[231] Plato, Republic, vii. pp. 526-527.
Astronomy — how useful — not useful as now taught — must be studied by ideal figures, not by observation.
After Geometry — the measurement of lines and superficial areas — the proper immediate sequel is Stereometry, the measurement of solids. But this latter is nowhere properly honoured and cultivated: though from its intrinsic excellence, it forces its way partially even against public neglect and discouragement.[232] Most persons omit it, and treat Astronomy as if it were the immediate sequel to Geometry: which is a mistake, for Astronomy relates to solid bodies in a state of rotatory movement, and ought to be preceded by the treatment of solid bodies generally.[233] Assuming Stereometry, therefore, as if it existed, we proceed to Astronomy.
[232] Plato, Republic, vii. p. 528 A-C.
[233] Plato, Republic, vii. p. 528 A-B. ἐν περιφορᾷ ὂν ἤδη στερεὸν λαβόντες, πρὶν αὐτὸ καθ’ αὑτὸ λαβεῖν. Also 528 E.
Certainly (remarks Glaukon) Astronomy, besides its usefulness in regard to the calendar, and the seasons, must be admitted by every one to carry the mind upwards, to the contemplation of things not below but on high. I do not admit this at all (replies Sokrates), as Astronomy is now cultivated: at least in my sense of the words, looking upwards and looking downwards. If a man lies on his back, contemplating the ornaments of the ceiling, he may carry his eyes upward, but not his mind.[234] To look upwards, as I understand it, is to carry the mind away from the contemplation of sensible things, whereof no science is attainable — to the contemplation of intelligible things, entities invisible and unchangeable, which alone are the objects of science. Observation of the stars, such as astronomers now teach, does not fulfil any such condition. The heavenly bodies are the most beautiful of all visible bodies and the most regular of all visible movements, approximating most nearly, though still with a long interval of inferiority, to the ideal figures and movements of genuine and self-existent Forms — quickness, slowness, number, figure, &c., as they are in themselves, not visible to the eye, but conceivable only by reason and intellect.[235] The movements of the heavenly bodies are exemplifications, approaching nearest to the perfection of these ideal movements, but still falling greatly short of them. They are like visible circles or triangles drawn by some very exact artist; which, however beautiful as works of art, are far from answering to the conditions of the idea and its definition, and from exhibiting exact equality and proportion.[236] So about the movements of the sun and stars: they are comparatively regular, but they are yet bodily and visible, never attaining the perfect sameness and unchangeableness of the intelligible world and its forms. We cannot learn truth by observation of phenomena constantly fluctuating and varying. We must study astronomy, as we do geometry, not by observation, but by mathematical theorems and hypotheses: which is a far more arduous task than astronomy as taught at present. Only in this way can it be made available to improve and strengthen the intellectual organ of the mind.[237]
[234] Plato, Republic, vii. p. 529 B.
[235] Plato, Republic, vii. p. 529 D.
[236] Plato, Republic, vii. pp. 529-530.
[237] Plato, Republic, vii. p. 530 B. Προβλήμασιν ἄρα χρώμενοι ὥσπερ γεωμετρίαν, οὕτω καὶ ἀστρονομίαν μέτιμεν· τὰ δ’ ἐν τῷ οὐράνῳ ἐάσομεν, &c.