By B. L. Van Der Waerden

Originally, my goal used to be to jot down a "History of Algebra", in or 3 volumes. In getting ready the 1st quantity I observed that during historic civiliza­ tions geometry and algebra can't good be separated: increasingly more sec­ tions on historic geometry have been additional. accordingly the recent name of the e-book: "Geometry and Algebra in historic Civilizations". A next quantity at the heritage of modem algebra is in training. it is going to deal customarily with box conception, Galois concept and concept of teams. i would like to specific my deeply felt gratitude to all those that helped me in shaping this quantity. specifically, i need to thank Donald Blackmore Wagner (Berkeley) who placed at my disposal his English translation of the main fascinating components of the chinese language "Nine Chapters of the artwork of Arith­ metic" and of Liu Hui's statement to this vintage, and likewise Jacques Se­ siano (Geneva), who kindly allowed me to exploit his translation of the re­ cently found Arabic textual content of 4 books of Diophantos no longer extant in Greek. hot thank you also are as a result of Wyllis Bandler (Colchester, England) who learn my English textual content very conscientiously and steered numerous increase­ ments, and to Annemarie Fellmann (Frankfurt) and Erwin Neuenschwan­ der (Zurich) who helped me in correcting the evidence sheets. leave out Fellmann additionally typed the manuscript and drew the figures. I additionally are looking to thank the editorial employees and creation division of Springer-Verlag for his or her great cooperation.

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Geometry and Algebra in Ancient Civilizations

Initially, my goal used to be to jot down a "History of Algebra", in or 3 volumes. In getting ready the 1st quantity I observed that during historic civiliza­ tions geometry and algebra can't good be separated: a growing number of sec­ tions on historical geometry have been extra. accordingly the recent name of the e-book: "Geometry and Algebra in historic Civilizations".

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The Greek and Egyptian testimonies concerning the Harpedonaptai were thoroughly discussed by S. Gandz in his paper "Die Harpedonapten oder Seilspanner" (Quell en und Studien Gesch. der Math. B 1, 1930, 24 1 Pythagorean Triangles p. 255-277). In an inscription describing the foundation of a temple at Abydos by Sethos I (1300 B. " Still earlier, Thutmose III (1500 B. ) is said to have spanned the rope towards the sungod Amon at the horizon. In his paper just quoted, Gandz has discussed a fragment of Democritos according to which the harpedonaptai were experts in "composing lines".

11 0. In Greece and India: Constructions of altars satisfying geometrical conditions. Wrath of Gods if constructions are not exact. Construction of a square equal in area to a given rectangle. 12°. In the West, in Egypt and India: "Cord-Stretchers" performing geometrical constructions for ritual purposes. 13 0. In Egypt, Greece, and China: One and the same incorrect rule for the area of a circle segment. 14°. In Egypt, Babylonia, and China: Collections of mathematical problems with solutions. 15°.

In the West, in Egypt and India: "Cord-Stretchers" performing geometrical constructions for ritual purposes. 13 0. In Egypt, Greece, and China: One and the same incorrect rule for the area of a circle segment. 14°. In Egypt, Babylonia, and China: Collections of mathematical problems with solutions. 15°. In China and Egypt: One and the same correct rule for the volume of a truncated pyramid. In my opinion, this network of interrelations and similarities can only be explained by assuming a common origin for the mathematics and astronomy of these ancient countries.

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