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Rh princes. While in garrison at Breda, he saw one day a placard in Flemish to which the attention of a considerable crowd had been attracted. It was the statement of a mathematical problem, to which the author, after the fashion of the times, invited solutions. Not understanding the language in which it was written, Descartes asked one of the bystanders to translate it to him. This man was Beeckman, Principal of the College of Dort, himself a mathematician. Surprised to find a young soldier interested in such a matter, Beeckman explained the terms of the challenge with his most learned air. Descartes said at once that he would solve the problem, and brought the solution to Beeckman on the next day, having mastered it in less than an hour. The winter of 1619 was spent in quarters at Neuburg, on the Danube, to a large extent in study, and was, according to Dr. William Wallace, in the Encyclopaedia Britannica, the critical period of Descartes's life. "Here, in his warm room, he indulged those meditations which afterward led to the Discourse on Method. It was here that, on the eve of St. Martin's day, he 'was filled with enthusiasm, and discovered the foundations of a marvelous science.' He retired to rest with anxious thoughts of his future career, which haunted him through the night in three dreams, that left a deep impression on his mind. 'Next day,' he continues, 'I began to understand the first principles of my marvelous discovery.'" In the next year he sought out the Rosicrucians, to obtain some knowledge of their supposed mystical wisdom, but without success. Descartes retired from military life upon the defeat and death of Count Bucquoy at the hands of Bethlen Gabor's revolted Hungarians in 1621.

During his career in the army, Descartes composed a Latin treatise on music, which he intrusted to Beeckman. It was surreptitiously copied, and was published without the knowledge of the author in 1618. It seems to have been considerably successful, and was reprinted several times and translated into English and French. But Beeckman's treachery cost him Descartes's friendship. Among other writings of this period, unpublished or lost, but mentioned in the catalogue prepared by Chanut on the order of Queen Christina of Sweden, are General Considerations on Science; a fragment on Algebra; Democritia, or Fugitive Thoughts; Experiments, or a Collection of Observations; and a collection of mathematical speculations entitled Parnassus. Descartes continued his travels in a private way, having in view, as he expressed his purpose, to look into the courts of princes, to become acquainted with men of different humors and different conditions, to inform himself concerning the natural products of different climates and the various civil usages and customs observed among different peoples; and to seek in the great book of the world