The text of the tract De arcubus similibus was published for the first time by M. Curtze in 1887. However, after examining some more Latin manuscripts and the Arabic MS Oxford, Bodleian Library, Marsh 663 it appeared, that Curtze's edition was rather an adaptation. Also Curtze's suggestion that Jordanus Nemorarius was the author was very probably wrong. The author of the tract was the Egyptian mathematician Ahmed ibn Jusuf as appears from the Latin manuscripts, and its translator, very probably, Gerard (...) of Cremona. In the tract Ahmed tried to prove, that the assertion ‘similar arcs are also equal arcs’ was wrong . His starting points were the propositions Euclid III, 20 and 21. Consequently, the tract can be looked upon as a commentary on the third book of the Elements. (shrink)

Im folgenden sollen zwei Arbeiten zur theoretischen Mathematik vorgestellt werden, die im 14. Jahrhundert entstanden. Die eine stammt von Thomas Bradwardine (um 1290 - 1349), einem der wichtigsten Mathematiker dieser Zeit, die andere von dem praktisch unbekannten Wigandus Durnheimer. Bei Bradwardine soll insbesondere die Frage beantwortet werden, welche der arithmetischen Schriften, die ihm zugeschrieben werden, wirklich von ihm stammt. Bei Durnheimers Schrift, einer Kompilation, die u.a. auf Bradwardines Abhandlung beruht, werden der Inhalt der einzelnen Kapitel und deren Quellen angegeben.

The twelfth century was a period of transmission and absorption of Arabic learning though it filtered outside of the Arabic world as early as the second half of the tenth century. In general, the lure of Spain began to act only in the twelfth century, and the active impulse toward the spread of Arabic mathematics came from beyond the Pyrenees and from men of diverse origins. The chief names are Adelard of Bath, Robert of Chester, Hermann of Carinthia and Gerard (...) of Cremona. In this time the Latin world became acquainted with the Hindu numerals, the Arabic Algebra and Euclid'sElements. However, not only Spain, but also the Norman kingdom of southern Italy and Sicily occupies a position of peculiar importance, though the works of the translators did not become very influential. There were made direct translations from Greek into Latin. One had to wait a century more to obtain a translation from Greek into Latin of the chief Archimedean scientific and mathematical treatises by William of Moerbeke. In the thirteenth century Fibonacci and Jordanus Nemorarius stand at the threshold of European mathematics. Not only was Fibonacci the first to explain Arabic arithmetic, but his works, especially his later ones, contain many original ideas. Jordanus continued the Greco-Roman tradition rather than the Greco-Arabic one, but he did so with much independence. To Nicole Oresme (fourteenth century) was due a broadened view of proportionality, a geometric proof to determine the summation of convergent infinite series and the proof, evidently the first in the history of mathematics, that the harmonic series is divergent. The Configuration Doctrine was treated by Merton College authors and by Oresme. In the fifteenth century theDe triangulis omnimodis of Regiomontan, a systematic account of the methods for solving triangles, marked the rebirth of trigonometry. (shrink)

In diesem Aufsatz möchte ich einen Überblick über unser heutiges Wissen bezüglich der Übersetzung der Elemente Euklids ins Lateinische geben. Cicero hat als Quästor in Sizilien das Grab des Archimedes aufgesucht und instandsetzen lassen, er nennt gelegentlich Euklid und Archimedes und er zitiert in Academica I, Buch II, § 116, die Definitionen von Punkt und Linie. Vor dem 6.

WALTER BURLEIGH, Von der Reinheit der Kunst der Logik. Erster Traktat: Von den Eigenschaften der Termini. Übersetzt und mit Einfuhrung und Anmerkungen herausgegeben von Peter Kunze. Lateinisch-deut...

ZusammenfassunuIn dem vorliegenden Bericht über einige Arbeiten des Verfassers und eine daran anschliessende Arbeit von G. Emde, Marburg, wird eine Reihe von Ergebnissen behandelt, die die Kombinationen der Grundmodalitäten « Möglichkeit » und « Notwendigkeit » betreffen. Ausgehend von sehr allgemeinen Rahmenkodifikaten wird die durch Basisreduktion zu gewinnende Liste der endlich vielen implikativen Modalitätenlogiken mit idempotenter Möglichkeit erörtert; bei wichtigen Unterklassen der nicht notwendig idempotenten implikativen Modalitätenlogiken treten neben der Basisreduktion vor allem spezielle Entscheidungsprobleme in den Vordergrund.RésuméDans le rapport ci‐dessus (...) concernant quelques travaux de l'auteur et le travail de M. G. Emde qui s'y rapporte, il s'agit d'un ensemble de résultats sur la combinaison des modalités fondamentales de « possibilité» et de « nécessité». Partant de quelques codifications cadres très générales, I'auteur discute la liste en nombre fini des logiques modales implicatives à« possibilité» idempotente, une liste qui est obtenue par une réduction des bases. Quant à certaines sous‐classes importantes des logiques implicatives qui ne sont pas nécessairement idempotentes, outre la réduction des bases, les problèmes de décision qui leur sont spéciaux, se trouvent placés au premier plan.In the present report on some papers of the author and on a sequel to them by G. Emde, Marburg, a series of results concerning the combination of the basic modalities « possibility » and « necessity » are treated. Starting from some very general framing‐codifications, the list of the finitely many implicative modal logics with idempotent « possibility » which is obtainable through basis reduction is discussed. Besides basis reduction, in the case of some important subclasses of the not‐necessarily‐idempotent implicative modal logics, attention is given to the special decision problems. (shrink)

The spatial dynamics of the optical emission from an array of 50 times 50 individual microcavity plasma devices is investigated. The array is operated in argon and argon-neon mixtures close to atmospheric pressure with an ac voltage. The optical emission is analysed with phase and space resolution. It has been found that the emission is not continuous over the entire ac period, but occurs once per half period. Each of the observed emission phases shows a self-pulsing of the discharge, with (...) several bursts of emission of fixed width and repetition rate. The number of emission bursts depends on applied voltage and frequency. Spatially resolved measurements prove that the emission bursts are formed by overlapping emission pulses from single discharge cavities. Intensity differences between positive and negative half-wave can be interpreted through spatially resolved measurements of single discharge cavities. (shrink)