"Thus the analysis of angular sections involves geometric and arithmetic secrets which hitherto have been penetrated by no one." (François Viète, cca 1615)
"I am not content with algebra, in that it yields neither the shortest proofs nor the most beautiful constructions of geometry. Consequently, in view of this, I consider that we need yet another kind of analysis, geometric or linear, which deals directly with position, as algebra deals with magnitude." (Gottfried Leibniz, [letter to Christiaan Huygens] 1670)
"The nature, mother of the eternal diversities, or the divine spirit, are zaelous of her variety by accepting one and only one pattern for all things, By these reasons she has invented this elegant and admirable proceeding. This wonder of Analysis, prodigy of the universe of ideas, a kind of hermaphrodite between existence and non-existence, which we have named imaginary root?" (Gottfried W Leibniz, "De Bisectione Latereum", 1675)
"As in Mathematics, so in Natural Philosophy, the Investigation of difficult Things by the Method of Analysis, ought ever to precede the Method of Composition. This Analysis consists in making Experiments and Observations, and in drawing general Conclusions from them by Induction, and admitting of no Objections against the Conclusions but such as are taken from Experiments, or other certain Truths." (Sir Isaac Newton, "Opticks", 1704)
""As in Mathematics, so in Natural Philosophy, the Investigation of difficult Things by the Method of Analysis, ought ever to precede the Method of Composition. This Analysis consists in making Experiments and Observations, and in drawing general Conclusions from them by Induction, and admitting of no Objections against the Conclusions but such as are taken from Experiments, or other certain Truths." (Sir Isaac Newton, "Opticks", 1704)
"Often I have considered the fact that most of the difficulties which block the progress of students trying to learn analysis stem from this: that although they understand little of ordinary algebra, still they attempt this more subtle art. From this it follows not only that they remain on the fringes, but in addition they entertain strange ideas about the concept of the infinite, which they must try to use." (Leonhard Euler, "Introduction to Analysis of the Infinite", 1748)
"A function of a variable quantity is an analytic expression composed in any way whatsoever of the variable quantity and numbers or constant quantities. […] Functions are divided into algebraic and transcendental. The former are those made up from only algebraic operations, the latter are those which involve transcendental operations.(Leonhard Euler, "Introduction to Analysis of the Infinite", 1748)
"I consider it as one of the most important steps made by Analysis in the last period, that of not being bothered any more by imaginary quantities, and to be able to submit them to calculus, in the same way as the real ones." (Joseph-Louis de Lagrange, [letter to Antonio Lorgna] 1777)
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