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even yet been done to fill the gap, and it was therefore with pleasurable 

 anticipations that we opened this book. But the title is misleading ; the 

 main item is an annotated list of mathematical instruments which were 

 exhibited in the Bodleian Library in the summer of 1919. To this are 

 appended useful notes on mathematical instrument makers. The introduc- 

 tory " Notes on Early Mathematicians " raised our hopes, but on examina- 

 tion were found to contain little information that is new. One is, perhaps, 

 rather tired of reading the rhyme about the introduction of Euclid into 

 England in the time of Athelstan, and his mention in a book on Oxford 

 is bound to suggest what Maitland called " the oldest of all inter-university 

 contests — a lying match." In connection with Euclid, isn't it about time 

 that somebody really read the versions of Adelard of Bath, with their 

 curious abbreviated proofs, and determined the relation of his translation 

 to those of Gerard of Cremona and Campanus ? The literature of the subject 

 is already large, but it is confusing and inconclusive. 



IMr. Gunther doesn't even mention the mathematics of Roger Bacon, 

 one of IMr. Wells's twelve greatest men, or of Grosseteste, while Sacrobosco 

 and the Merton School of the fourteenth century are dismissed in a few lines, 

 the latter with the pious regret that their MSS. have never been printed. 

 Robert Recorde, however, is dealt with in more detail, and interesting 

 facsimiles and quotations from his works are given. One question and 

 answer from the Grounde of Artes is worth requoting : 



" Scholar. Syr, what is the chief e use of Multiplication. 



" Mayster. The use of it is greater than you can yet understand." 

 The St. Andrew's cross used in the process of casting out the nines and in 

 the multiplication of integers between five and ten should not, however, 

 be described as a sign of multiplication (see Cajori in the Mathematical 

 Gazette, October 1922, pp. 126-43). Also there seems to be some doubt as 

 to the date of the first edition of the Grounde of Artes ; the D.N.B. gives edi- 

 tions in 1540, 1542, etc. ; Cajori gives 1543 (?), and Mr. Gunther 1542. 



The author points out with justice that the only two Cambridge 

 mathematicians of any note in the first half of the sixteenth century both 

 migrated from Oxford, but it is surely going too far to describe Cambridge 

 as the home of " what has been the most brilliantly successful mathematical 

 school in the world." 



Emphasis is naturally laid in this account on the invention of mathe- 

 matical instruments, the quadrant of Gunter, the slide-rule of Oughtred, 

 and the beam compasses of Francis Potter, so that the pure mathematician 

 of to-day reads with appreciation the tale, quoted from Aubrey's Lives, of 

 how Sir Henry Savile, being about to appoint his first Professor of Geometry 

 in Oxford, sent for Gunter, who came " and brought with him his sector 

 and quadrant, and fell to resolving of triangles and doeing a great many 

 fine things. Said the grave knight. Doe you call this reading of Geometrie ? 

 This is showing of tricks, man ! and so dismisst him with scorne, and sent 

 for Henry Briggs from Cambridge." 



The list of instruments itself is full of interesting information, and the 

 plates of instruments are excellent, but one may not, perhaps, be inclined 

 to accept Roger Bacon's dictum : " Without mathematical instruments 

 no science can be mastered," with which the introductory notes terminate. 



But when will the History of Mathematics in England be written ? 



F. P. W. 



