilation. From the elementary arithmetical puzzles which were known in the sixteenth and seventeenth centuries to those modern ones the mathematical discussion of which has taxed the energies of the ablest investigator, very few questions have been left unrepresented. The sources of the author’s in- formation are indicated with great fulness.... The book is a welcome addition to English mathematical literature.—The Oxford Magazine.

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[PDF page 360] 344 A HISTORY OF THE STUDY OF MATHEMATICS AT CAMBRIDGE By W.W. ROUSE BALL. [Pp. xvi + 264. Price 6s.] THE UNIVERSITY PRESS, CAMBRIDGE. This work contains an account of the development of the study of mathematics in the university of Cambridge from the twelfth century to the middle of the nineteenth century, and a description of the means by which proficiency in that study was tested at various times. The first part of the book is devoted to a brief account of the more eminent of the Cambridge mathematicians, the subject matter of their works, and their methods of exposition. The second part treats of the manner in which mathematics was taught, and of the exercises and examinations required of students in past times. A sketch is given of the origin and history of the Mathematical Tripos; this includes the substance of the earlier parts of the author’s work on that subject, Cambridge, 1880. To explain the relation of mathematics to other departments of study an outline of the general history of the university and the organization of education therein is added. The present volume is very pleasant reading, and though much of it necessarily appeals only to mathematicians, there are parts—e.g. the chapters on Newton, on the growth of the tripos, and on the history of the university—which are full of inter- est for a general reader.... The book is well written, the style is crisp and clear, and there is a humorous appreciation of some of the curious old regulations which have been superseded by time and change of custom. Though it seems light, it must rep- resent an extensive study and investigation on the part of the author, the essential results of which are skilfully given. We can most thoroughly commend Mr. Ball’s volume to all readers who are interested in mathematics or in the growth and the position of the Cambridge school of mathematicians.—The Manchester Guardian. Voici un livre dont la lecture inspire tout d’abord le regret que des travaux analogues n’aient pas été faits pour toutes les Écoles célèbres, et avec autant de soin

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[PDF page 361] 345 et de clarté.... Toutes les parties du livre nous out vivement intéressé.—Bulletin des sciences mathématiques. A book of pleasant and useful reading for both historians and mathematicians. Mr. Ball’s previous researches into this kind of history have already established his reputation, and the book is worthy of the reputation of its author. It is more than a detailed account of the rise and progress of mathematics, for it involves a very exact history of the University of Cambridge from its foundation.—The Educational Times. Mr. Ball is far from confining his narrative to the particular science of which he is himself an acknowledged master, and his account of the study of mathematics becomes a series of biographical portraits of eminent professors and a record not only of the intellectual life of theélite but of the manners, habits, and discussions of the great body of Cambridge men from the sixteenth century to our own.... He has shown how the University has justified its liberal reputation, and how amply prepared it was for the larger freedom which it now enjoys.—The Daily News. Mr. Ball has not only given us a detailed account of the rise and progress of the science with which the name of Cambridge is generally associated but has also written a brief but reliable and interesting history of the university itself from its foundation down to recent times.... The book is pleasant reading alike for the mathematician and the student of history.—St. James’s Gazette. Averyhandyandvaluablebookcontaining, asitdoes, avastdealofinteresting information which could not without inconceivable trouble be found elsewhere.... It is very far from forming merely a mathematical biographical dictionary, the growth of mathematical science being skilfully traced in connection with the suc- cessive names. There are probably very few people who will be able thoroughly to appreciate the author’s laborious researches in all sorts of memoirs and transactions of learned societies in order to unearth the material which he has so agreeably con- densed.... Along with this there is much new matter which, while of great interest to mathematicians, and more especially to men brought up at Cambridge, will be found to throw a good deal of new and important light on the history of education in general.—The Glasgow Herald. Exceedingly interesting to all who care for mathematics.... After giving an account of the chief Cambridge Mathematicians and their works in chronological order, Mr. Rouse Ball goes on to deal with the history of tuition and examinations in the University ... and recounts the steps by which the word “tripos” changed its meaning “from a thing of wood to a man, from a man to a speech, from a speech to two sets of verses, from verses to a sheet of coarse foolscap paper, from a paper to a list of names, and from a list of names to a system of examination.”—Never did word undergo so many alterations.—The Literary World. In giving an account of the development of the study of mathematics in the University of Cambridge, and the means by which mathematical proficiency was tested in successive generations, Mr. Ball has taken the novel plan of devoting the first half of his book to ... the more eminent Cambridge mathematicians, and of reserving to the second part an account of how at various times the subject was

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[PDF page 362] 346 taught, and how the result of its study was tested.... Very interesting information is given about the work of the students during the different periods, with specimens of problem-papers as far back as 1802. The book is very enjoyable, and gives a capital and accurate digest of many excellent authorities which are not within the reach of the ordinary reader.—The Scots Observer.

