Greetings from Philip Melanchthon to Johannes Reiffensteyn

I decided that no more fitting ornament can be added to the beginning of this book which provides access to geometry than the sign which Plato is said to have painted on the gates of his school, namely: ‘Let no one enter who is not trained in geometry (ageōmetrētos oudeis eisitō)’ The interpretation of that saying has engaged the conjectures of many people. Some judge that Plato kept away from his school – as if they were defiled and impious – those inexperienced in geometry, the elements of which used to be taught then straight away from an early age to all those who were given a liberal education. Others transfer it to morals and believe that it meant, for students of philosophy, that they should preserve in all duties a certain moderateness and impartiality by analogy with geometry, just as in the Gorgias, when Plato rebukes the unjust opinion of Callicles, he says that the latter neglects geometry. Even though it is sufficiently clear from Plato's writings that he liked to apply geometrical examples to morals, nevertheless it cannot be doubted that, at the same time, by doing so he points out something about the order of subjects, and that he felt that those who were to undertake philosophy should be prepared in geometry. There are many most weighty reasons for his aphorism.