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It is true that all the land of Egypt, except that of priests and soldiers (so H. himself, c. 168), was held of the king and paid to him one-fifth of the produce; the Jewish story attributed this arrangement to Joseph (Gen. xlvii); there is no reason for assigning it to any one king (Meyer, i. 224, puts it as early as the fourth and fifth dynasties). Probably, however, there was a basis of truth for the tradition which connected land taxation with the conquering Sesostris; as kings developed a spirited foreign policy, the burden of taxation on their subjects was organized and increased. H. is wrong as to lots being equal.
Translate ‘might pay in future in proportion to the rent fixed’ (cf. ἐπιτάξαντα ἀποφορήν above); i. e. rent was diminished in proportion to the amount of land lost, but the rate of assessment was unchanged.
The πόλος was a concave, hemispherical ‘dial’, so called from being shaped like the vault of the sky; on this a shadow was cast by the γνώμων (a ‘pointer’), which marked the time of day by its direction, and the chief seasons of the year (the solstice, equinox, &c.) by its length at midday. The period from sunrise to sunset was divided into ‘twelve parts’, which of course varied in length with the season of the year. Diogenes Laertius (ii. 1) says Anaximander invented the γνώμων: but this need only mean that he introduced it from Egypt. It is most natural to suppose (cf. D. of A. s. v. Polus) that H. is speaking of one ‘compound instrument’. Others, however (e. g. D. of A. s. v. Horologium), think that he means to distinguish the γνώμων and the πόλος. Both certainly were used independently of each other; the γνώμων was the earlier, in the form of a pillar, which measured time by the length of its shadow. That geometry was an Egyptian invention was the general belief of the Greeks. For the whole subject cf. the ‘Eudemian summary’ (based by Proclus, circ. 450 A. D., on the history of Eudemus, circ. 330 B. C.). This is translated in Gow's Hist. of Gk. Math., pp. 134 seq. (a short paraphrase in Smith, D. B. s. v. Euclides). According to this (for other evidence cf. Gow, p. 131) geometry was invented because the Nile floods destroyed all ordinary boundaries (cf. Strabo 787 for the same statement). Thales introduced geometry into Greece; but it was the Greeks who made it a science; in Egypt it was confined almost entirely to the practical requirements of the surveyor (Gow, p. 126).
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