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[PDF page 363] 347 AN ESSAY ON THE GENESIS, CONTENTS, AND HISTORY OF NEWTON’S “PRINCIPIA” By W.W. ROUSE BALL. [Pp. x + 175. Price 6s. net. ] MACMILLAN AND CO. Ltd., LONDON AND NEW YORK. This work contains an account of the successive discoveries of Newton on gravitation, the methods he used, and the history of his researches. It commences with a review of the extant authorities dealing with the subject. In the next two chapters the investigations made in 1666 and 1679 are discussed, some of the documents dealing therewith be- ing here printed for the first time. The fourth chapter is devoted to the investigations made in 1684: these are illustrated by Newton’s pro- fessorial lectures (of which the original manuscript is extant) of that autumn, and are summed up in the almost unknown memoir of Febru- ary, 1685, which is here reproduced from Newton’s holograph copy. In the two following chapters the details of the preparation from 1685 to 1687 of the Principia are described, and an analysis of the work is given. The seventh chapter comprises an account of the researches of Newton on gravitation subsequent to the publication of the first edition of thePrincipia, and a sketch of the history of that work. In the last chapter, the extant letters of 1678–1679 between Hooke andNewton, andofthoseof1686–1687betweenHalleyandNewton, are reprinted, and there are also notes on the extant correspondence con- cerning the production of the second and third editions of thePrincipia. For the essay which we have before us, Mr Ball should receive the thanks of all those to whom the name of Newton recalls the memory of a great man. The Principia, besides being a lasting monument of Newton’s life, is also to-day the classic of our mathematical writings, and will be so for some time to come.... The

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[PDF page 364] 348 value of the present work is also enhanced by the fact that, besides containing a few as yet unpublished letters, there are collected in its pages quotations from all documents, thus forming a complete summary of everything that is known on the subject.... The author is so well known a writer on anything connected with the history of mathematics, that we need make no mention of the thoroughness of the essay, while it would be superfluous for us to add that from beginning to end it is pleasantly written and delightful to read. Those well acquainted with thePrincipia will find much that will interest them, while those not so fully enlightened will learn much by reading through the account of the origin and history of Newton’s greatest work.—Nature. An Essay on Newton’s Principiawill suggest to many something solely mathe- matical, and therefore wholly uninteresting. No inference could be more erroneous. Thebookcertainlydealslargelyinscientifictechnicalitieswhichwillinterestexperts only; but it also contains much historical information which might attract many who, from laziness or inability, would be very willing to take all its mathematics for granted. Mr. Ball carefully examines the evidence bearing on the development of Newton’s great discovery, and supplies the reader with abundant quotations from contemporary authorities. Not the least interesting portion of the book is the ap- pendix, or rather appendices, containing copies of the original documents (mostly letters) to which Mr. Ball refers in his historical criticisms. Several of these bear upon the irritating and unfounded claims of Hooke.—The Athenæum. La savante monographie de M. Ball est rédigée avec beaucoup de soin, et à plusieurs égards elle peut servir de modèle pour des écrits de la même nature.— Bibliotheca Mathematica. Newton’sPrincipia has world-wide fame as a classic of mathematical science. But those who know thoroughly the contents and the history of the book are a select company. It was at one time the purpose of Mr. Ball to prepare a new critical edition of the work, accompanied by a prefatory history and notes, and by an analytical commentary. Mathematicians will regret to hear that there is no prospectintheimmediatefutureofseeingthisimportantbookcarriedtocompletion by so competent a hand. They will at the same time welcome Mr. Ball’sEssay on the Principia for the elucidations which it gives of the process by which Newton’s great work originated and took form, and also as an earnest of the completed plan.—The Scotsman. In this essay Mr. Ball presents us with an account highly interesting to math- ematicians and natural philosophers of the origin and history of that remark- able product of a great geniusPhilosophiae Naturalis Principia Mathematica, ‘The Mathematical Principles of Natural Philosophy,’ better known by the short term Principia.... Mr. Ball’s essay is one of extreme interest to students of physical sci- ence, and it is sure to be widely read and greatly appreciated.—The Glasgow Herald. To his well-known and scholarly treatises on the History of Mathematics Mr. W.W. Rouse Ball has addedAn Essay on Newton’s Principia. Newton’sPrin- cipia, as Mr. Ball justly observes, is the classic of English mathematical writings; and this sound, luminous, and laborious essay ought to be the classical account

