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The article presents an introduction on the histories of science in early modern Europe. The papers here argue that there were indeed histories of mathematics before Jean-Etienne Montucla which are worthy of scholarly attention and that the dismissal of Renaissance histories of science as nothing more than a cloud of fine adjectives and metaphors is a fallacy. Three of the papers in this collection address histories of mathematics, which were written from the late fifteenth century to the early seventeenth century. It also provides a new approach that considers the relationship which humanist culture had with the emerging new sciences.