From the time of the XXVth Dynasty there is a great increase in written documents of a legal character, sales, loans, &c., apparently due to a change in law and custom; but after the reign of Darius I. there is again almost a complete cessation until the reign of Alexander, probably only because of the disturbed condition of the country. Under Ptolemy Philadelphus Greek documents begin to be numerous: under Euergetes II. (Physcon) demotic contracts are particularly abundant, but they cease entirely after the first century of Roman rule.
Marriage contracts are not found earlier than the XXVIth Dynasty. Women had full powers of inheritance (though not of dealing with their property), and succession through the mother was of importance. In the royal line there are almost certain instances of the marriage of a brother with an heiress-sister in Pharaonic times: this was perhaps helped by the analogy of Osiris and Isis: in the Ptolemaic dynasty it was an established custom, and one of the stories of Khamois, written in the Ptolemaic age, assumes its frequency at a very remote date. It would be no surprise to find examples of the practice in other ranks also at an early period, as it certainly was prevalent in the Hellenistic age, but as yet it is very difficult to prove its occurrence. The native contracts with the wife gave to her child all the husband’s property, and divorce or separation was provided for, entailing forfeiture of the dowry. The “native law” of Roman times allowed a man to take his daughter away from her husband if the last quarrelled with him.
Slavery is traceable from an early date. Private ownership of slaves, captured in war and given by the king to their captor or otherwise, is certainly seen at the beginning of the XVIIIth Dynasty. Sales of slaves occur in the XXVth Dynasty, and contracts of servitude are found in the XXVIth Dynasty and in the reign of Darius, appearing as if the consent of the slave was then required. Presumably at this late period there were eunuchs in Egypt, though adequate evidence of their existence there is not yet forthcoming. They must have originated among a more cruel people. That circumcision (though perhaps not till puberty) was regularly practised is proved by the mummies (agreeing with the testimony of Herodotus and the indications of the early tomb sculptures) until an edict of Hadrian forbade it: after that, only priests were circumcised.
See A. H. Gardiner, The Inscription of Mes (from Sethe’s Untersuchungen zur Geschichte und Altertumskunde Ägyptens, iv.); J. H. Breasted, Ancient Records, Egypt, passim, esp. i. § 190, 535 et seqq., 773, ii. 54, 671, iii. 45, 367, iv. 416, 499, 795; F. Ll. Griffith, Catalogue of the John Rylands Demotic Papyri; B. P. Grenfell and J. P. Mahaffy, Revenue Laws of Philadelphus (Oxford, 1896); B. P. Grenfell and A. S. Hunt, Tebtunis Papyri, part i. (London, 1902); Bouché-Leclercq, Histoire des Lagides, tome iv. (Paris, 1907).
Science.—The Egyptians sought little after knowledge for its own sake: they might indulge in religious speculation, but their science was no more than the knowledge of practical methods. Undoubtedly the Egyptians acquired great skill in the application of simple means to the fulfilment of the most difficult tasks. But the books that have come down to us prove how greatly their written theoretical knowledge fell short of their practical accomplishment. The explanation of the fact may partly be that the mechanical and other discoveries of the most ingenious minds among them, when not in constant requisition by later generations, were misunderstood or forgotten, and even in other cases were preserved only as rules of thumb by the craftsmen and experts, who would jealously hide them as secrets of trade. Men of genius were not wanting in the long history of Egypt; two doctors, Imhōtp (Imuthes), the architect of Zoser, in the IIIrd Dynasty, and Amenōphis (Amenhotp), son of Hap, the wise scribe under Amenōphis III. in the XVIIIth, eventually received the honours of deification; and Hardadf under Cheops of the IVth Dynasty was little behind these two in the estimation of posterity. Such men, who, capable in every field, designed the Great Pyramids and bestowed the highest monumental fame on their masters, must surely have had an insight into scientific principles that would hardly be credited to the Egyptians from the written documents alone.
Mathematics.—The Egyptian notation for whole numbers was decimal, each power of 10 up to 100,000 being represented by a different figure, on much the same principle as the Roman numerals. Fractions except 2⁄3 were all primary, i.e. with the numerator unity: in order to express such an idea as 9⁄13 the Egyptians were obliged to reduce it to a series of primary fractions through double fractions 2⁄13 + 2⁄13 + 2⁄13 + 2⁄13 + 1⁄13 = 4(1⁄8 + 1⁄52 + 1⁄104) + 1⁄13 = ½ + 2⁄13 + 1⁄26 = ½ + 1⁄8 + 1⁄26 + 1⁄52 + 1⁄104; this operation was performed in the head, only the result being written down, and to facilitate it tables were drawn up of the division of 2 by odd numbers. With integers, besides adding and subtracting, it was easy to double and to multiply by 10: multiplying and dividing by 5 and finding the 1½ value were also among the fundamental instruments of calculation, and all multiplication proceeded by repetitions of these processes with addition, e.g. 9 × 7 = (9 × 2 × 2) + (9 × 2) + 9. Division was accomplished by multiplying the divisor until the dividend was reached; the answer being the number of times the divisor was so multiplied. Weights and measures proceeded generally on either a decimal or a doubling system or a combination of the two. Apart from a few calculations and accounts, practically all the materials for our knowledge of Egyptian mathematics before the Hellenistic period date from the Middle Kingdom.
The principal text is the Rhind Mathematical Papyrus in the British Museum, written under a Hyksos king c. 1600 b.c.; unfortunately it is full of gross errors. Its contents fall roughly into the following scheme, but the main headings are not shown in the original:—
I. Arithmetic.—A. Tables and rule to facilitate the employment of fractions.
(a) Table of the divisions of 2 by odd numbers from 3 to 99 (e.g. 2 ÷ 11 = 1⁄6 + 1⁄66), see above.
(b) Conversions of compound fractions (e.g. 2⁄3 × 1⁄3 = 1⁄6 + 1⁄18), with rule for finding 2⁄3 of a fraction.