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[PDF page 365] 349 of the Principia. The essay is the outcome of a critical edition of Newton’s great work, which Mr. Ball tells us that he once contemplated. It is much to be hoped that he will carry out his intention, for no English mathematician is likely to do the work better or in a more reverent spirit.... It is unnecessary to say that Mr. Ball has a complete knowledge of his subject. He writes with an ease and clearness that are rare.—The Scottish Leader. Le volume de M. Rouse Ball renferme tout ce que l’on peut désirer savoir sur l’histoire desPrincipes; c’est d’ailleurs l’œuvre d’un esprit clair, judicieux, et méthodique.—Bulletin des Sciences Mathématiques. Mr. Ball has put into small space a very great deal of interesting matter, and his book ought to meet with a wide circulation among lovers of Newton and the Principia.—The Academy. Admirers of Mr. W.W. Rouse Ball’sShort Account of the History of Mathe- matics will be glad to receive a detailed study of the history of thePrincipia from the same hand. This book, like its predecessors, gives a very lucid account of its subject. We find in it an account of Newton’s investigations in his earlier years, which are to some extent collected in the tractde Motu(the germ of thePrincipia) the text of which Mr. Rouse Ball gives us in full. In a later chapter there is a full analysis of thePrincipia itself, and after that an account of the preparation of the second and third editions. Probably the part of the book which will be found most interesting by the general reader is the account of the correspondence of Newton with Hooke, and with Halley, about the contents or the publication of thePrin- cipia. This correspondence is given in full, so far as it is recoverable. Hooke does not appear to advantage in it. He accuses Newton of stealing his ideas. His vain and envious disposition made his own merits appear great in his eyes, and be-dwarfed the work of others, so that he seems to have believed that Newton’s great perfor- mance was a mere expanding and editing of the ideas of Mr. Hooke—ideas which were meritorious, but after all mere guesses at truth. This, at all events, is the most charitable view we can take of his conduct. Halley, on the contrary, appears as a man to whom we ought to feel most grateful. It almost seems as though Newton’s physical insight and extraordinary mathematical powers might have been largely wasted, as was Pascal’s rare genius, if it had not been for Halley’s single-hearted and self-forgetful efforts to get from his friend’s genius all he could for the enlight- enment of men. It was probably at his suggestion that the writing of thePrincipia was undertaken. When the work was presented to the Royal Society, they under- took its publication, but, being without the necessary funds, the expense fell upon Halley. When Newton, stung by Hooke’s accusations, wished to withdraw a part of the work, Halley’s tact was required to avert the catastrophe. All the drudgery, worry, and expense fell to his share, and was accepted with the most generous good nature. It will be seen that both the technical student and the general reader may find much to interest him in Mr. Rouse Ball’s book.—The Manchester Guardian. Une histoire très bien faite de la genèse du livre immortel de Newton.... Le livre de M. Ball est une monographie précieuse sur un point important de l’histoire des mathématiques. Il contribuera à accroître, si c’est possible, la gloire de Newton, en révélant à beaucoup de lecteurs, avec quelle merveilleuse rapid-

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[PDF page 366] 350 ité l’illustre géomètre anglais a élevé à la science ce monument immortel, les Principia.—Mathesis.

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[PDF page 367] 351 NOTES ON THE HISTORY OF TRINITY COLLEGE, CAMBRIDGE By W.W. ROUSE BALL. [Pp. xiv + 183. Price 2s. 6d. net. ] MACMILLAN AND CO. Ltd., LONDON AND NEW YORK. This booklet gives a popular account of the History of Trinity Col- lege, Cambridge, and so far as the author knows, it is as yet (1905) the only work published on the subject. It was written mainly for the use of his pupils, and contains such information and gossip about the College and life there in past times as he believed would be interesting to most undergraduates and members of the House. This modest and unpretending little volume seems to us to do more for its subject than many of the more formal volumes ... treating of the separate col- leges of the English universities.... In nine short, extremely readable, and truly informing chapters it gives the reader a very vivid account at once of the origin and development of the University of Cambridge, of the rise and gradual supremacy of the colleges, of King’s Hall as founded by Edward II, of the suppression of King’s Hall by Henry VIII on December 17, 1546, the foundation of Trinity College by royal charter on December 19, and the subsequent fortunes of the premier college of Cambridge. The subject is in a way treated under the successive heads of the college, but this is quite subordinate to the handling and characterisation of the subject under four great periods—namely, that during the Middle Ages, that dur- ing the Renaissance, that under the Elizabethan statutes, and that during the last half-century. The colleges arose from the determination of the University to pre- vent students who were very young from seeking lodging, whether under the wing of one or other of the religious orders—a circumstance which shows this University to have been an essentially lay corporation. Early in the sixteenth century the college had absorbed all the members of the University, and henceforth the University was little more than the degree-granting body to students who lived and moved and had their educational being under the colleges.... The University finally took the form of an aggregate of separate and independent corporations, with a federal con- stitution analogous in a rough sort of way to that of the United States of America,

