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Pada kesempatan kali ini, saya akan berbagi EBOOK unexpected LINKS between EGYPTIRN and BRBYLONIRN Mathematics karya Joran Friberg Chalmers University of Technology. Gothenburg, Sweden. Semoga dengan ebooks ini kita tingkatkan literasi kita.

unexpected LINKS between EGYPTIRN and BRBYLONIRN Mathematics

Preface

Ancient Mesopotamian mathematics is known from hundreds of texts recorded on clay tablets in the cuneifonn script. Some of the mathematical cuneiform texts are quite large and contain many exercises or long tables of numbers or measures. The great majority of these texts are Old Babylonian, from the first half of the second millennium BCE. I A few are Kassite, from the latter half of the second millennium BeE, some are Late Babylonian/Seleucid, from the latter half of the first millennium BCE, and others are pre-Babylonian, from various periods within the third millennium, or the last part of the fourth millennium. New clay tablets with mathematical cuneiform texts keep appearing from time to time, excavated in the field, extracted from the archives of large museums in Europe, America, and the Near East, or offered for sale in the antiquities market. Therefore, the writing of the history of Mesopotamian mathematics is a dynamic, never-ending process. Egyptian mathematics, on the other hand, is known from a comparatively much smaller number of original documents, belonging to three distinct groups. The first group consists of texts from the earlier part of the second millennium BCE, written in the hieratic script. It contains two mathematical papyrus rolls, P.Rhind = P.BM 10057/8 (Peet, RMP (1923), Chace, Bull, and Manning, RMP (1927-29), Robins & Shute, RMP (1987)), and P.Moscow E 4676 (Struve, QSA 1 (1930)), the Mathematical Leather Roll P.RM 10250 (Glanville, MLR (1927)), the papyrus fragments P.Rerlin 6619 (Schack-Schackenburg, zAS 38 (1900)), and the Lahun mathematical fragments, fonnerly known as the Kahun fragments (Griffith, HPKG (1898), Imhausen and Ritter, UCLLP (2004)). There are also two wooden tablets WT.Cairo 23567/8 and two ostraca. Texts belonging to this first group, in the following referred to as “hieratic mathematical papyri”, will be discussed in Chapter 2. The second group of known Egyptian mathematical texts consists of documents from the Hellenistic and Roman periods, mostly from the last part of the first millennium BCE, written in the demotic script. The group consists of one large papyrus, P.Cairo, and six smaller texts or fragments, all published by Parker in lNES 18 (1959), Cent. 14 (1969), DMP (1972), and lEA 61 (1975), plus several ostraca. A number of exercises from Parker’s “demotic mathematical papyri”, will be discussed in Chapter 3. The third group of known Egyptian mathematical texts consists of documents from the Hellenistic and Roman periods, that is from the last part of the first millennium BeE and the first half of the first millennium CE, written in Greek. A small subgroup including 6 ostraca, a papyrus roll, and three papyrus fragments, all related in one way or another to Euclid’s Elements, will not be considered here. However, the third group also includes texts that show almost no signs of having been influenced by high level Greek mathematics. The most interesting examples of such “nonEuclidean” Greek mathematical texts include a codex of six papyrus leaves, P.Akhmfm (Baillet, BMA (1892», a large papyrus roll, P. Vindob.G. 19996 (Gerstinger and Vogel, GLP 1 (1932», six smaller papyri or papyrus fragments, an ostracon, and a wooden tablet. These “Greek Egyptian mathematical documents” will be discussed in Chapter 4. All the mentioned hieratic mathematical texts had already been published by 1930, the demotic mathematical texts by 1975, and the Greek­Egyptian mathematical texts by 1981. Since then not much has happened in the study of Egyptian mathematics. The few books and papers that have been written about “Egyptian mathematics” have been concerned exclu­ sively with the hieratic mathematical texts and have mostly reiterated the interpretations and presentations of those texts that were offered already in the original publications. Very little seems to have been written about the demotic mathematical texts since they were published by Parker, and not much about the Greek-Egyptian mathematical texts. My original impetus to search for links between Egyptian and Babylonian mathematics came from an observation that two small but particularly interesting mathematical texts from the Old Babylonian city Mari have clear Egyptian parallels, one in an exercise in the well known hieratic Papyrus Rhind, the other in a relatively unknown Greek-Egyptian papyrus fragment. The details will be presented below in Chapter 1. My observation that there seems to exist clear links between Egyptian and Babylonian mathematics is in conflict with the prevailing opinion in formerly published works on Egyptian mathematics, namely that practically no such links exist. However, in view of the mentioned dynamic character of the history of Mesopotamian mathematics, not least in the last couple of decades, it appeared to me to be high time to take a renewed look at Egyptian mathematics against an up-to-date background in the history ofMesopotamian mathematics! That is the primary objective of this book. My search for links between Egyptian and BabyIonian mathematics has been unexpectedly successful, in more ways than one. Not only has the search turned up numerous possible candidates for such links, but the comparison ofEgyptian and BabyIonian mathematics has in many cases led to a much better understanding of the nature of important Egyptian mathematical texts and of particularly interesting exercises that they contain. In addition, my careful examination of a great number of individual Egyptian hieratic, demotic, and Greek mathematical exercises has made this book into a useful survey of a substantial part of the whole corpus of Egyptian mathematics. Several of the techniques and concepts that I have developed in the course of my intensive study of mathematical cuneiform texts during the last 25 years have proven themselves to be eminently suitable also for a study of Egyptian mathematical texts. An obvious example of a helpful technique is the use of “conform” transliterations for detailed outlines of mathematical texts. A particularly useful concept is that of a “mathematical recombination text”, which is an appropriate name for a large mathematical text with a somewhat chaotic collection of individual exercises. The detailed comparison in this book of a large number of known Egyptian and Mesopotamian mathematical texts from all periods has led me to the conclusion that the level and extent of mathematical knowledge must have been comparable in Egypt and in Mesopotamia in the earlier part of the second millennium BeE, and that there are also unexpectedly close connections between demotic and “non-Euclidean” Greek-Egyptian mathematical texts from the Ptolemaic and Roman periods on one hand and Old or Late Babylonian mathematical texts on the other.