XIV 



THE PROGRESS OF 



roquetes nt Paris, a situation which employed | 

 Much of his time, he found leisure to devote 

 himself to algebra. He first employed letters to 

 denote both the known and unknown quantities ; 

 so that it was with him dial the language of 

 algebra first became capable of expressing gen- 

 oral truths, and acquired that extension which 

 li.-is since rendered it such a powerful instrument 

 of investigation. He likewise discovered the 

 relation between the roots of an equation of any 

 degree, and the coefficients of its terms, though 

 only when none of the terms are wanting, and 

 when all the terms are positive. This general 

 truth, which Vieta only saw imperfectly, wa 

 further extended, in 1069, by Albert Gerard. 

 But it was first developed in all its generality by 

 Harriot, whose discoveries in algebra have been 

 so much extolled by Wallis. 



These successive improvements brought alge- 

 bra nearly to its present stole, and prepared it 

 for a step which was about to be taken by Des- 

 rartes, and which forms one of the most impor- 

 tant epochs in mathematical science. This was 

 the application of algebraic analysis to define 

 the nature, and investigate the properties of 

 curve lines ; and consequently to represent the 

 notion of variable quantities. This invention 

 opened up a vast field for succeeding mathema- 

 ticians. The work in which it was contained, 

 is a tract of no more than 106 quarto pages. 

 Probably there is no book of the same size, 

 which has conferred so great, and so well merited 

 a reputation on its author. 



It would be impossible in the short space to 

 which we are obliged to confine ourselves, to 

 give even an idea of the improvements which 

 algebra has received during the two centuries 

 which have elapsed since Descartes applied it to 

 the investigation of curves. It cannot be said 

 that any new principle has been discovered ; but 

 its language and symbols have been perfected, 

 and it has been applied with effect to almost 

 every kind of physical investigation. Indeed, 

 if we consider the calculus of infinitesimal quan- 

 tities as merely an extension of algebra, as 

 might very well be done, we may say with 

 truth, that it now constitutes the grand instru- 

 ment by means of which physical science is 

 promoted. 



OF OBSERVATION AND EXPERIMENT. 



IT was not to be expected that mankind 

 should at first make any rapid progress in inves- 

 tigating the laws, which regulate the changes 

 that take place in the material world. The 

 objects were too numerous, ind too varied, and ' 



escaped his attention by their very regularity. 

 Every where in the early ages of the world, we 

 meet with descriptions of prodigies and wonders, 

 while the regular operations of nature scarcely 

 attracted attention. 'I lie method of investiga- 

 ting nature by observation and experiment was 

 scarcely thought of, except by two individuals, 

 who, by means of them, made some progress in 

 mechanics and hydrostatics, and in astronomy; 

 these were Archimedes and Hipparchus. The 

 mechanical discoveries of Archimedes w r ere 

 slightly extended by Ctesibius and I^ero, by 

 Anthemius, and by Pappus ; while the astrono- 

 mical observations begun by Hipparchus, were 

 continued by Ptolemy. 



But at the revival of letters in the 16th cen- 

 tury, a spirit of observation and inquiry awoke, 

 which nothing could damp, and men began In 

 pry into the secrets of nature, by the way of 

 experiment. Galileo, in Italy, and Gilbert, in 

 England, especially the former, constitute re- 

 markable examples of successful investigation by 

 experiment. But it was Francis Bacon, lord 

 Verulam, who first investigated the laws ac- 

 cording to which such experimental investiga- 

 tions should be conducted, who pointed out the 

 necessity of following these laws in all attempts 

 to extend the physical sciences, and who foretold 

 the brilliant success that would one day repay 

 those who should adopt the methods which he 

 pointed out. This he did in his Novum Orga- 

 num, published in the early part of the 17th 

 century. 



Before laying down the rules to be followed 

 in his new, or inductive process, Bacon enumer- 

 ated the causes of error, which he divided into 

 four sets, and distinguished, according to the 

 fashion of the times, by the following fanciful, 

 but expressive names : 



Idols of the tribe, 



Idols of the den, 



Idols of the forum, 



Idols of the theatre. 



The Idols of the tribe, are the causes of error 

 founded on human nature in general. Thus all 

 men have a propensity to find in nature, a greater 

 degree of order, simplicity, and regularity, than 

 is actually indicated by observation. This pro- 

 pensity, usually distinguished by the title of spirit 

 of system, is one of the greatest enemies to its 

 progress, that science has to struggle with. 



The Idols of the den, are those that spring 

 from the peculiar character of the individual. 

 Each individual, according to Bacon, has his 

 own dark cave or den, into which the light is 

 imperfectly admitted, and in the obscurity of 

 which an idol lurks, at whose shrine the truth 

 is often sacrificed. Some minds are best adapted 

 to catch the differences, others the resemblances 



