SCIENCE 



[N. S. Vol. XXX. No. 781 



the science itself. Especially is this true of 

 the Greek period, in which all data about 

 teaching are closely interwoven with state- 

 ments relating to geometrical research. Dr. 

 Stamper devotes the first three chapters to 

 the Greeks, Romans and Orientals, one chap- 

 ter to the Middle Ages, one long chapter to 

 the seventeenth, eighteenth and nineteenth 

 centuries, and two chapters to present-day 

 teaching. The last three chapters contain 

 much that is original with the author. Teach- 

 ers of geometry will find them suggestive and 

 valuable. Texts have been examined to which 

 no references are usually found in histories. 

 Doubtless it is more difficult to secure data 

 on the teaching than on the progress of 

 a science. In illustration of the difficulty of 

 securing data on teaching we refer to the au- 

 thor's acknowledged inability to fix the time 

 when Euclid began to be used as a test-book 

 in English secondary schools within a closer 

 range than three quarters of a century. Dr. 

 Stamper claims that in England there were 

 no texts on the practical side of geometry, nor 

 any combining the practical with the logical, 

 such as prevailed on the continent up to about 

 the middle of the seventeenth century. We 

 doubt the accuracy of this statement. The 

 present writer has before him books explain- 

 ing the use of the slide rule by William 

 Oughtred (1660, 1st ed., 1632), Seth Part- 

 ridge (1662), Hunt (1697), Everard (1Y05), 

 Leadbetter (1755), which may certainly be 

 classed among works of practical geometry. 

 These books offer fine examples of the corre- 

 lation of geometry with arithmetic and trig- 

 onometry. The title-page of Coggeshall's 

 book refers to the " Use of Scamozzi's Lines, 

 for finding the Lengths and Angles of Hips, 

 Rafters, etc., at any Pitch, in Square, Bevel- 

 ing or Tapering Frames," explained by John 

 Ham, mentioned later in the text as " Master 

 of the Mathematical School at the Chapel in 

 Hatton-Garden, Holborn." The book con- 

 tains also a regular " compendium of prac- 

 tical geometry." Nor must we forget John 

 Ward's " Young Mathematician's Guide " 

 (1707) where, out of a total of 427 pages, 64 

 are given to geometry, the subject being 



treated in a manner quite remote from 

 Euclid's. In 1771 this text reached its 

 twelfth edition. In the preface we read: 



This treatise hath proved a very helpful Guide 

 to near five thousand persons; and perhaps most 

 of them such as would never have looked into 

 mathematioks at all but for it. . . . And not only 

 so, but it hath been very well received amongst 

 the Learned, and (I have often been told) so well 

 approved on at the Universities, in England, Scot- 

 land, and Ireland, that it is ordered to be pub- 

 lickly read to their pupils. 



In this country Ward's text was used at 

 Harvard College as early as 1737, and as late 

 as 1787 at Yale and Dartmouth. 



While the author worked industriously, 

 there are some gaps in his history. For in- 

 stance, no reference is made to the texts of 

 Basedow and his efforts at reform, nor to the 

 remarkable works of Louis Bertrand. Nor 

 has he used all the available secondary sources 

 of information, such as J. H. Graf's history 

 of mathematics in Bern and L. Isely's history 

 of mathematics in the French part of Switzer- 

 land. 



The book lacks an alphabetical index, but 

 has a full table of contents and a list of the 

 original and secondary sources used in its 

 preparation. This list will be welcomed by 

 all who may desire to undertake research 

 work on the teaching and history of elemen- 

 tary geometry. Floeian Cajori 



A Treatise on Zoology. Edited by Sir E. 



Eat Lankester. Part I., Introduction and 



Protozoa. First Fascicle, by S. J. Hickson, 



J. J. Lister, F. W. Gamble, A. Willey, H. 



M. Woodcock, E. Ray Lankesteb and the 



late W. F. R. Weldon. Pp. ix-xxii -f 296 ; 



151 figs. London, A. & C. Black. 1909. 



The present volume, together with the 



previoxTsly published second fascicle dealing 



with Foraminifera, Sporozoa and Infusoria, 



completes the account of Protozoa in Lan- 



kester's well-known " Treatise on Zoology." 



The Proteomyxa and Lobosa are described by 



S. J. Hickson; the Heliozoa by the late W. F. 



R. Weldon and S. J. Hickson; the Mycetozoa 



by J. J. Lister; the Radiolaria by F. W. 



