_Report on the Theory of Numbers, British Association, 1859; Collected Mathematical Papers, Vol. 1, p. 38._ =1646.= The invention of the symbol ≡ by Gauss affords a striking example of the advantage which may be derived from an appropriate notation, and marks an epoch in the development of the science of arithmetic.--MATHEWS, G. B. _Theory of Numbers (Cambridge, 1892), Part 1, sect. 29._ =1647.= As Gauss first pointed out, the problem of cyclotomy, or division of the circle into a number of equal parts, depends in a very remarkable way upon arithmetical considerations. We have here the earliest and simplest example of those relations of the theory of numbers to transcendental analysis, and even to pure geometry, which so often unexpectedly present themselves, and which, at first sight, are so mysterious.--MATHEWS, G. B. _Theory of Numbers (Cambridge, 1892), Part 1, sect. 167._ =1648.= I have sometimes thought that the profound mystery which envelops our conceptions relative to prime numbers depends upon the limitations of our faculties in regard to time, which like space may be in its essence poly-dimensional, and that this and such sort of truths would become self-evident to a being whose mode of perception is according to _superficially_ as distinguished from our own limitation to _linearly_ extended time.--SYLVESTER, J. J. _Collected Mathematical Papers, Vol. 4, p. 600, footnote._ CHAPTER XVII ALGEBRA =1701.= The science of algebra, independently of any of its uses, has all the advantages which belong to mathematics in general as an object of study, and which it is not necessary to enumerate. Viewed either as a science of quantity, or as a language of symbols, it may be made of the greatest service to those who are sufficiently acquainted with arithmetic, and who have sufficient power of comprehension to enter fairly upon its difficulties. --DE MORGAN, A. _Elements of Algebra (London, 1837), Preface._ =1702.= Algebra is generous, she often gives more than is asked of her.--D’ALEMBERT. _Quoted in Bulletin American Mathematical Society, Vol. 2 (1905), p. 285._ =1703.= The operations of symbolic arithmetick seem to me to afford men one of the clearest exercises of reason that I ever yet met with, nothing being there to be performed without strict and watchful ratiocination, and the whole method and progress of that appearing at once upon the paper, when the operation is finished, and affording the analyst a lasting, and, as it were, visible ratiocination.--BOYLE, ROBERT. _Works (London, 1772), Vol. 3, p. 426._