`Disturbed' by Euclid: Thomas Fincke and the reading of Ramist mathematics in sixteenth-century Germany (Q2034535)

Thomas Fincke's 1583 \textit{Geometria rotundi}, one of a number of trigonometric textbooks that reshaped the subject during the last two decades of the 16th century, contains a number of novelties, including the coining of the terms ``tangent'' and ``secant''. This paper discusses features of its pedagogical style, which follows the tradition of Petrus Ramus, as opposed to that found in Euclid's \textit{Elements}: a terse, structured account that emphasizes clarity and natural reason at the cost of longer demonstrations. The article also describes the annotations found within a bound volume dated 1586 containing several texts, including \textit{Geometria rotundi}, that seems to have been used for pedagogical purposes in Wittenberg. The annotations, which summarize and place into a branching structure some of the contents of the printed text, reveal Ramist influences.