458 



NATURE 



[Sept. 12, 1889 



dangers and drawbacks incidental to it, but not to for- 

 get the limitless possibilities for good which it ofifers," 

 and further, "almost without a struggle is established 

 the possibility of a complete national system of technical 

 instruction." It is for this that we have reason to be 

 thankful to the Government : it has placed the instru- 

 ment in our hands, and it is for us now to use it 

 efficiently. 



CAMBRIDGE MA THEM A TICS. 

 A History of the Study of Mathematics at Cambridge. 

 By W. W. Rouse Ball. (Cambridge : University Press, 

 1889.) 



AUGUSTUS DE MORGAN, writing more than fifty 

 years ago, says that "the Hterary history of this 

 country requires separate and minute accounts of the rise 

 of science in Oxford, in Cambridge, and in the north of 

 England, which should severally end (if it might be no 

 later) with Wallis, Newton, and Thomas Simpson."^ To 

 what extent this long-felt want has been supplied by other 

 publications, we cannot tell ; but we know of none readily 

 accessible to the student of mathematical history, and 

 therefore hail with satisfaction the appearance of the 

 small octavo volume which is the subject of our review. 



What we should call the study of mathematics at 

 Cambridge is of comparatively recent origin : for, although 

 Seth Ward " brought mathematical learning into vogue 

 in the University, . . . where he lectured his pupils in 

 Master Oughtred's 'Clavis,'"^ the first Mathematical 

 Professor there was Isaac Barrow (Ward's junior by about 

 twelve years), and the lectures of his illustrious suc- 

 cessor were so ill attended that M. Bertrand says : " II 

 professa trente ans a Cambridge sans y former un disciple 

 digne de lui ; la salle du cours restait souvent deserte le 

 jour de sa legon, et Newton retournait alors tranquillement 

 a ses travaux." ^ Oughtred, whose "Clavis Mathematica " 

 was published in 1631, did not reside long at Cambridge : 

 his secluded life is thus described by our author : — 



" Although living in a country vicarage he kept up his 

 interest in mathematics. Equally with Briggs he re- 

 ceived one of the earliest copies of Napier's * Canon ' on 

 logarithms, and was at once impressed with the great 

 value of the discovery. Somewhat later in life he wrote 

 two or three works. He always gave gratuitous 

 instruction to any who came to him, provided they would 

 learn to 'write a decent hand.' He complained 

 bitterly of the penury of his wife, who always took away 

 his candle after supper, ' whereby many a good motion 

 was lost and many a problem unsolved ' ; and one of his 

 pupils who secretly gave him a box of candles earned his 

 warmest esteem. He is described as a little man, with 

 black hair, black eyes, and a great deal of spirit. Like 

 nearly all the mathematicians of the time, he was some- 

 what of an astrologer and alchemist. He died at his 

 vicarage of Albury in Surrey on June 30, 1660."* 



Mr. Ball leaves us in doubt as to the nature of the 

 " two or three works " written " somewhat later in life " 

 by Oughtred. Fortunately we are able to supply this omis- 

 sion from an old book'^ on our shelves, which says that 



' " Notices of English Mathematical and Astronomical Writers between 

 the Norman Conquest and the Year 1600 " This important article appeared 

 anonymously in the Companion to the Almanac for 1837, but was undoubtedly 

 written by De Morgan, and m fact was claimed by him six years afterwards. 



^ Ball, p. 37. In referring to the work before us, both here and subse- 

 quently, for brevity we cite unly the author's name and the number of the 

 page. 



■' " Les Fondateurs de I'Astronomie l\!oderne " (8vo, Paris, n.d.) p. 303. 



4 Ball, p. 30. 



" Lord Napier, in 1614, publishing at Edinburgh his 

 ' Mirifici logarithmorum canonis descriptio, ejusque usus 

 in utraque trigonometria, &c.,' it presently fell into the 

 hands of Mr. Briggs, then geometry-reader of Gresham 

 College in London ; and that gentleman, forming a design 

 to perfect Lord Napier's plan, consulted Oughtred upon it ; 

 who probably wrote his ' Treatise of Trigonometry ' about 

 the same time, since it is evidently formed upon the plan of 

 Lord Napier's ' Canon.' In prosecuting the same subject, he 

 invented, not many years after, an instrument, called ' The 

 Circles of Proportion.' . . . All such questions in arithmetic, 

 geometry, astronomy, and navigation, as depended upon 

 simple and compound proportion, might be wrought by 

 it ; and it was the first sliding rule that was projected for 

 those uses, as well as that of gauging." 



Authorities differ as to the day of Oughtred's death : thus 

 the " Penny Cyclopaedia ' makes it happen on " Jan. 

 30th " (a misprint, probably, for the same day of June) ; 

 in the article just quoted it is " about the beginning of 

 May" ; and in the historical introduction to Hammond's 

 " Algebra " ^ we read that " he lived to the Age of Four- 

 score and Seven, and died then of Joy, on May i, 1660, 

 at hearing the House of Commons had voted the King's 

 Return." 



One circumstance compels us to reject this account: we 

 cannot understand how Oughtred, living in the neighbour- 

 hood of Guildford, could know what took place in Parlia- 

 ment, on May i, before the next day. But the mere fact 

 of his death being currently attributed to such a cause 

 illustrates so well the intense political excitement of the 

 times in which he lived that it ought not to be passed 

 over in silence. It is of more value than many boxes of 

 candles. 



From the time of Newton down to the beginning of the 

 present century, mathematics (though diligently studied) 

 made very little progress, either at Cambridge or in other 

 parts of England. In Cambridge this was due to the 

 excessive reverence paid to authority ; at first by all, and 

 afterwards by those " senior members of the senate, who 

 regarded any attempt at innovation as a sin against the 

 memory of Newton," ^ and who were the worthy suc- 

 cessors of the Cambridge dons described by Pope, in 



1742, as 



" A hundred head of Aristotle's friends. ^ 



We may be mistaken, but we strongly suspect that one 

 of them was William Farish (b. 1759, d. 1837), whose 

 memory is embalmed in the following extract : — 



" He is celebrated in the domestic history of the Uni- 

 versity for having reduced the practice of using Latin as 

 the official language of the schools and the University to 

 a complete farce. On one occasion, when the audience 

 in the schools was unexpectedly increased by the presence 

 of a dog, he stopped the discussion to give the peremp- 

 tory order, Verte canein ex. At another time one of the 

 candidates had forgotten to put on the bands which are 



5 As no edition of this work is mentioned by De Morgan in his " References 

 for the History of the Mathematical Sciences," we give its title in full, as 

 follows : " A New and General Biographical Dictionary ; containing an His- 

 torical and Critical Account of the Lives and Writings of the Most Eminent 

 Persons in every Nation ; particularly the British and Irish ; from the Earliest 

 Accounts of Time to the present Period. Wherein Their remarkable Actions 

 and Sufferings, Their Virtues, Pans, and Learning, are Accurately Dis- 

 played. With a Catalogue of their Literary Productions. A New Ed.tion, 

 in Twelve Volumes, greatly enlarged and improved" (Svo, London, 1784). 



6 The third edition, Svo. London, 1764. 



7 Ball, p. 117. , , ,,,„ _,., , 



8 " Dunciad," iv. 192. A note to this verse reads thus :— Ihe Philosophy 

 of Aristotle had suffered a long disgrace in this learned University : being 

 first e.xpelled by the Cartesian, which, in its turn gave place to the he^v- 

 tonian. But it had ail this while some faithful followers in secret, who never 

 bowed the knee to Baal, nor acknowledged any strange God in Philosophy. 



