The paper lists several editions of Euclid's in the Early Modern Age, giving for each of them the axioms and postulates employed to ground elementary mathematics.

In the early years of the twentieth century, the so-called 'postulate analysis'-the study of systems of axioms for mathematical objects for their own sake-was regarded by some as a vital part of the efforts to understand those objects. I consider the place of postulate analysis within early twentieth-century mathematics by focusing on the example of a group: I outline the axiomatic studies to which groups were subjected at this time and consider the changing attitudes towards such investigations.

In my 2018 article in this journal, I described 15th-century Italian astronomer Giovanni Bianchini's treatment of the problem of stellar coordinate conversion in his , the first correct European solution. In this treatise Bianchini refers to a book he had written previously, containing the same error that had plagued his predecessors' work on the problem. In this article, we announce the discovery of this earlier treatise. We compare its canons and tables to Bianchini's later work, noting the places where the contents overlap (roughly one quarter of the text). We analyze his mathematical methods and the unique tables he constructed for converting stellar coordinates, including the earliest known European arc sine table, that he would abandon only a few years later.

The Jeffreys-Lindley paradox exposes a rift between Bayesian and frequentist hypothesis testing that strikes at the heart of statistical inference. Contrary to what most current literature suggests, the paradox was central to the Bayesian testing methodology developed by Sir Harold Jeffreys in the late 1930s. Jeffreys showed that the evidence for a point-null hypothesis scales with and repeatedly argued that it would, therefore, be mistaken to set a threshold for rejecting at a constant multiple of the standard error. Here, we summarize Jeffreys's early work on the paradox and clarify his reasons for including the term. The prior distribution is seen to play a crucial role; by implicitly correcting for selection, small parameter values are identified as relatively surprising under . We highlight the general nature of the paradox by presenting both a fully frequentist and a fully Bayesian version. We also demonstrate that the paradox does not depend on assigning prior mass to a point hypothesis, as is commonly believed.