MATHEMATICAL SCIENCES SEVENTEENTH CENT. 149 



to which it is capable by itself of attaining a knowledge. You are not 

 to seek for what others have written or thought before you, but are to 

 rely only upon that which you yourself can recognize as evident truth. 

 Descartes was as declared a foe to prejudices as Bacon himself, and 

 as convinced of the obstinacy with which men cling to them, to the 

 hindering of true knowledge. "I perceived," he remarks, "that a man 

 can more easily burn down his own house than get rid of his prejudices." 

 The biography of Descartes acquaints us step by step with the road 

 along which his intellect travelled in pursuit of truth. At the early age 

 of fifteen he began to doubt; for in the lessons of his masters he found 

 not truths, but only opinions, and he perceived that everything was a 

 matter for disputation. At seventeen he reviewed his stock of acquired 

 truths, and was so dissatisfied that he renounced science altogether, 

 in the conviction that true knowledge was unattainable. But at nine- 

 teen he resumed the study of mathematics, for which he had always 

 entertained much inclination. At twenty-one he began to travel, 

 in order to study mankind, the result being that seeing men every- 

 where deceived by example, custom, and opinion, in order to escape 

 such trammels he at twenty-three betook himself to complete solitude, 

 resolved to clear his mind from all opinions and prejudices. At 

 twenty-four he determined to dispense with all books, and even with 

 all intercourse with men of learning, and to betake himself exclusively 

 to reading the great book of nature, or, in other words, to multiply his 

 own observations and experiments. But again, at the age of twenty- 

 seven he became dissatisfied with physical science and also with 

 mathematics : the former appeared too uncertain, the latter too ab- 

 struse. He took up the study of the moral sciences, but again reverted 

 to mathematical study, and for several years devoted himself alternately 

 to abstract sciences and to moral science. Finally, at the age of thirty- 

 two, he set himself to the task of reconstructing philosophy on a new 

 basis. 



No book of its size ever gained so much renown for its author or 

 produced a more powerful effect on the progress of science than the 

 short treatise on Geometry which Descartes first published in 1637. 

 Such of our readers as possess a little knowledge of mathematics will 

 of course be already acquainted with the Cartesian geometry, but we 

 think it desirable that our non-mathematical readers should and might 

 form some idea of the nature of Descartes' invention, even if they are 

 unable to realize its full power and significance. A little effort may 

 therefore be profitably devoted to acquir-ing some notion of the nature 

 of the Cartesian geometry, and, to assist the unlearned reader, we shall 

 select some simple illustrations of the principle, without reference to 

 the method in which the subject is presented in Descartes' own work. 



The ancient geometry recognized a few regular curved lines, as the 

 circle, the ellipse, etc., each of which results from a particular mode 

 of construction, and its properties are investigate^ on principles per- 



