But while the endeavor to arrive at certain knowledge by the Deductive Method, by attempting to reason from Principles to Facts, from Generals to Particulars, failed so completely as far as the Anticipative or Hypothetical branch, of the Method was concerned, the same mode of procedure was productive of the most satisfactory results when applied to Mathematics, and furnished a rapid and easy means of arriving at the ulterior Facts of this department of the universe with precision and certainty. We have thus the curious exhibition of the same process leading into utter confusion when applied to one set of phenomena, and into exactitude and surety when applied to another; and behold the Scientific world condemning as utterly useless for other departments of investigation, and throwing aside, a Method which is still retained in the only Science that is called _exact_, and in which proof amounts to _demonstration_, in the strict sense of the term. This anomaly will be recurred to and explained farther on. Soon after the invention of printing, with its resulting multiplication of books and increased intellectual activity, the mind of Europe began to emerge from the deep darkness in which it had been shrouded for centuries, and a number of great intellects engaged in the search after knowledge by the close and laborious examination of the actual existences and operations of nature around them. Leonardo da Vinci and Galileo in Italy; Copernicus, Kepler, and Tycho Brahe in Central Europe; and Gilbert in England, peered into the hidden depths of the universe, collected Facts, and established those Principles which are the foundations of the magnificent structures of modern Astronomy and Physics. About the same time, Francis Bacon put forth the formal and elaborate statement of that Method of acquiring knowledge which is often called after him the Baconian, but more commonly the Inductive Method; substantially the Method pursued by the great scientific dicoverers whom we have just named.