On Two Astronomical Passages in Plutarch’s De Animae Procreatione in Timaeo

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The following investigations arose from a question of Prof. A. Bidez. He drew my attention to § 31 (1028 F) of the work mentioned in the title, in which Plutarch speaks about a “Chaldean” doctrine according to which the four seasons of the year can be arranged in certain harmonic proportions. The discovery of the unequal length of the four seasons is undoubtedly one of the most fundamental achievements of ancient astronomy because it is equivalent to the discovery of an inequality in the movement of the sun. The explanation of this inequality as apparent by assuming a certain eccentricity of the sun’s orbit with respect to the earth is the basis for the ancient theory of the eccentric movements, a theory which finally led to Kepler’s discovery of the elliptic orbits of the planets. On the other hand, the cuneiform astronomical tablets of the Seleucid period show that the inventors of these mathematical devices also were fully conscious of the fundamental role of an adequate description of the inequality of the movement of the sun in the prediction of the visibility of the moon’s crescent and of eclipses. The careful investigation of every ancient statement about the unequal length of the seasons is therefore fully justified.