scholarly journals On a Collection of Geometrical Riddles and their Role in the Shaping of Four to Six “Algebras”

2001 ◽  
Vol 14 (1-2) ◽  
pp. 85-131 ◽  
Author(s):  
Jens Høyrup
Keyword(s):  
Theoretical Investigation ◽  
Ancient Greek ◽  
New Approach ◽  
Islamic World ◽  
Near Eastern ◽  
Old Babylonian ◽  
Greek Mathematics ◽  
Practical Geometry

For more than a century, there has been some discussion about whether medieval Arabic al-jabr (and hence also later European algebra) has its roots in Indian or Greek mathematics. Since the 1930s, the possibility of Babylonian ultimate roots has entered the debate. This article presents a new approach to the problem, pointing to a set of quasi-algebraic riddles that appear to have circulated among Near Eastern practical geometers since c. 2000 BCE, and which inspired first the so-called “algebra” of the Old Babylonian scribal school and later the geometry of Elements II (where the techniques are submitted to theoretical investigation). The riddles also turn up in ancient Greek practical geometry and Jaina mathematics. Eventually they reached European (Latin and abbaco) mathematics via the Islamic world. However, no evidence supports a derivation of medieval Indian algebra or the original core of al-jabr from the riddles.

Ancient Greek Mathematics

2015 ◽  
Author(s):  
José Ferreirós
Keyword(s):  
Elementary Mathematics ◽  
Euclidean Geometry ◽  
Advanced Mathematics ◽  
Ancient Greek ◽  
Greek Tradition ◽  
The Common ◽  
Greek Mathematics ◽  
Joint Consideration ◽  
Practical Geometry ◽  
Further Development

This chapter focuses on the ancient Greek tradition of geometrical proof in light of recent studies by Kenneth Manders and others. It advances the view that the borderline of elementary mathematics is strictly linked with the adoption of hypotheses. To this end, the chapter considers Euclidean geometry, which elaborates on both the problems and the proof methods based on diagrams. It argues that Euclidean geometry can be understood as a theoretical, idealized analysis (and further development) of practical geometry; that by way of the idealizations introduced, Euclid's Elements builds on hypotheses that turn them into advanced mathematics; and that the axioms or “postulates” of Book I of the Elements mainly regiment diagrammatic constructions, while the “common notions” are general principles of a theory of quantities. The chapter concludes by discussing how the proposed approach, based on joint consideration of agents and frameworks, can be applied to the case of Greek geometry.

Θεωρία in Ancient Greek Exegetical Literature

2020 ◽  
pp. 85-104
Author(s):  
Борис Тимофеев
Keyword(s):  
Mystical Experience ◽  
Near East ◽  
Literary Form ◽  
Traditional View ◽  
Ancient Greek ◽  
Symbolic Form ◽  
Near Eastern ◽  
The World ◽  
Genesis 1 ◽  
Book Of Genesis

Современная научная богословская мысль склонна к унификации терминов и явлений в сфере своих компетенций. Эта тенденция в современных исследованиях в некоторых случаях распространяется и на древние христианские памятники. Так, например, слово θεωρία многие учёные определяют как мистический метод духовного толкования Священного Писания. Это определение нередко применяется в качестве универсального технического определения при анализе экзегетических произведений древних авторов. При этом игнорируется узус самих экзегетов, которые употребляют это слово в иных значениях. В рамках данной статьи предпринимается попытка выявить и показать основные значения слова θεωρία в древней греческой экзегетической литературе. The article deals with the theology, composition and literary form of the narrations which constitute the prologue part of the book of Genesis (1, 1-11, 26). During the second half of the 19th and at the turn of the 20th cent., following the emergence of the Documentary hypothesis as well as the comparison of the Holy Scripture with the newly-discovered literary monuments of Ancient Near East, the greater part of the narrations that constitute the Prologue were labeled myths and ancient Hebrew folklore (J. Wellhausen, H. Gunkel, J. Frazer). In addition to the then detected Near Eastern parallels, this new attitude towards the narrations of the Prologue was fostered by its lack of a clearly expressed historical dedication and the symbolic form of their exposition. Defending the traditional view of the Prologue as sacred history and prophetic revelation, bishop Kassian (Bezobrazov) proposed to consider all the biblical narrations that contain theophanies as metahistorical. Archpriest Sergey Bulgakov, A. F. Losev and B. P. Vysheslavtsev, who analyzed the phenomenon of myth-making, called the Biblical narration of the origins of the world a myth, but in a sense different from that proposed by Gunkel and Frazer. They have founded a new and positive conception according to which a myth is not fi but rather a kind of reality based upon mystical experience. The author of the article analyzes each of the terms enumerated - «history», «myth», «metahistory» - in their use relating them to the Prologue; he also examines the possibility of their harmonizing with the traditional ecclesiastical view of this part of the book of Genesis.

A New Approach to Digital Process Control

1976 ◽  
Vol 9 (9) ◽  
pp. 315-319
Author(s):  
K. R. R. Bowden
Keyword(s):  
Process Control ◽  
Digital Control ◽  
Subsequent Development ◽  
Technical Conference ◽  
Ancient Greek ◽  
Paper Briefly ◽  
New Approach ◽  
The Past ◽  
Eastern Usa ◽  
Process Plants

In recent years, the application of digital computers to process control has been shown to have real advantages over the traditional analogue (electronic and pneumatic) techniques. However, there have often been severe practical difficulties which prevented the achievement of these advantages, and which have slowed down the acceptance of digital control, particularly for smaller systems. This paper briefly discusses the advantages, then examines the potential problems, of digital control. Then follows a description of a new system which is shown to provide most of the advantages of digital control, whilst avoiding the mysteries and difficulties which have been so common in the past. The author, Dr Romilly Bowden, was the prime operator in the early design, and in the subsequent development both in England and America, of the Diogenes project on which this article is based. The classical name for the process controller was coined, rather whimsically, at an impromptu technical conference somewhere over the eastern USA. The constant reference to diodes (as programming devices, mostly) evoked the response “It's positively diogenous!” (ie, full of diodes). From this it required very little to produce the name of the ancient Greek philosopher. Despite the high-flying etymology, in down-to-earth terms, systems are operating successfully in a variety of American process plants, and work is in hand for further systems in Europe.

Historically Speaking—: The Bernoulli Family

1966 ◽  
Vol 59 (3) ◽  
pp. 276-278
Author(s):  
Howard Eves
Keyword(s):  
United States ◽  
Eighteenth Century ◽  
General Rule ◽  
The United States ◽  
Great Mathematician ◽  
Ancient Greek ◽  
Isaac Newton ◽  
Greek Mathematics ◽  
Successive Generations ◽  
Father And Son

There is a general rule to the effect that any given family possesses at most one outstanding mathematician and that, in fact, most families possess none. Thus a search through the ancestors, descendents, and relatives of Isaac Newton fails to turn up any other great mathematician. There are exceptions to this general rule. For example we have, here in the United States, the two Lehmers (father and son) and the two Birkhoffs (father and son). One also recalls the two Cassinis (father and son) of the late seventeenth and early eighteenth centuries, and perhaps one can build a case for the two Clairaut children of the eighteenth century. And of course there were Theon and Hypatia (father and daughter), who lived during the closing years of ancient Greek mathematics. But such cases are relatively rare. All the more striking, then, is the Bernoulli family of Switzerland, which in three successive generations produced no less than eight noted mathematicians.

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