=954.= The thirteen books of Euclid must have been a tremendous advance, probably even greater than that contained in the “Principia” of Newton.--DE MORGAN, A. _Smith’s Dictionary of Greek and Roman Biography and Mythology (London, 1902), Article, “Eucleides.”_ =955.= To suppose that so perfect a system as that of Euclid’s Elements was produced by one man, without any preceding model or materials, would be to suppose that Euclid was more than man. We ascribe to him as much as the weakness of human understanding will permit, if we suppose that the inventions in geometry, which had been made in a tract of preceding ages, were by him not only carried much further, but digested into so admirable a system, that his work obscured all that went before it, and made them be forgot and lost.--REID, THOMAS. _Essay on the Powers of the Human Mind (Edinburgh, 1812), Vol. 2, p. 368._ =956.= It is the invaluable merit of the great Basle mathematician Leonhard _Euler_, to have freed the analytical calculus from all geometrical bonds, and thus to have established _analysis_ as an independent science, which from his time on has maintained an unchallenged leadership in the field of mathematics.--HANKEL, H. _Die Entwickelung der Mathematik in den letzten Jahrhunderten (Tübingen, 1884), p. 12._ =957.= We may safely say, that the whole form of modern mathematical thinking was created by Euler. It is only with the greatest difficulty that one is able to follow the writings of any author immediately preceding Euler, because it was not yet known how to let the formulas speak for themselves. This art Euler was the first one to teach.--RUDIO, F. _Quoted by Ahrens W.: Scherz und Ernst in der Mathematik (Leipzig, 1904), p. 251._