=1710.= The rules of algebra may be investigated by its own principles, without any aid from geometry; and although in many cases the two sciences may serve to illustrate each other, there is not now the least necessity in the more elementary parts to call in the aid of the latter in expounding the former. --CHRYSTAL, GEORGE. _Encyclopedia Britannica, 9th Edition; Article “Algebra.”_ =1711.= Algebra, as an art, can be of no use to any one in the business of life; certainly not as taught in the schools. I appeal to every man who has been through the school routine whether this be not the case. Taught as an art it is of little use in the higher mathematics, as those are made to feel who attempt to study the differential calculus without knowing more of the principles than is contained in books of rules. --DE MORGAN, A. _Elements of Algebra (London, 1837), Preface._ =1712.= We may always depend upon it that algebra, which cannot be translated into good English and sound common sense, is bad algebra.--CLIFFORD, W. K. _Common Sense in the Exact Sciences (London, 1885), chap. 1, sect. 7._ =1713.= The best review of arithmetic consists in the study of algebra.--CAJORI, F. _Teaching and History of Mathematics in U. S. (Washington, 1896), p. 110._ =1714.= [Algebra] has for its object the resolution of equations; taking this expression in its full logical meaning, which signifies the transformation of implicit functions into equivalent explicit ones. In the same way arithmetic may be defined as destined to the determination of the values of functions.... We will briefly say that _Algebra is the Calculus of Functions_, and _Arithmetic the Calculus of Values_.--COMTE, A. _Philosophy of Mathematics [Gillespie] (New York, 1851), p. 55._ =1715.= ... the subject matter of algebraic science is the abstract notion of time; divested of, or not yet clothed with, any actual knowledge which we may possess of the real Events of History, or any conception which we may frame of Cause and Effect in Nature; but involving, what indeed it _cannot_ be divested of, the thought of _possible_ Succession, or of pure, _ideal_ Progression.--HAMILTON, W. R. _Graves’ Life of Hamilton (New York, 1882-1889), Vol. 3, p. 633._ =1716.= ... instead of seeking to attain consistency and uniformity of system, as some modern writers have attempted, by banishing this thought of time from the _higher_ Algebra, I seek to _attain_ the same object, by systematically introducing it into the _lower_ or earlier parts of the science.--HAMILTON, W. R.