CHAPTER II.

The Brethren of the Common Life.

What is said on pp. 31-34 about the Brethren, must partly be corrected. Recent investigations have proved that they were not, as Raumer had represented them, an order of teachers like the Jesuits. They taught, indeed, in a few schools, as in that of Liège; but in most schools with which they were connected, they received boarders and looked chiefly after their moral and religious training, while the secular instruction was in the hands of other teachers, who, however, were mostly imbued with the spirit of the Brethren. See Paulsen, _Geschichte des g. U._, 2nd ed., vol. I, pp. 158-160, where this author modifies, in the same way, the statements expressed in the first edition of his work. Further see the recent valuable work on _Jakob Wimpfeling_, by Dr. Knepper (Herder, 1902), page 7.

CHAPTERS V AND VII.

Jesuit Scholars.

CHAPTER V, p. 156.--The importance of Father Saccheri’s work is being recognized more and more. Professor Ricci of Padua contributed a highly interesting article to the _Jahresbericht der mathematischen Verbindung_ (Vol. XI, October-December 1902), on the “Origin and Development of the Modern Conception of the Foundations of Geometry.” There it is said that “Saccheri’s works prove him a man of indisputable merit, and one of the first geometricians of his century.... The _Euclides vindicatus_ alone is a work which could claim the labors of a whole life. In this work he erects an edifice of classical beauty which testifies to the extraordinary ability and geometrical taste of the architect.” It is a perplexing problem to modern mathematicians how Saccheri could endeavor to refute his own arguments, with which he had so ably attacked the Euclidian system. Of this attempt Professor Ricci says: “To-day it is hard to understand that a man of so sublime an intellect did not see the truth which he almost could grasp with his hands, and that he stubbornly tried to destroy with sophisms what he had built up with so much correct geometrical skill. Able and sagacious as he is in constructing his system, he is awkward and unskilful, in tearing it down.”--If for once I may be allowed to venture a conjecture, I would ask: Is it not possible that Saccheri _did_ grasp the truth, but did not think fit to publish it boldly? He may have feared lest his contemporaries would raise a cry of indignation against such a mathematical heresy. Besides, as at that time such hypotheses would have been looked upon as mere freaks, there may have been apprehensions that the publication of such a work would injure the reputation of the college in which Saccheri taught mathematics. The attacks on the Jesuits on account of the bold theories of Hardouin (see p. 160), and similar instances in which the whole Society was reprehended for the attitude of individuals, would have been a sufficient cause for the wariness of the author. If this explanation were the correct one, it would certainly account for the weakness of the arguments which he used to pull down his splendid structure. These arguments, accordingly, would have been merely a thin veil to hide the purport of his work. I communicated this conjecture to Father Hagen of Georgetown, and was surprised to learn that this distinguished mathematician had given the same explanation of the curious phenomenon to Professor Halsted of the University of Texas, the translator of Father Saccheri’s works. However, this is only a conjecture, though not void of probability. But even if the author did not see the full truth of his deductions at the time, this has happened to many great discoverers. Professor Whewell says of Kepler, with reference to a similar instance, that it seems strange that he did not fully succeed; “but this lot of missing what afterwards seems to have been obvious, is a common one in the pursuit of truth.” (_History of the Inductive Sciences_, vol. II, p. 56. Appleton’s ed., 1859.)