This article deals with six aspects of analogical thinking in mathematics: 1. Platonism and continuity principle or the “geometric voices of analogy” (as Kepler put it), 2. analogies and the surpassing of limits, 3. analogies and rule stretching, 4. analogies and concept stretching, 5. language and the art of inventing, 6. translation, or constructions instead of discovery. It takes especially into account the works of Kepler, Wallis, Leibniz, Euler, and Laplace who all underlined the importance of analogy in finding out (...) new mathematical truth. But the meaning of analogy varies with the different authors. Isomorphic structures are interpreted as an outcome of analogical thinking. (shrink)