M*: 



SCIENCE 



[Vol. IV., No. 92. 



from any subsequent cases should be destroyed in 

 such manner as to stamp out the disease." 



The conference adjourned, to meet in Washington 

 on the second Tuesday of December. 



various editions among different nations and by cen- 

 turies. This is done in the following table: — 



EUCLID AS A 



TEXT-BOOK OF GEOME- 

 TRY. 



Although Euclid has long since been superseded 

 in the schools of this country, the following statisti- 

 cal notes on the extent to which Euclid's 'Elements' 

 are still used in other countries may prove of some 

 interest to the readers of Science. The figures are 

 derived from a list of editions of Euclid's ' Elements ' 

 and ' Data' up to the year 1879, contained in a new 

 Russian school edition of the ' Elements ' by Professor 

 Yashchenko-Zakharchenko. 1 This is a noteworthy 

 work in several other respects. Besides numerous 

 and extensive notes, and additions to the text, de- 

 signed to render Euclid's treatment of geometry more 

 palatable to modern taste, and to fill up some lacunae 

 in the old work, the author has prefixed to his trans- 

 lation a valuable dissertation on the axioms and pos- 

 tulates and on the so-called non-Euclidean geometry 

 of Bolyai and Lobachefsky, of which a sufficient- 

 ly full sketch is presented. That a man so well 

 acquainted with modern investigations of the princi- 

 ples of the science of space as Mr. Vashchenko- 

 Zakharchenko (a bibliography of this subject is also 

 appended to the volume) should prove such an ardent 

 adherent of Euclid, pure and simple, for the schools, 

 is a truly remarkable fact. A closer inspection of his 

 own list of editions of Euclid might have shown him 

 that the modern mind does not tend at all in the 

 direction of a revival of Euclid's system and methods 

 in geometry. 



This list has 455 entries, of which 2 belong to 

 the fifteenth, 84 to the sixteenth, 92 to the seven- 

 teenth, 118 to the eighteenth, and 159 to the nine- 

 teenth century. This enumeration includes reprints. 

 Of really different editions there were, according to 

 the author's count, 80 in the sixteenth, 59 in the 

 seventeenth, 50 in the eighteenth, and 115 in the nine- 

 teenth century. 



Mr. Yashchenko-Zakharchenko, however, does 

 not pretend that his list is complete: indeed, he has 

 not attempted to present a full and correct bibliog- 

 raphy of all editions of Euclid. The titles are given 

 in such an abridged form as to make identification in 

 some cases difficult; and typographical errors abound. 

 No American edition appears in Mr. Zakharchenko's 

 list, although several have been published in the 

 United States. 2 Still, for our purpose the list, as it 

 is, will yield some interesting results. We have only 

 to group its data so as to show the distribution of the 



i " The Elements of Euclid, with an explanatory introduction 

 and annotations, by M. E. Vashchenko-Zakharchenko. Kieff, 

 1880." 15+747 pp. 



2 The library of congress possesses two American reprints of 

 R. Simson's Euclid, published by Desilver of Philadelphia in 

 1825 and 1834 respectively, and an addition of the first three 

 books of the ' Elements ' (Playfair's text), with notes, under the 

 title " The geometry of Euclid : with annotations by Horatio 

 Hubbell, Phila., J. B. Lippincott & Co., 1861." 



Period. 



c3 



cS 



03 

 0) 



5 



"Si 

 s 

 W 



| 



3 



o 



c 



5 

 "3 



o 

 3 



G 



a 

 a 

 a 



00 



■5 



% 

 as 



3 



1 

 2 



6 



3 



3 



3 

 2 



5 



"3 



P4 



2 

 2 



a 

 fi 



1 

 1 



V 



a 



if. 



a 

 1 



1 



1 



5 



z 







1 

 1 



S 



s 



1 

 1 



"S 



< 



3 

 1 



2 

 6 



6 



5 



1 



1 



2 



"3 



o 

 H 



2 



84 

 92 



118 

 56 



103 



455 



15th century . 

 16th " . . 

 17th " . . 

 18th " . . 

 1800 to 1839 . . 

 1840 to 1879 . . 



2 



60 



43 



31 



9 







1 

 3 



26 

 15 



95 



2 

 9 

 17 

 21 

 1 



50 



4 

 16 



18 

 1 



39 



12 

 10 

 11 

 1 

 3 



37 



7 

 5 



12 



2 

 2 

 3 



7 



Total . . . 



145 



140 



There can be only one interpretation of these 

 figures. They illustrate in a striking way the fact 

 that at present Euclid is used as a text-book in the 

 schools in no country but England. 



The English editions constitute thirty-one per cent 

 of the whole number in the list, and fifty-three per 

 cent of those in the four principal living languages 

 (English, French, German, Italian). But this dis- 

 proportion only appears in its full significance when 

 we take into account the time of publication. In- 

 deed, the table shows that up to 1840 the number of 

 editions in the above-mentioned four languages is 

 almost the same, — viz., 45 in English, 39 in French, 

 49 in German, 34 in Italian, — while, within the last 

 forty years, 95 English editions have appeared, but 

 only 1 German, French, and 3 Italian editions. 



In France the yoke of Euclid was thrown off as 

 early as the end of the last century. The last 

 French school edition of Euclid, according to Mr. 

 Zakharchenko's list, was published in 1778. Thus, 

 in France the end of Euclid's reign coincides with 

 the beginning of the epoch of greatest splendor in 

 the history of mathematical research; and, indeed, 

 it is well known that this change is directly due to 

 the influence of that celebrated school of French 

 geometers who gave such lustre to the latter part 

 of the eighteenth century, and won for France her 

 unrivalled supremacy in mathematical science during 

 this period. Legendre's 'Elements' took the place of 

 Euclid's, until he, in his turn, had to yield to more 

 modern influences. And as early as 1814, Delambre 

 and Prony, in their report on Peyrard's critical tri- 

 lingual edition of the 'Elements' and 'Data,' we're 

 justified in speaking of Euclid's method as ' une 

 maniere passee de mode,' and of his style as ' au- 

 jourd'hui peu connu.' 



Italy, Spain, Russia, and other countries, soon fol- 

 lowed suit. Everywhere the influence of the French 

 school was felt; and, until the last quarter of a cen- 

 tury, Legendre supplanted Euclid, when in many of 

 these countries there arose schools of geometers who 

 independently provided their countries with excellent 

 text-books of their own. In Germany, Euclid held 

 his own longer than anywhere else. But, on the 

 other hand, opposition to the old system is nowhere 

 so universal and uncompromising now; and no- 

 where has modern geometry found so many enthusi- 

 astic disciples. A. Ziwet. 



