A Matemática na Natureza

[...]. Fibonacci destacou-se ao escrever o livro Liber Abaci, em 1202, a primeira obra importante sobre matemática desde Eratóstenes. Neste seu livro, Fibonacci coloca um problema, a partir da observação do crescimento de uma população de coelhos: "num pátio fechado coloca-se um casal de coelhos. Supondo que em cada mês, a partir do segundo mês de vida, cada casal dá origem a um novo casal de coelhos, ao fim de um ano, quantos casais de coelhos estão no pátio?" A resolução desse problema deu origem à famosa sucessão (ou sequência) de Fibonacci (ou os números de Fibonacci): 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,... outra razão apontada para a projeção mundial de Fibonacci. [...].

A democracia na teoria do direito constitucional

Texto incluído na obra colectiva "Liber Amicorum em homenagem ao Prof. Doutor João Mota de Campos, Coimbra: Coimbra Editora, 2013, 467-502 pp.

Le Protévangile de Jacques latin dans l'homélie Inquirendum est pour la fête de la Nativité de Marie

L'article est le fruit d'une recherche sur la survie du Protévangile de Jacques en latin. Il contient l'édition critique et la traduction d'une homélie pour la fête de la Nativité de Marie, désignée par son incipit, Inquirendum est, et conservant les ch. 1-8 du Protévangile de Jacques (PJ). Dans trois des six manuscrits utilisés pour l'édition, l'homélie fait partie d'un recueil de sermons de l'époque carolingienne, l'« Homéliaire de Saint-Père de Chartres ». Elle a été composée en même temps que cet homéliaire, entre 820 et 950, dans un milieu marqué par des échanges entre l'Angleterre et la France. L'auteur de l'homélie a inséré dans un cadre homilétique les ch. 1-8 du PJ. Il a utilisé une version latine amplifiée du Protévangile (traduction II), dont dépendent également plusieurs autres témoins: le manuscrit de Paris, Sainte-Geneviève 2787 (PJlatG); les Latin Infancy Gospels édités par M. R. James (JAr et JHer, formes Arundel et Hereford de la « compilation J »); le récit irlandais de l'enfance du Liber Flavus Fergusiorum (InfLFF). Certaines amplifications du récit primitif sont présentes dans l'ensemble de ces témoins, comme l'épisode de la révélation céleste du nom de Marie (traduction IIa). D'autres sont communes à l'homélie, à JAr-JHer et/ou à InfLFF, comme l'ordre supplémentaire donné par Joachim à ses bergers (traduction IIb). A côté de ces éléments traditionnels, l'article met en évidence une série de particularités rédactionnelles (omissions, retouches, additions). L'auteur de l'homélie tient notamment à souligner le caractère naturel de la conception de Marie.

