This study of the history and contents of a hitherto unedited work on geometry by Vincenzo Viviani seeks to present a picture of the scientific environment in Italy in the second half of the 17th century, with particular emphasis on Tuscany and the impact the condemnation of Galileo had on ongoing scholarship. Information derived from unedited or less well-known material serves to illuminate a range of prominent and marginal figures who adopted different strategies for the dissemination of Galileo’s thought and (...) the application of its principles. A selection of texts, edited here for the first time, is presented in two appendices, while in a third decidedly unusual methods are used to elucidate the mathematical aspects. (shrink)