"Those who devised the eccentrics seen thereby in large measure to have solved the problem of apparent motions with approximate calculations. But meanwhile they introduced a good many ideas which apparently contradict the first principles of uniform motion. Nor could they elicit or deduce from the eccentrics the principal consideration, that is, the structure of the universe and the true symmetry of its parts. " (Nicolaus Copernicus, "De revolutionibus orbium coelestium", 1543)
"Having gotten, with God’s help, to the very desired place, i.e. the mother of all cases called by the people 'the rule of the thing' or the 'Greater Art', i.e. speculative practice; otherwise called Algebra and Almucabala in the Arab language or Chaldean according to some, which in our [language] amounts to saying 'restaurationis et oppositionis', Algebra id est Restau ratio. Almucabala id est Oppositio vel contemptio et Solutio, because by this path one solves infinite questions. And one picks out those which cannot yet be solved." (Luca Pacioli, "Summa de arithmetica geometria proportioni et proportionalita", 1494)
"Each problem that I solved became a rule which served afterwards to solve other problems. [...] thus each truth discovered was a rule available in the discovery of subsequent ones." (René Descartes,"Discourse on Method", 1637)
"Thus, you see, most noble Sir, how this type of solution bears little relationship to mathematics, and I do not understand why you expect a mathematician to produce it, rather than anyone else, for the solution is based on reason alone, and its discovery does not depend on any mathematical principle. Because of this, I do not know why even questions which bear so little relationship to mathematics are solved more quickly by mathematicians than by others." (Leonhard Euler, [letter to Carl Leonhard Gottlieb Ehler, mayor of Danzig] 1736)
"All that can be said upon the number and nature of elements is, in my opinion, confined to discussions entirely of a metaphysical nature. The subject only furnishes us with indefinite problems, which may be solved in a thousand different ways, not one of which, in all probability, is consistent with nature." (Antoine-Laurent Lavoisier,"Elements of Chemistry", 1790)
"Concerning the theory of equations, I have tried to find out under what circumstances equations are solvable by radicals, which gave me the opportunity of investigating thoroughly, and describing, all transformations possible on an equation, even if it is the case that it is not solvable by radicals." (Évariste Galois, [letter to Auguste Chevalier] 1832)
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