Through an in-depth analysis of the notes that Leibniz made while reading Pascal’s manuscript treatise on conic sections, we aim to show the real extension of what he called “hexagrammum mysticum”, and to highlight the main results he achieved in this field, as well as proposing plausible proofs of them according to the methods he seems to have developed.

In this paper we discuss in some depth the main theorems pertaining to Carnot’s theory of transversals, their initial reception by Servois, and the applications that Brianchon made of them to the theory of conic sections. The contributions of these authors brought the long-forgotten theorems of Desargues and Pascal fully to light, renewed the interest in synthetic geometry in France, and prepared the ground from which projective geometry later developed.

This is an attempt to explain Kepler’s invention of the first “non-cone-based” system of conics, and to put it into a historical perspective.

In 1813, J.-V. Poncelet discovered that if there exists a polygon of n-sides, which is inscribed in a given conic and circumscribed about another conic, then infinitely many such polygons exist. This theorem became known as Poncelet’s porism, and the related polygons were called Poncelet’s polygons. In this article, we trace the history of the research about the existence of such polygons, from the “prehistorical” work of W. Chapple, of the middle of the eighteenth century, to the modern approach of (...) P. Griffiths in the late 1970s, and beyond. For reasons of space, the article has been divided into two parts, the second of which will appear in the next issue of this journal. (shrink)

In this paper, we give a thorough account of Brianchon and Poncelet’s joint memoir on equilateral hyperbolas subject to four given conditions, focusing on the most significant theorems expounded therein, and the determination of the “nine-point circle”. We also discuss about the origin of this very rare example of collaborative work for the time, and the general challenge of finding the nature of the loci described by the centres of the conic sections required to pass through m points and to (...) be tangent to n straight lines given in position, m + n = 4, which was posed at the end of their work. In the case m = 4, i.e. when the conic sections have to pass through the vertices of a quadrilateral, the locus of centres is another conic section passing through the intersection points of the opposite sides and the two diagonals of the quadrilateral, respectively, and, as Gergonne showed analytically shortly after, through other significant points connected with the quadrilateral; this curve was later given the name of the “nine-point conic”, being a natural generalization of the above mentioned circle. (shrink)

Published here, and discussed, are some manuscripts and a letter of Sophie Germain concerning her work on Fermat’s Last theorem. These autographs, held at Bibliothèque Nationale of Paris, at the Moreniana Library of Florence and at the University Library of Göttingen, contribute to a substantial revaluation of her work on this subject.

The first part of the article appeared in the previous issue of this journal. It deals with the history of the research on Poncelet’s porism, and related subjects, which were developed from the middle of the eighteenth century until the end of the nineteenth century. In this second part, we take the research developed in the twentieth century. We also offer a comparison of the main works on the subject, and we draw some conclusions.

In this paper, we try to understand what considerations and possible sources of inspiration Desargues used to formulate his concepts of involution and transversal, and to state the related theorems that are at the basis of his Brouillon project. To this end, we trace some clues which are found scattered throughout his works, we connect them together in the light of his experience and knowledge in the field of perspective, and we investigate what were his motivations within Mersenne’s academy. As (...) a result of our research, we can safely say that were his great geometrical insight and his projective vision of space which, guided by some classical theorems, led him to these completely new concepts in the panorama of the geometry of that time that were destined to remain misunderstood for about two centuries. (shrink)

To solve the direct problem of central forces when the trajectory is an ellipse and the force is directed to its centre, Newton made use of the famous Lemma 12 that was later recognized equivalent to proposition 31 of book VII of Apollonius’s Conics. In this paper, in which we look for Newton’s possible sources for Lemma 12, we compare Apollonius’s original proof, as edited by Borelli, with those of other authors, including that given by Newton himself. Moreover, after having (...) retraced its editorial history, we evaluate the dissemination of Borelli's edition of books V-VII of Apollonius’s Conics before the printing of the Principia. (shrink)

In this paper, we describe the genesis of Boscovich’s Sectionum Conicarum Elementa and discuss the motivations which led him to write this work. Moreover, by analysing the structure of this treatise in some depth, we show how he developed the completely new idea of “eccentric circle” and derived the whole theory of conic sections by starting from it. We also comment on the reception of this treatise in Italy, and abroad, especially in England, where—since the late eighteenth century—several authors found (...) inspiration in Boscovich’s work to write their treatises on conic sections. (shrink)

