Theophrastus, Eudemus, and Aristoxenus are among the best-known names of these helpers, and from these we have valuable work extant. Physical geography was entrusted to Dikæarchus. All these researches were carried out in the same spirit, and with that unity of purpose that marks a school. There was apparently but one division of all the domain of science in which Aristotle did no original work, and yet his contribution to it is not to be underrated. This was the field of pure mathematics. For we know that he entrusted to his ablest pupil, Eudemus the Rhodian, the task of writing the history of what other men had done in this field. These books on the history of arithmetic, of geometry, and of astronomy (then called astrology) were well known and valued, and the modern critics declare that whatever is now known about the earlier development of mathematics was derived from this pure and rich source. Still more remarkable is it that this, the part of the edifice to which Aristotle himself did not contribute, should have been the only one that took root and flourished without any period of corruption or decay. As to Aristotle’s personal competence in this matter, I am assured by the best mathematicians that his not infrequent allusions to mathematics, by way of metaphor or illustration, show a clear and sound understanding of the subject. It is not, therefore, the vagary of an idle admirer, but the deliberate expression of a weighty judge, when we learn from him in his Discussion on Beauty--which he, being a Greek, of course seeks in form, symmetry, and proportion--that the highest and noblest examples of earthly beauty are to be found in mathematics. Euclid was almost the contemporary of Aristotle, and so the Peripatetic Mathematics found at Alexandria a new home and a mighty development, which lasted for centuries and is not stayed to this day. But the rest of the vast system of Aristotle seems, after about two generations, to have fallen into incompetent hands. The activity of the Greek intellect passed into other channels and became again purely philosophical and ethical instead of scientific, as I shall show when I speak of the Stoic and Epicurean systems.