## Ancient Egyptian Science: Ancient Egyptian mathematicsThis 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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algebraic Ancient Egypt ancient Egyptian arithmetical aroura base Berlin Berlin Papyrus Chapter Four column correct cubic cubits cubit-rods cubit-strips denominator des-jug diameter discussion divided division Document IV Document IV.2 Egyptian mathematics equal equations expressed follows formula fragment frustum geometrical Gillings given granary Griffith height hekat Hence heqat Hieratic text Hieroglyphic transcription Horus-eye fractions ibid Kahun Kahun Papyrus khar khet loaves of bread loaves of pefsu measures Moscow Mathematical Papyrus Moscow Papyrus Multiply Neugebauer number of loaves octagon odd numbers ostracon palms Papyrus from Chace Peet's Plate Problem 48 procedure produce pyramid reader Reckon rectangle red auxiliaries Reisner Reisner Papyrus remainder result Rhind Mathematical Papyrus Rhind Papyrus scribe seqed setjat solution someone says square root Struve Take text and Hieroglyphic tion Total translation trapezoid triangle unit fractions unknown quantity Upper-Egyptian grain volume Waerden wedyet-flour

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Page 6 - 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,...

Page 159 - 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?

Page 215 - This papyrus contains nineteen problems, some of which give us new types of calculation unknown till now, and therefore somewhat difficult to comprehend. Four of these problems are geometrical ones. The first shows how to define the length of the sides of a quadrilateral, when the relation of the sides and the area of the quadrilateral are known.

Page 160 - 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.

Page 60 - ... 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.

Page 144 - Assume 7 1 7 1/7 1 Total 8. As many times as 8 must be multiplied to give 19, so many times 7 must be multiplied to give the required number.

Page 28 - ... 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...

Page 183 - Sum the geometrical progression of five terms, of which the first term is 7 and the multiplier 7.

Page 210 - The volume of a frustum is equal to the sum of the areas of the two bases and the square root of their product multiplied by one-third of the altitude.

Page 90 - 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 the frustrum into 4 parts, viz.