Ancient Egyptian Science: Ancient Egyptian mathematics
American Philosophical Society, 1989 - 462 lappuses
This volume continues Marshall Clagett's studies of the various aspects of the science of Ancient Egypt. The volume gives a discourse on the nature and accomplishments of Egyptian mathematics and also informs the reader as to how our knowledge of Egyptian mathematics has grown since the publication of the Rhind Mathematical Papyrus toward the end of the 19th century. The author quotes and discusses interpretations of such authors as Eisenlohr, Griffith, Hultsch, Peet, Struce, Neugebauer, Chace, Glanville, van der Waerden, Bruins, Gillings, and others. He also also considers studies of more recent authors such as Couchoud, Caveing, and Guillemot.
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added addition amount Ancient answer appears arithmetical assumed base beer Berlin bread calculation called Chace Chapter circle column common complete concerning correct cubits denominator determined discussion divided division Document double edition Egyptian Egyptian mathematics equal equations evident Example expressed Facsimile fact figure follows formula Four fragment geometrical Gillings give given grain height Hence heqat Hieratic text Hieroglyphic transcription interpretation involving khet length loaves means measures method Moscow Moscow Mathematical Papyrus Multiply Museum namely palms Peet pefsu Photograph Plate preceding presented Problem procedure produce pyramid quantity reader Reckon rectangle Register remainder result Rhind Mathematical Papyrus Rhind Papyrus says scribe setjat side simple solution square Struve suggested Take taken tion translation triangle unit fractions unknown volume whole
2. lappuse - It was this king [Sesotris], moreover, who divided the land into lots and gave everyone a square piece of equal size, from the produce of which he exacted an annual tax. Any man whose holding was damaged by the encroachment of the river would go and declare his loss before the king, who would send inspectors to measure the extent of the loss, in order that he might pay in future a fair proportion of the tax at which his property had been assessed. Perhaps this was the way in which geometry was invented,...
155. lappuse - Divide 100 loaves among 5 men in such a way that the shares received shall be in arithmetical progression and that 1/7 of the sum of the largest three shares shall be equal to the sum of the smallest two. What is the difference of the shares?
104. lappuse - Das Wesen einer Gleichung besteht nun allerdings weit weniger in dem Wortlaute als in der Auflösung, und so müssen wir, um die Berechtigung unseres Vergleichs zu prüfen, zusehen, wie Ahmes seine Haurechnungen vollzieht.
120. lappuse - L'Egypte à l'Exposition universelle de tsûl. (Gazelle des Beauz-Artt, t. XXII et XXIII, Ier et _'' semestres, 1867, in-8*.) Note relative à un papyrus égyptien contenant un fragment d'un traité de géométrie appliquée à l'arpentage.
202. lappuse - Mathematischer Papyrus des Staatlichen Museums der Schönen Künste in Moskau.
81. lappuse - Take away 1/9 of 9, namely, 1; the remainder is 8. Multiply 8 times 8; it makes 64. Multiply 64 times 10; it makes 640 cubed cubits.
86. lappuse - ... are concerned with grain barns. An outstanding accomplishment of the Egyptian mathematics is found however in the entirely correct calculation of the volume of the frustrum of a pyramid with square base, as found in the Moscow papyrus (Plate 5a), by means of the formula where h is the height and a and b the sides of the lower and upper base. It is not to be supposed that such a formula can be found empirically. It must have been obtained on the basis of a theoretical argument; how? By dividing...
56. lappuse - ... must now determine whether the progression fulfills the second requirement of the problem: namely, that the number of loaves shall total 100. In other words, multiply the progression whose sum is 60 (see above) by a factor to convert it into 100; the factor, of course, is 1%. This the papyrus does: "As many times as is necessary to multiply 60 to make 100, so many times must these terms be multiplied to make the true series.
24. lappuse - ... of five. As being the part which completed the row into one series of the number indicated, the Egyptian r-fraction was necessarily a fraction with, as we should say, unity as the numerator. To the Egyptian mind it would have seemed nonsense and self-contradictory to write...