This paper publishes the correspondence between S. Germain and C.F. Gauss. The mathematical notes enclosed in her letters are published for the first time. These notes, in which she submitted some of her results, proofs and conjectures to Gauss for his evaluation, were inspired by her study of the Disquisitiones Arithmeticae. The interpretation of these mathematical notes not only shows how deeply she went into Gauss’s treatise and mastered it long before any other mathematician, but also, more importantly, shows that (...) she obtained interesting results in the theory of power residues that have never previously been attributed to her. (shrink)

According to the actualist view, what is essential to the truth conditions of a future-tensed sentence ‘it will be the case that ϕ’ is reference to the unique course of events that will become actual. On the other hand, the modal view has it that the truth conditions of such a sentence require that the truth of ϕ be already “settled” at the time of utterance, where “being settled at time t” is defined by universal quantification over a domain of (...) courses of events, the futures compatible with what has happened up to time t. On the proposal we discuss in this paper, the actualist view and the modal view are seen as two related attitudes that speakers can have when they evaluate future-tensed sentences, and the corresponding interpretations undergo a unified semantic treatment based on a contextual notion of settledness. A central feature of our approach is a dynamic view of contexts of utterance, whereby the world of the utterance is not fixed once and for all, as different worlds, by the passing of time, can play this role in turn. Finally, one major goal of the paper is to show how the unified analysis we propose accounts for a particularly interesting interpretation of future-tensed sentences, often referred to as ‘epistemic reading’. (shrink)

Reseña de la obra de Rodolfo Gutiérrez y Andrea Mosquera. Devenires de un acontecimiento. Mayo del 68 cincuenta años después. Madrid: Cenaltes Ediciones, 2020.

Christoph Andreas Leonhard Creuzer (1768-1844), che dedicherà la propria vita alIa carriera ecclesiastica e aIle attività benefiche, pubblica nel 1793 - ancora giovane ed entusiasta della filosofia - un'opera che suscita un certo scalpore, le Considerazioni scettiche sulla libertà del volere, sulla quale prendono posizione, polernicamente, anche Fichte e Schelling. Pur accogliendo i princlpi della filosofia critica, Creuzer sostiene che l'idea di libertà come autonornia della volontà, quale Kant l'ha definita, conduca nienterneno che alio spinozismo, ossia alia negazione dei concetti (...) di imputazione, merito e colpa. Mascherandosi dietro uno scetticismo di comodo, Creuzer mostra corne tale conclusione spinoziana, a cui Kant ha tentato inutilmente di sottrarsi, sia l'esito obbligato tanto della sua filosofia teoretica quanto di quella pratica, che pure mirava in prima istanza a salvaguardare la responsabilità morale. (shrink)

El kitsch no es solo una categoría que ha definido una de las posibles gramáticas estéticas de la modernidad, sino también una dimensión antropológica que ha tenido diferentes configuraciones en el curso de los procesos históricos. El ensayo ofrece una mirada histórico-crítica sobre las transformaciones que condujeron desde el kitsch de principios del siglo XX hasta el neokitsch contemporáneo: desde la génesis del kitsch hasta su afirmación como una de las manifestaciones más tangibles de la cultura de masas. Integrándose con (...) la estética posmoderna, el kitsch se transforma en neokitsch, una estética que utiliza el kitsch como su propia sintaxis en el complejo escenario de la estética contemporánea. /// -/- Kitsch is not just a category that has defined one of the possible aesthetic grammars of modernity, but also an anthropological dimension that has had different configurations in the course of historical processes. The essay offers a historical-critical look at the transformations that led from the early twentieth century kitsch to the contemporary neokitsch: from the genesis of kitsch to its affirmation as one of the most tangible manifestations of mass culture. Integrating with postmodern aesthetics, kitsch turns into neokitsch, an aesthetic that deliberately uses kitsch as its own syntax in the complex scenario of contemporary aesthetics. (shrink)

In this paper, we describe the genesis of Boscovich’s Sectionum Conicarum Elementa and discuss the motivations which led him to write this work. Moreover, by analysing the structure of this treatise in some depth, we show how he developed the completely new idea of “eccentric circle” and derived the whole theory of conic sections by starting from it. We also comment on the reception of this treatise in Italy, and abroad, especially in England, where—since the late eighteenth century—several authors found (...) inspiration in Boscovich’s work to write their treatises on conic sections. (shrink)

El presente artículo plantea, partiendo de las vivencias de padres oyentes ante la llegada de un hijo sordo a partir de sus narraciones y experiencias de vida, por un lado, la comprensión de las etapas por las que atraviesan desde el momento en que se sospecha la existencia de la discapacidad de su hijo, hasta el momento en que es confirmada y asumida; por otro lado, describir los cambios que se producen al interior de la dinámica familiar ante la llegada (...) de un hijo en situación de discapacidad auditiva. (shrink)

Business Ethics: A European Review, EarlyView.

