Ancient Egyptian Science: Ancient Egyptian mathematics

Pirmais vāks
American Philosophical Society, 1989 - 863 lappuses
Continues Clagett's studies of the various aspects of the science of Ancient Egypt. Like its predecessors, it has two main objectives: first to summarize & analyze the principal features of a nascent & yet important part of that science, namely its mathematics, & second to present in English six of the most important mathematical documents on which the preceding analysis was based. Thus we find treated in the first part of the work Egyptian measurement that lay behind the various calculating procedures, the procedures themselves, & the model problems that were gathered together to aid the calculators in their efforts to complete practical measures. Includes detailed descriptions of the various kinds of tables that the Egyptians depended upon in their calculations, an important one being the Table of Two that presented the division of 2 by the odd numbers from 3 to 101. This table reveals the nature of Egyptian fractions & their form of notation as the sums of unit fractions, a form leading to the use of a concept very useful for measurement, that of significant fractional approximations achieved by dropping one or more of the lesser fractions at the end of a set of unit fractions. The Table of Two occupies the first section of the most important of all Egyptian mathematical documents, the Rhind Papyrus, the papyrus which stands at the head of the documents in Part II of the volume. Following the series of documents in Part II with their extensive endnotes, the author gives in Part III a bibliography, an Index of Egyptian Terms, & an Index of Proper Names & Subjects. Includes an extensive collection of illustrations along with pertinent diagrams & tables, & reproductions of the hieratic texts of the documents with their hieroglyphic transcriptions.
 

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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,...
284. lappuse - Philologische und historische Abhandlungen der Königlichen Akademie der Wissenschaften zu Berlin aus dem Jahre 1840.
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...

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