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can scarce be understood in its perfection, without under- 

 standing the process by which it has been improved. In- 

 deed, in the last treatises upon any science, the first prin- 

 ciples which were proven till they had become familiar, 

 are at length merely announced as dogmas; the reason- 

 ing from which they were derived is forgotten or lost, 

 and can only be supplied by retracing the steps by which 

 it had, in the first instances, been ascertained. As an 

 example of this we may note, that, in nearly all the En- 

 glish Arithmetics, the principle of the Arabic notation, 

 the very base of the science, is not explained at all, 

 though a proper understanding and use of this is said to 

 have first recommended Pestalozzi to the public notice. 

 The use of the principle had made it common, and by 

 common authors its bare annunciation was accounted 

 sufficient. But apart from the aid which a true history 



use in preserving chronicles of its progress, and insuring 

 that the origin and manner of any invention shall be as 

 well known as the invention itself. They exhibit, as it 

 were, the crystallizations of thought, and show the 

 modes in which mental effort has been directed to any 

 one point of consideration; and in that way will always 

 prevent the uncertainty which attaches to the works of 

 philosophers of earlier times. We do not know, for in- 

 stance,* that Descartes had ever read Bacon, and there 

 is some doubt whether he have not appropriated thoughts 

 which originally were not his own. Twenty-five years 

 after the publication of the Optics of Descartes, Dr. Gre- 

 gory, of St. Andrews, discovered by his own effort, the 

 law of the refraction of light, never having seen the work 

 of the French philosopher in which it had been first de- 

 monstrated. The rule called Cardan's rule, for the irre- 

 ducible case of cubic equations, is said not to have been 

 his invention, though first published by him. And the 

 question, whether Leibnitz or Newton first discovered the 

 principles of the differential calculus, was for many years 



