Thus we read these lines in the manuscripts and in the printed editions ; thus the lines were read in the Middle Ages and, perhaps, already in antiquity.

Thus we read these lines in the manuscripts and in the printed editions ; thus the lines were read in the Middle Ages and, perhaps, already in antiquity.

Thus we read these lines in the manuscripts and in the printed editions ; thus the lines were read in the Middle Ages and, perhaps, already in antiquity.

This famous passage has given rise to much discussion and some perplexity. Theodoras the mathematician is represented by Theaetetus as proving the irrationality of the square roots of the numbers from 3 to 17: ‘He took the separate cases up to the root of 17 square feet; and there, for some reason, he stopped.’ The passage is of great importance in the history of Greek mathematics for more than one reason. Theaetetus is said to have generalized the proof of the (...) irrationality of square roots of non-square integers; and thus his connexion with this passage is important because Plato here obviously implies that Theodorus was not giving a generalized proof—otherwise, why should he go up to 17 ? If Theodorus did not know the generalized proof, he clearly had to proceed by enumeration and proof of particular case. (shrink)

It is the purpose of these notes to make a contribution towards solving a problem the difficulty of which has inhibited all modern editors of the Silvae: the apparent impossibility of establishing a satisfactory relation between the Madrid manuscript and the readings noted by Politian in his copy of the first edition now in the Corsinian library in Rome. It is the task of the editor to draw up a stemma that would reconcile the evidence of our text with the (...) testimony of the great humanist. (shrink)

In a recent issue of this journal Professor P. Thielscher criticizes my hypothesis concerning the manuscript tradition of the Silvae of Statius. He censures me for what he calls my ‘errors’ and ‘mistakes’. Here are my answers.

This famous passage has given rise to much discussion and some perplexity. Theodoras the mathematician is represented by Theaetetus as proving the irrationality of the square roots of the numbers from 3 to 17: ‘He took the separate cases up to the root of 17 square feet; and there, for some reason, he stopped.’ The passage is of great importance in the history of Greek mathematics for more than one reason. Theaetetus is said to have generalized the proof of the (...) irrationality of square roots of non-square integers; and thus his connexion with this passage is important because Plato here obviously implies that Theodorus was not giving a generalized proof—otherwise, why should he go up to 17? If Theodorus did not know the generalized proof, he clearly had to proceed by enumeration and proof of particular case. (shrink)

It is the purpose of these notes to make a contribution towards solving a problem the difficulty of which has inhibited all modern editors of theSilvae: the apparent impossibility of establishing a satisfactory relation between the Madrid manuscript and the readings noted by Politian in his copy of the first edition now in the Corsinian library in Rome. It is the task of the editor to draw up a stemma that would reconcile the evidence of our text with the testimony (...) of the great humanist. (shrink)

Este trabajo discute una reciente propuesta para identificar a conversos al Islam en al- Andalus basada en su onomástica tal y como ésta se conserva en los diccionarios biográficos árabes del medievo. Se propone demostrar que esta propuesta no es viable en la práctica y, como consecuencia de ello, que no se puede identificar a tales conversos de forma que puedan someterse a un análisis estadístico.

El artículo analiza un pasaje autobiográfico de la vida de al-Ṭurṭūšī (c. 451/1059-520/1126, o Ŷumādā al-awwal 525/abril de 1131) contenido en el Siyar A‘lām al-Nubalā’ de al-Ḏahabī (673/1274-748/1348). El texto informa sobre una notable serie de fenómenos meteorológicos acaecidos durante la visita de al-Ṭurṭūšī a Bagdad en 478/1085-86. Fierro interpretó la historia como la descripción de un eclipse y como el origen del cambio de al-Ṭurṭūšī hacia el ascetismo, paralela a una historia similar sobre el anterior Muḥammad Iḅn Waḍḍāḥ. Aquí (...) demuestro, basado en registros astronómicos, que no hubo eclipse en aquel tiempo en Bagdad, por lo que en consecuencia, lo que al-Ṭurṭūšī experimentó no pudo haber sido tal. Además, al-Ṭurṭūšī tampoco lo entendió así. No pudo, por lo tanto, haber sido la causa de su vuelta al ascetismo. La descripción apunta más bien a una tormenta de polvo o simún. Por lo tanto, no hay vínculo alguno, literario o de otro orden, entre este punto de la vida de al-Ṭurṭūšī y el de Muḥammad Iḅn Waḍḍāḥ. (shrink)

The period between the fall of the Umayyads of Cordoba and the emergence of the successor states in the Iberian peninsula is shadowy and unclear. In this article, I attempt to offer a micro-study of the process in one place. Using literary and numismatic sources, I attempt a reconstruction of events in and connected with Toledo, and of the list of rulers who were active there, in the first two decades of the fifth Islamic century. This list is much longer (...) than was previously suspected. Because of the importance of Toledo as a frontier city, it is particularly important to know something of the process of the transfer of authority there at this time. Most of the local leaders seem not to have atributed much importance to the city; the local population, on the other hand, seems to have been willing to accept virtually any ruler who might protect them against the threat of Christian encroachment. The study shows the potential value of micro-studies in illuminating broader issues, such as factional in-fighting in such cifies, but it also brings out the metropolitan bias and other limitations of our sources. In three appendices I look at numismatic evidence for two of these newly identified rulers, at a textual crux in the anonymous Fath al-Andalus, and at a difficult passage in the Naqt al-‛Arūs of Ibn Hazm. (shrink)