In the framework of his critical philosophy, Kant, as is well known, felt obliged to adopt a position with regard to the problem of the foundations of geometry. One of the ways in which he did this was to consider whether the concept of a straight biangle was consistent or involved a contradiction. Kant then entangled himself in a striking difficulty, which, however, appears to have been noted by few. To my knowledge, the only other person who has as yet seen it is Gottfried Martin² and his proposed solution is also the only one that I yet know.