ANNIVERSARY ADDRESS. 13 



directly, in place of resorting to corrupt Arabian translations; and 

 by means of the then recently invented printing press, the intel- 

 lectual wealth of the past was rapidly disseminated. The genius, 

 assiduity, and enthusiasm of Johann Miiller [Regiomontanus, 

 1436 - 1476] one of the greatest men ever given by Germany to 

 the world, stirred up civilized Europe. His translations of ancient 

 mathematical and astronomical literature, his construction of 

 elaborate trigonometrical tables for practical use, his treatises on 

 arithmetic and trigonometry — the form of this last being to-day 

 substantially as it left his hands — and his splendid mastery of 

 mathematics and astronomy, were a propitious inauguration of the 

 new era. 



The contributions to algebra during the remainder of the 16th 

 century by Tartaglia [1500 - 1557], 1 by the clever but unscrupulous 

 Cardano [1501-1576], and by Yieta [1540 - 1603], we cannot 

 pause to survey ; and must content ourselves with referring to 

 the brilliant discovery by Yieta of twenty-three roots of an equa- 

 tion of the 45th degree, and to the ardent admiration which that 

 evoked from the propounder of the problem, Adriaan van Roomen, 2 

 who, with Ludolph van Ceulen will be remembered in connection 

 the value of tt, or the " Ludolphian " number, so named after the 

 latter, who carried the computation to thirty-five places of figures. 



From the beginning of the 17th century the mathematical 

 wealth, which burst upon the world, is beyond all computation. 

 Mathematical discoveries became meteoric in their brilliancy, and 

 the intellectual firmament coruscated with their frequency and 

 splendour. 



1 Cajori gives 1506 as the date of Tartaglia' s birth, evidently assuming 

 that his mutilation occurred when he was six years of age, and on the 

 occasion of the French, under Gaston de Foix, sacking Brescia in 1512. 

 But Tartaglia was an esteemed teacher of mathematics at Verona as 

 early as 1521. 



2 Henry IV. of France submitted to Vieta a problem propounded by 

 'Adrianus Romanus/ a Belgian mathematician : — 45y - 3735y s + 95634t/ 5 — 

 . .. + 945y 41 - 4oV 3 + y i5 = C. Vieta saw at once that this was the equa- 

 tion by which C = 2 sin <$> was expressed in terms of y = 2 sin 45 4*' 



