862 



SCIENCE. 



[N. S. Vol. VII. No. 182. 



in 1867 : " C'est aux indications du Dr. Baltzer 

 que je dois la connaissance de ces importants 

 travaux." 



Thus interested, Holiel besought aid of an 

 architect of Temesvir who had written to en- 

 quire of him about French mathematical books. 

 The coincidence was most fortunate, for this 

 architect was Fr. Schmidt, whose father, Anton 

 Schmidt, had often told him of a young ofiicer 

 of engineers with whom he always feared to 

 come in contact, who, to prove the might of his 

 arm and the temper of his Damascus blade, 

 was accustomed to show his visitors how with 

 one stroke he could cut off a heavy nail driven 

 into his door-post. This was Bolyai J4nos. 

 The facts collected by Fr. Schmidt in 1867, 

 published in Grunert's Archiv and by Hoiiel in 

 1868, were all the world knew of the two 

 Bolyai for nearly thirty years. 



Moreover, the first biographer became a sort 

 of local representative for the world of science 

 in all matters pertaining to Bolyai J4nos. He 

 procured for Hoiiel two copies of the exceed- 

 ingly rare ' Science Absolute,' from one of which 

 Hoiiel made his French translation, sending the 

 other to Battaglini, who translated it into Ital- 

 ian, both translations appearing in 1868. In 

 1872 Schmidt furnished Frischauf the original 

 for his German version. Now in 1897 he pub- 

 lishes at his own expense the Latin, with the 

 first rendering in the native tongue of the author, 

 the Magyar, and a new biography of J&nos, but 

 far too short, nine pages. 



The Hungarian Academy of Science, in their 

 costly edition of the father's Tentamen, have so 

 rearranged the material that the immortal Ap- 

 pendix of the son is displaced from the first vol- 

 ume, the only one yet issued. Both the above 

 books are, therefore, needed by one who would 

 contrast the concise elegance of the son, who 

 solved the problem of the ages, with the florid 

 freedom of the father, who had failed. 



The ' Science Absolute ' has appeared in six 

 languages and a Japanese reprint of the English. 



The Tentamen will probably never be trans- 

 lated. Sutik points out how it anticipates 

 Riemann and Helmholtz. 



(1) Space is continuous (V. I., p. 442). 



(2) Rigid bodies exist independent of place, 

 freely movable (principle of congruence, p. 444). 



(3) Rigid bodies can move with one or two 

 points fixed, not in general three (p. 446). 



(4) Monodromie (p. 447) (motion which con- 

 tinued brings a point again into its first place). 



From Lie's reinvestigation results that this 

 fourth principle is a consequence of the others, 

 though here Sutiik has the hardihood to attack 

 Lie. 



This anticipation is carried out consequently, 

 and would have been complete, except that W. 

 Bolyai postulates the infinity of space. 



Now follows the first appreciation ever printed 

 of the non-Euclidean geometry. W. Bolyai has 

 the double honor, first to have praised in print 

 each of the two founders of this marvellous doc- 

 trine. He was the first convert who dared pro- 

 fess his regeneration openly. The world waited 

 thirty-five years for a second. 



One sentence from the Tentamen must serve 

 as specimen of his praise and penetration: 

 ' ' The Author of the Appendix, attacking the 

 matter with singular acumen, comprehending 

 in general (if except the remaining axioms 

 none be assumed) all systems subjectively pos- 

 sible for us (that is, of which one only exists, 

 though which is really true we cannot decide) 

 makes a geometry absolutely true for every 

 case ; though in the Appendix of this volume 

 he has given from a great mass only the strictly 

 necessary, much (as the general solution of the 

 tetrahedron, and many other elegant disquisi- 

 tions) for the sake of brevity being omitted." 

 His praise and discriminating exposition of 

 Lobach6vski was printed twenty years later. 



In his ' Kurzer Grundriss eines Versuchs' 

 (1851), § 32, speaking of ' the admirable work ' 

 of Lobachevski (1840), he says : " This alone is 

 a proof of an extraordinary genius. Probably 

 in the ' gelehrten Schriften ' of Kazan University 

 still more is communicated of that wherewith he 

 has made debtor the centuries. 



"Here also in the year 1832 appeared at the 

 end of the first (Latin) volume an appendix so 

 very like to that, that to both (since neither had 

 seen the other) must have appeared the same 

 Original of truth after thousands of years." 



Then follows a comparison of Lobachevski 

 with Bolyai Jiluos, and an elegant characteriza- 

 tion of the non-Euclidean geometry. 



Fresh after half a century, should not this 



