Introduction.- 1 From Aristotle to the Classical Age : the Debate around Indivibilism.- 2 Cavalieri's Indivisibles.- 3 Kepler, Cavalieri, Guldin.- 4 Indivisibles in the Work of Galileo.- 5 Torricelli's indivisibles.- 6 The method of indivisibles that Gregory of Saint Vincent could have used for his own quadrature of Hyperbola.- 7 Descartes and the use of indivisibles.- 8 Roberval's indivisibles.- 9 Pascal's indivisibles.- 10 Two jesuits against indivibles, Lalouvere and Tacquet.- 11 Isaac Barrow's indivisibles.- 12 The role of indivisibles in Mengoli's quadratures.- 13 Wallis on indivisibles.- 14 Leibniz's rigorous foundations of the method of indivisibles.- 15 Newton on indivisibles.-16 An epistemological route in the historiography on indivisibles.- 17 Archimedes and indivisibles.- 18 Indivisibles and Latitude of Forms.- 19 How to explain the use of the term indivisibles as late as 1700 for the discovery of multiple rainbows?