The study here is a qualitative research based on multiple case studies of banking service providers to analyze the role of corporate social responsibility (CSR) in the definition of the corporate identity of these kinds of organizations. The results show that, although companies increasingly integrate CSR into their business strategies, there are some aspects of its management such as its communication or the measurement of its results that detract from its success. These results have important implications for those managers pursuing (...) an effective management of CSR policies and strategies in their organizations, especially as the information comes from 6 of the biggest and most important banking institutions in a European country, with a declared assets (loans) volume which represents 62.75% of the total assets in the national banking industry, and thus largely representing the possible heterogeneity of the market in terms of company size, location, legal status, and management styles. (shrink)

The authors describe the intensity and orientation of the corporate social responsibility reporting in four Spanish industries and explore the relationship that exists between both concepts and an independent measurement of reputation for CSR. The results demonstrate that the CSR reporting is especially relevant and useful in the finance industry. Finance companies report significantly more CSR information than most industries in Spain, and this reporting is more closely linked to their CSRR than the CSR reporting of basic, consumer goods and (...) services industries. (shrink)

Although research on the corporate social responsibility (CSR) dimension of corporate image has notably increased in recent years, the definition and measurement of the concept for academic purposes still concern researchers. In this article, literature regarding the measurement of CSR image from a customer viewpoint is revised and areas of improvement are identified. A multistage method is implemented to develop and to validate a reliable scale based on stakeholder theory. Results demonstrate the reliability and validity of this new scale for (...) measuring customer perceptions regarding the CSR performance of their service providers. With regard to this, CSR includes corporate responsibilities towards customers, shareholders, employees and society. The scale is consistent among diverse customer cohorts with different gender, age and level of education. Furthermore, results also confirm the applicability of this new scale to structural equation modelling. (shrink)

Because previous scholars have offered few comprehensive models to understand the benefits of corporate social responsibility image in terms of customer behaviour, the authors of this paper propose a hierarchy of effects model to study how customer perceptions of the social responsibility of companies influence customer affective and conative responses in a service context. The authors test a structural equation model using information collected directly from 1,124 customers of banking services in Spain. The findings demonstrate that corporate social responsibility image (...) influences customer identification with the company, the emotions evoked by the company and satisfaction positively. Identification also influences the emotions generated by the service performance and customer satisfaction determines loyalty behaviour. The findings have significant implications for service managers because they demonstrate that there are two paths to explain the satisfaction and loyalty of service customers. The first path is composed of the beliefs and emotions generated by the company at the institutional level. The second path is composed of the thoughts, attitudes, emotions and feelings generated by the company’s services. (shrink)

During the last decades an intense debate has developed around the characterization of emotions, in which two approaches were presented as incompatible with each other: the somatic and the cognitive perspective of emotions. In this paper I propose to evaluate whether these are in fact irreconcilable positions, starting from the systematization of the theses that have identified each of these perspectives. Having disarticulated some points of divergence, I finally consider in what sense the debate remains irreducible.

"Mente e mondo", il libro che raccoglie le tanto celebrate quanto discusse "John Locke Lectures" di John McDowell, appartiene ad un genere filosofico classico, quello dell'"indagine sui poteri della mente umana". Secondo McDowell, un'indagine di questo tipo è necessaria alla risoluzione di alcuni fra i principali problemi epistemologici e semantici. Attraverso una dettagliata analisi dei lavori di McDowell ed un'approfondita discussione del problema del "seguire una regola" e del connesso paradosso di Kripke-Wittgenstein, questo volume cerca di dimostrare che la posizione (...) di McDowell è la conseguenza di una concezione errata delle nozioni normative ed una forma di quello che Sellars chiamava "Il mito del dato". (shrink)