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[PDF page 368] 352 and different from similar corporations at Paris by the fact that these latter were always subject to University supervision.... There is a good account of the effort now going on to re-assert the University at the expense of the colleges. No one who begins Mr. Ball’s book will lay it down till he has read it from beginning to end.—The Glasgow Herald. It is a sign of the times, and a very satisfactory one, when ... a tutor ... takes the trouble to make the history of his college known to his pupils. Considering the lack of good books about the Universities, we may thank Mr. Ball that he has been good enough to print for a larger circle. Though he modestly calls his book only “Notes,” yet it is eminently readable, and there is plenty of information, as well as abundance of good stories, in its pages.—The Oxford Magazine. Mr. Ball has put not only the pupils for whom he compiled these notes, but the large world of Trinity men, under a great obligation by this compendious but lucid and interesting history of the society to whose service he is devoted. The value of his contribution to our knowledge is increased by the extreme simplicity with which he tells his story, and the very suggestive details which, without much comment, he has selected, with admirable discernment, out of the wealth of materials at his disposal. His initial account of the development of the University is brief but extremely clear, presenting us with facts rather than theories, but establishing, with much distinctness, the essential difference between the hostels, out of which the more modern colleges grew, and that monastic life which poorer students were often tempted to join.—The Guardian. An interesting and valuable book.... It is described by its author as “little more than an orderly transcript” of what, as a Fellow and Tutor of the College, he has been accustomed to tell his pupils. But while it does not pretend either to the form or to the exhaustiveness of a set history, it is scholarly enough to rank as an authority, and far more interesting and readable than most academic histories are. It gives an instructive sketch of the development of the University and of the particular history of Trinity, noting its rise and policy in the earlier centuries of its existence, until, under the misrule of Bentley, it came into a state of disorder which nearly resulted in its dissolution. The subsequent rise of the College and its position in what Mr. Ball calls the Victorian renaissance, are drawn in lines no less suggestive; and the book, as a whole, cannot fail to be welcome to every one who is closely interested in the progress of the College.—The Scotsman. Mr. Ball has succeeded very well in giving in this little volume just what an intelligent undergraduate ought and probably often does desire to know about the buildings and the history of his College.... The debt of the “royal and religious foundation” to Henry VIII is explained with fulness, and there is much interest- ing matter as to the manner of life and the expenses of students in the sixteenth century.—The Manchester Guardian.

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[PDF page 369] LICENSING. 353 *** END OF THE PROJECT GUTENBERG EBOOK MATHEMATICAL RECREATIONS *** ***** This file should be named 26839-pdf.pdf or 26839-pdf.zip ***** This and all associated files of various formats will be found in: https://www.gutenberg.org/2/6/8/3/26839/ Updated editions will replace the previous one—the old editions will be renamed. Creating the works from print editions not protected by U.S. copyright law means that no one owns a United States copyright in these works, so the Foundation (and you!) can copy and distribute it in the United States without permission and without paying copyright royalties. Special rules, set forth in the General Terms of Use part of this license, apply to copying and distributing Project Gutenberg-tm electronic works to protect the PROJECT GUTENBERG-tm concept and trademark. Project Gutenberg is a registered trademark, and may not be used if you charge for an eBook, except by following the terms of the trademark license, including paying royalties for use of the Project Gutenberg trademark. If you do not charge anything for copies of this eBook, complying with the trademark license is very easy. Y ou may use this eBook for nearly any purpose such as creation of derivative works, reports, performances and research. Project Gutenberg eBooks may be modified and printed and given away—you may do practically ANYTHING in the United States with eBooks not protected by U.S. copyright law. Redistribution is subject to the trademark license, especially commercial redistribution. START: FULL LICENSE THE FULL PROJECT GUTENBERG LICENSE PLEASE READ THIS BEFORE YOU DISTRIBUTE OR USE THIS WORK To protect the Project Gutenberg-tm mission of promoting the free distribution of electronic works, by using or distributing this work (or any other work associated in any way with the phrase “Project Gutenberg”), you agree to comply with all the terms of the Full Project Gutenberg-tm License available with this file or online at www.gutenberg.org/license. Section 1. General Terms of Use and Redistributing Project Gutenberg-tm electronic works 1.A. By reading or using any part of this Project Gutenberg-tm electronic work, you indicate that you have read, understand, agree to and accept all the terms of this license and intellectual property (trademark/copyright) agreement. If you do not agree to abide by all the terms of this agreement, you must cease using and return or destroy all copies of Project Gutenberg-tm electronic works in your possession. If you paid a fee for obtaining a copy of or access to a Project Gutenberg-tm electronic work and you do not agree to be bound by the terms of this agreement, you may obtain a refund from the person or entity to whom you paid the fee as set forth in paragraph 1.E.8. 1.B. “Project Gutenberg” is a registered trademark. It may only be
