[4] Moving to Athens in early youth, he became the pupil of Aeschines Socraticus,[5] but subsequently joined himself to Plato,[6] whom he accompanied to Sicily in 361.

[8] In 339/8 BC, Xenocrates succeeded Speusippus in the presidency of the school,[9] defeating his competitors Menedemus of Pyrrha and Heraclides Ponticus by a few votes.

Soon after the death of Demosthenes (c. 322 BC), he declined the citizenship offered to him at the insistence of Phocion[10] as a reward for his services in negotiating peace with Antipater after Athens' unsuccessful rebellion.

[12] Being unable to pay the tax levied upon resident aliens, he is said to have been saved only by the courage of the orator Lycurgus,[13] or even to have been bought by Demetrius Phalereus, and then emancipated.

Besides Polemon, the statesman Phocion, Chaeron (tyrant of Pellene), the academic Crantor, the Stoic Zeno and Epicurus are said to have frequented his lectures.

[25] Xenocrates made a more definite division between the three departments of philosophy, than Speusippus,[30] but at the same time abandoned Plato's heuristic method of conducting through doubts (aporiai), and adopted instead a mode of bringing forward his doctrines in which they were developed dogmatically.

Even here Xenocrates's preference for symbolic modes of sensualising or denoting appears: he connected the above three stages of knowledge with the three Fates: Atropos, Clotho, and Lachesis.

[36] Probably we should connect with this the statement that Xenocrates called unity and duality (monas and duas) deities, and characterised the former as the first male existence, ruling in heaven, as father and Zeus, as uneven number and spirit; the latter as female, as the mother of the gods, and as the soul of the universe which reigns over the mutable world under heaven,[37] or, as others have it, that he named the Zeus who ever remains like himself, governing in the sphere of the immutable, the highest; the one who rules over the mutable, sublunary world, the last, or outermost.

The divine power of the world-soul is then again represented, in the different spheres of the universe, as infusing soul into the planets, Sun and Moon, - in a purer form, in the shape of Olympic gods.

[41] How Xenocrates tried to establish and connect scientifically these assumptions, which appear to be taken chiefly from his books on the nature of the gods,[42] we do not learn, and can only discover the one fundamental idea at the basis of them, that all grades of existence are penetrated by divine power, and that this grows less and less energetic in proportion as it descends to the perishable and individual.

[45] It is probable, that, after the example of Plato, he designated the divine principium as alone indivisible, and remaining like itself; the material, as the divisible, partaking of multiformity, and different, and that from the union of the two, or from the limitation of the unlimited by the absolute unity, he deduced number, and for that reason called the soul of the universe, like that of individual beings, a self-moving number, which, by virtue of its twofold root in the same and the different, shares equally in permanence and motion, and attains to consciousness by means of the reconciliation of this opposition.

[48] In them he thought he had discovered what, according to Plato,[49] God alone knows, and he among men who is loved by him, namely, the elements or principia of the Platonic triangles.

He may very well, in accordance with this, have regarded the point as a merely subjectively admissible presupposition, and a passage of Aristotle respecting this assumption[51] should perhaps be referred to him.

While, however, Xenocrates (and with him Speusippus and the other philosophers of the older Academy)[54] would not accept that these intermediate things, such as health, beauty, fame, good fortune, etc.

[29] Plutarch writes that Xenocrates once attempted to find the total number of syllables that could be made from the letters of the alphabet.