Apocrypha Hiberniae. I. Evangelia infantiae

In 1927 M. R. James published Latin Infancy Gospels, identified by him in two related but not identical manuscripts (one the British Library Arundel 404; the other from Hereford), together with a parallel text from the Irish manuscript known as the Leabhar Breac. Later researches brought to light more manuscripts of this Latin work, and also of the Irish text. James recognized that his apocryphal Latin Infancy text was compiled from a combination of the Protevangelium of James and a hitherto unknown text which he named "The Source". Recent research has identified a full Latin translation of the Protevangelium of James. A hitherto unrecognized Irish Infancy Narrative has also been identified in the Dublin manuscript known as the Liber Flavus Fergusiorum. A deep study of this related tradition was called for. This has been carried out over the past ten years by an Irish team in conjunction with Professor Daniel Kaestli and AELAC. The fruits of this labour are published in these two volumes. Volume 13 has a general introduction with a historical sketch of New Testament apocrypha in Ireland and a history of research on the subject. This is followed by a comparison of the Infancy Narratives in the Leabhar Breac and the Liber Flavus Fergusiorum. There are special introductions to these Infancy texts, followed by critical editions of the Irish texts, accompanied by English translations and rich annotation. Next there is similar treatment of the Irish versified Narrative (from ca. 700) of the Childhood Deeds of Jesus (commonly known as the Infancy Narrative (or Gospel) of Thomas. There is then (in volume 14, but with continuous pagination) the edition and translation of an Irish thirteenth-century poem with elements from Infancy Narratives, and both Latin and Irish texts on the wonders at Christ's birth, accompanied by translations and notes. The edition of the Irish material is followed by a critical edition of the full Arundel and Hereford forms of the Infancy Narrative (here referred to as the "J Compilation"), together with a detailed study of all the questions relating to this work. The volume concludes with a critical edition (by Rita Beyers) of the Latin text of the Protevangelium of James, accompanied by a detailed study of the work.. The work contains a detailed study of the Latin translations of the Protevangelium of James and the transmission of this work in the West. The "J Compilation" (a combination of the Protevangelium and texts of Pseudo-Matthew) can be traced back in manuscript transmission to ca. 800,and must have originated some time earlier. Behind it stands an earlier "I ("I" for Irish) Compilation" without influence from Pseudo-Matthew, the form found in the Irish witnesses. It is argued that M. R. James's "Source" may be of Judaeo-Christian origin and may really be the Gospel of the Nazoreans. Among the indexes there is a list of all the Irish words found in the texts. This edition of the Irish and related Latin texts is a major contribution to the study of the apocryphal Infancy Narratives. It should also be of particular interest to Celtic scholars, to students of Irish ecclesiastical learning, and in general to all medievalists.

The Irish Infancy Narratives and their Relationship with Latin Sources

(Résumé de l'ouvrage) In 1927 M. R. James published Latin Infancy Gospels, identified by him in two related but not identical manuscripts (one the British Library Arundel 404; the other from Hereford), together with a parallel text from the Irish manuscript known as the Leabhar Breac. Later researches brought to light more manuscripts of this Latin work, and also of the Irish text. James recognized that his apocryphal Latin Infancy text was compiled from a combination of the Protevangelium of James and a hitherto unknown text which he named "The Source". Recent research has identified a full Latin translation of the Protevangelium of James. A hitherto unrecognized Irish Infancy Narrative has also been identified in the Dublin manuscript known as the Liber Flavus Fergusiorum. A deep study of this related tradition was called for. This has been carried out over the past ten years by an Irish team in conjunction with Professor Daniel Kaestli and AELAC. The fruits of this labour are published in these two volumes. Volume 13 has a general introduction with a historical sketch of New Testament apocrypha in Ireland and a history of research on the subject. This is followed by a comparison of the Infancy Narratives in the Leabhar Breac and the Liber Flavus Fergusiorum. There are special introductions to these Infancy texts, followed by critical editions of the Irish texts, accompanied by English translations and rich annotation. Next there is similar treatment of the Irish versified Narrative (from ca. 700) of the Childhood Deeds of Jesus (commonly known as the Infancy Narrative (or Gospel) of Thomas. There is then (in volume 14, but with continuous pagination) the edition and translation of an Irish thirteenth-century poem with elements from Infancy Narratives, and both Latin and Irish texts on the wonders at Christ's birth, accompanied by translations and notes. The edition of the Irish material is followed by a critical edition of the full Arundel and Hereford forms of the Infancy Narrative (here referred to as the "J Compilation"), together with a detailed study of all the questions relating to this work. The volume concludes with a critical edition (by Rita Beyers) of the Latin text of the Protevangelium of James, accompanied by a detailed study of the work.. The work contains a detailed study of the Latin translations of the Protevangelium of James and the transmission of this work in the West. The "J Compilation" (a combination of the Protevangelium and texts of Pseudo-Matthew) can be traced back in manuscript transmission to ca. 800,and must have originated some time earlier. Behind it stands an earlier "I ("I" for Irish) Compilation" without influence from Pseudo-Matthew, the form found in the Irish witnesses. It is argued that M. R. James's "Source" may be of Judaeo-Christian origin and may really be the Gospel of the Nazoreans. Among the indexes there is a list of all the Irish words found in the texts. This edition of the Irish and related Latin texts is a major contribution to the study of the apocryphal Infancy Narratives. It should also be of particular interest to Celtic scholars, to students of Irish ecclesiastical learning, and in general to all medievalists.