ad sin (ad) + be sin (be) + cd sin (cd)]. Hence, except in the case of a rectangle the formula gives a result which is too large. Peet (1923, 2)[1] is therefore in error when he argues (p. 94) that the tenant "never lost by this rough system of measurement" in paying taxes according to the extent of his field. "This method of measuring was admittedly no more than an approximation for taxation purpose, and fractions less than 1⁄64 of a square Khet, sometimes even1⁄32 of a square Khet, were omitted" (Peet); compare H. Maspero, Les finnances de l'Égypte sous les Lagides, Paris, 1905, p. 135.
An important supplement to the memoir of Lepsius is H. K. Brugsch Thesaurus I nscriptionum Aegyptiacarum. Astronomische und astralogische Inschriften, altaegyptischer Denkmaeler, 3. Abteilung, Geographische Inschriften Leipzig, I884, pp. 53l—618. For two other references to sources using the above method for computing quadrilateral areas, between 100 B. C. and about 550 A. D., see Greek Papyri in the British Museum. Catalogue, with Texts, edited by F. G. Kenyon, London, vol. 2, 1898, pp. 129-141;[2] B. P. Grenfell, A. S. Hunt, J. G. Smyly, The Tebtunis Papyri, London, part I, I902, pp. 385-393;[3] and H. R. Hall, Coptic and Greek Texts of the Christian Period from Ostraka in the British Museum, London, 1905, p. 128, ostracon 29750, and plate 88.[4] Compare Peet (1923, 2) pp. 93-95. A reference may also be given to: H. Weissenborn, “Das Trapez bei Euklid, Heron und Brahmagupta," Abhandlungen zur Geschichte der Mathematik. Leipzig, Heft 2, 1879. especially
- ↑ The form of abbreviation, "Peet (1923)," referring to a publication of Peet in 1923 listed under this date in this Bibliography, will be constantly employed for referring to authors in the following pages. If there is more than one publication by the same author listed under a given date, a second number in the parentheses will identify the one referred to. Since, for example, under 1923 there are two titles of Peet's publications the second will be singled out by the notation: Feet (1923, 2); similarly for the first.
- ↑ The papyrus here discussed is no. CCLXVII of the late first, or second, century (compare p. xxvi). Although the beginning and end of the papyrus are lost, about 8% feet, with 21 columns, are still preserved. Most of this is transcribed (without translation) and columns 17—18 are reproduced on plate 45 of the volume of Facsimiles. The papyrus is a register of land containing statements of the extents of land, calculated in arurae, assigned for sowing, woodland, uncultivated land, etc. In one of the fields (line 100) the sides are given as 17⁄16., 211⁄6, 2122⁄15, and 219⁄22 and the area is found to be 41⁄27/64 arurae. The linear unit is 100 royal cubits called a schoenia, the square of which is an arura. The above result is slightly large but correct, according to the rule for areas given above, to within less than a sixty-fourth of an arura.
- ↑ In these pages is given the transcription of the text of a late second century B. C. village survey list (30 X 66.5 cm.) numbered 87, together with introductory comment and notes.
- ↑ This is a brief memorandum of land measurements on a pottery ostracon (5 X 4 in.) hardly earlier than the sixth century.
1867, p. 460; also Gerbert, Opera Mathematica, ed. by N. Bubnov, Berlin, I899, p. 354. Compare Gunn under 1923. The Edfu formulæ for finding the areas of both an isosceles triangle (30, 30, I8) and a quadrilateral (34, 30, 32, 32) were used in the eighth century in a work attributed to Bede the Venerable, Venerabilis Bædæ . . . Opera, Cologne, 1612, vol. I, cols. I06, 109. For Roman use in a quadrilateral (30, 6, 40, 20) see F. Blume, K. Lachmann, A. Rudorff, 'Die Schriften der römischen Feldmesser herausgegeben und erlāutert, Berlin, vol. 1, 1848. p. 355.
