A difícil aceitação dos números negativos: um estudo da teoria dos números de Peter Barlow (1776-1862)

The present study seeks to present a historico-epistemological analysis of the development of the mathematical concept of negative number. In order to do so, we analyzed the different forms and conditions of the construction of mathematical knowledge in different mathematical communities and, thus, identified the characteristics in the establishment of this concept. By understanding the historically constructed barriers, especially, the ones having ontologicas significant, that made the concept of negative number incompatible with that of natural number, thereby hindering the development of the concept of negative, we were able to sketch the reasons for the rejection of negative numbers by the English author Peter Barlow (1776 -1862) in his An Elementary Investigation of the Theory of Numbers, published in 1811. We also show the continuity of his difficulties with the treatment of negative numbers in the middle of the nineteenth century

Aaron Isaacs Minnen : en judisk kulturbild fran gustaviansk tid

utg.: Abraham Brody och Hugo Valentin

A Possible Case of Möller-Barlow Disease in Northwestern Switzerland (7th Century)

The excavation site Reigoldswil is located at 550 m above sea level on the Jura chain hillside in north-western Switzerland. The mountains divide the Rhine valley from an agriculturally rich region. The origin of the village lies in the early medieval time. Until now the skeletons of one cemetery have been morphologically studied. Around 216 individuals were excavated from under the foundation walls of a church and in the open field. They date to the 7/8th up to the 10th century. The striking part is the high amount of subadult (0-18 years) individuals with 58% (n=126). One of these children, an approximately 1.5 year old toddler from the 7th century, was buried in a stone cist. Its bones show morphological traces like porotic lesions of the greater wings of the sphenoidale, the squama, the mandibule and the scapula as new bone formation on both femora and tibiae. These signs could be an indicator for Möller-Barlow disease (Ortner 2003, Brickley and Ives 2008, Stark in press). As scurvy is associated with an insufficient intake of vitamin C, malnutrition must be assumed. A reason might be the geographic location or/and a harsh climat with crop failure and famine the first settler had to face. Besides the morphological diagnose amino acids of the bone collagen have been analyzed (Kramis et. al.). Further examinations, such as radiocarbon dating and stable isotope ratios (C, N, O, S) to specify nutrition, are planned.

Möller-Barlow disease in archaeology: Preliminary study of biochemical detection

Human bone is the most direct source for reconstructing health and living conditions of ancient populations. However, many diseases remain undetected in palaeopathology. Möller-Barlow disease (scurvy) is a historically well-documented metabolic disease and must have been common in clinical and sub-clinical severity. Due to long incubation periods and the subtle nature of bone changes osteological evidence is relatively rare (Brickley & Ives 2008). Möller-Barlow disease is caused by deficiency of dietary vitamin C (ascorbic acid) and evokes symptoms like fatigue, haemorrhage, inflammations, delayed wound healing and pain. Vitamin C is a cofactor for the hydroxylation of the amino acids proline and lysine which are essential for the production of intact connective tissue by cross-linking the propeptides in collagen. In a preliminary study we tested the detectability of Möller-Barlow disease by analysis of relative quantitative variability of hydroxylated amino acids in collagen (Pendery & Koon 2013). Samples (N=9) were taken from children with (n=3, cranium, femur, tibia) and without (n=4, cranium, femur, tibia) apparent bone reactions indicative of Möller-Barlow disease, as well as from adults with lethal traumata (n=2; negative controls). The skeletal remains originated from two early medieval cemeteries from Switzerland. Gas chromatographic (GC) analysis revealed minor differences between the samples. So far children with no pathologic alterations had fairly same values as negative controls while children with bone reactions paradoxically exhibited even slightly higher values of hydroxyproline and hydroxylysine. Future research demands for larger sample size and has to discuss sampling strategies. Beside possible misdiagnosis of Möller-Barlow disease it is arguable if only the newly built bone should be analysed even though this could lead to problems related to small sample quantity. It also remains to be seen to which extent varying turnover rates of different skeletal elements, especially in children, must be taken into account.

Jewish antiquities : or, a course of lectures on the three first books of Godwin's Moses and Aaron, to which is annexed a Dissertation on the Hebrew language

by David Jennings

Aaron Aaronsohn zum Gedächtnis

a. b.

Moses im Gebet während der Schlacht gegen die Amalekiter, unterstützt von Aaron und Chur [Illustration] : Gruppe

Christian Rauch

Chief-Rabbi Aaron Hart [Illustration] : (Porträt)

Scan von Monochrom-Mikroform

Israel Aaron, Hoffaktor des Großen Kurfürsten und Begründer der Berliner Gemeinde

Oswald Lassally

Aaron Hakohen und sein Ritualwerk Orchot Chajim : ein literarhistorischer Versuch

Heinrich Gross

Aaron Hakohen und sein Ritualwerk Orchot Chajim : ein literarhistorischer Versuch

Heinrich Gross

Meyer Aaron Goldschmidt

Georg Morris Cohen Brandes