118 BULLETIN or THE 



Prof. Paucker gives, in addition to the solution of the problem 

 before mentioned, a second solution entirely independent of the 

 auxiliary circles, and which results immediately from a theorem 

 due to Mods. Pierre Tedenat, and which theorem is proven in 

 his memoir. He also gives the trigonometric solution as modified 

 from that of Crelle and Lehmus, and ends with several miscel- 

 laneous theorems on tangencies. The memoir is very complete 

 from the standpoint of the old geometry, but the author does not 

 appear to have had so broad a view as Steiner, and nowhere 

 goes into the question of how many solutions are possible as 

 Steiner has done, xsevertheless his paper is one of the most im- 

 portant contributions to the subject, and one which has nowhere 

 been found mentioned by any writer upon the subject that has 

 been consulted. 



In 1833, Prof. Zornow, of Konigsberg, published in Crelle's 

 Journal, Vol. X, an algebraic demonstration of Steiner's con- 

 struction, and the next year Prof. Pliicker, of Bonn, published 

 in the same journal a demonstration of the same, partially geo- 

 metric, but it is only completed by the aid of analysis. His 

 memoir bears date Oct. 1831, and "he was, therefore," says Mr. 

 Talbot, "the first who succeeded in demonstrating Steiner's 

 theorem." It would seem, however, that Prof. Paucker, whose 

 memoir was read before the St. Petersburg Academy, May 2, 

 1821, is entitled to the credit, as he seems both to have discovered 

 and demonstrated Steiner's theorem. 



In Hymer's Trigonometry, published in 1842, a very good 

 trigonometrical solution of the problem may be found, the results 

 obtained being the same as those found by Mr. E. B. Seitz, in 

 the Analyst, Yol. II, 1875, pp. 74-76. 



The next paper of importance seems to have been one by 

 Prof Adams, of Winterthur, who published a complete algebrai- 

 cal investigation of the subject in 1845, in a quarto pamphlet of 

 26 pages. The pamphlet does not appear to be accessible in 

 any of the libraries of this city, and the contents of tlio pamphlet 

 can only be judged from a brief review of it found in Nouvelles 

 Annales de Matheraatiques, Yol. YIII, p. 62. It is there in- 

 dicated that the pamphlet consists principally of twelve Lemmas 

 algebraically proved. 



In 1852, Prof. Schellbach, of Berlin, published in Crelle's 

 Journal, Yol. XLY, a new solution of Malfatti's Problem, accom- 



