European Renaissance was characterized by an unprecedented growth of information determined by discoveries of ancient texts and distant places, technological advancements, and a new attitude towards human culture and history. This growth urged scholars to reconsider the traditional schemas used to organize knowledge, and in doing so they were more often than not put at odds with a past that they were trying simultaneously to recover and challenge. The case of Francesco Maurolico is a prime example of the tension between tradition and innovation that marked Renaissance thinking: fully committed to the recovery of ancient mathematical knowledge and acutely aware of his own original contributions to the discipline, throughout his career Maurolico sought to hammer out a model of classification that could accommodate new mathematical content in a largely traditional structure. By analyzing Maurolico’s failed attempts at devising a satisfactory model, the essay aims to show how, during the Renaissance, mathematical research impacted culture at large, thus decisively contributing to the shaping of modernity.
Il saggio ricostruisce l’eccezionale esperimento educativo condotto dagli scolopi a Firenze nella prima metà del Seicento, con la fondazione della scuola di matematica ispirata al pensiero galileiano. In un contesto culturale dominato dall’aristotelismo e da forti resistenze ecclesiastiche, l’ordine calasanziano promosse un’educazione scientifica innovativa, fondata su matematica, astronomia e scienze sperimentali. Figura centrale fu Famiano Michelini, in stretto contatto con Galileo e il suo circolo, affiancato da altri scolopi come Clemente Settimi e Angelo Morelli. Nonostante pressioni e denunce da parte dell’Inquisizione, la scuola formò intellettuali di rilievo, tra cui Vincenzo Viviani, e contribuì alla nascita dell’Accademia del Cimento. Il testo analizza anche l’evoluzione dell’eredità galileiana tra XVII e XVIII secolo, mostrando come la scuola fiorentina lasciò un’impronta duratura nell’identità educativa degli scolopi, influenzando la cultura scientifica del Granducato di Toscana e oltre.
This essay examines Celestino Cominale’s (1722–1785) self-proclaimed ‘anti-Newtonianism’. Between 1754 and 1770, Cominale published four volumes under the title of Anti-Newtonianismi, in which he launched a sustained attack on Newton’s natural philosophy. Despite a modest resurgence of interest in his work, Cominale’s critique has largely been overlooked and is often dismissed as an isolated, provincial, and misguided attack on Newton’s theories. This article seeks to offer a comprehensive account of Cominale’s critique of Newton’s natural philosophy, with a particular focus on the opening chapters of the second volume of Anti-Newtonianismi. It will be shown that Cominale was deeply engaged with contemporary debates surrounding Newton’s natural philosophy and, at times, advanced original and insightful criticisms of Newton’s natural philosophical method.
Christoph Clavius’ Latin translation of Euclid’s Elements is studied by applying standard and less standard tools of computational linguistics. Clavius’ lexical choices are compared with the relevant Greek and Latin editions and translations. We shall thereby assess Clavius’ treatment of Latin sources, as well as his specific, scholarly aims and his general strategy.
The Latin and German commentaries on the first six books of the Elements by Johann Scheubel (1494-1570), professor at the University of T & uuml;bingen, and Wilhelm Xylander (1532-1576), professor at the University of Heidelberg, stand out within the sixteenth-century Euclidean tradition by their extensive use of arithmetic and cossic algebra (in the tradition of Christoff Rudolff and Michael Stifel) in their respective exposition of Euclid's geometrical propositions, which was primarily connected with their Protestant background and pedagogical context. By analysing Scheubel and Xylander's commentaries and their numerical approach to Euclid's geometrical propositions, this article aims to offer an insight into the evolution of the arithmetization of Euclidean geometry in early modern Europe.
Historical research on refraction in the modern era has often focused on the question of attributing the law of refraction to Descartes, Snel and Harriott. The discovery of Ibn Sahl’s work has put an end to the dispute over priority between these authors, leaving another problem largely unnoticed: most of the literature refers to this discovery without distinguishing the native form of the statements on refraction from the current conception of the law of refraction. This anachronism is problematic. Ancient texts do not contain a single statement of the law of refraction as we know it today. Descartes’ contribution is in line with Maurolico’s and Kepler’s work on refraction. Like them, Descartes makes no mention of sines or refractive indices, nor does he formulate a physical law of refraction. Since these ideas developed gradually between the late 17th century and the 19th century, the recognition of a “law of sines” or a “law of refraction” is not an idea native to the 16th and 17th centuries. We suggest that the work of Descartes does not fit into the modern quest for the laws of nature, but rather into the framework of the theory of proportions.
The article deals with a group of letters authored by Paul Falconieri, a man of letters and a trusted figure of the Medici family in Rome. Preserved in the Galilean Collection of the National Central Library of Florence, the letters address a wide range of topics, some of them concerning family matters. Among the figure appearing in the correspondence are the Dutch publishers Elzevier and Blaeu: the former published the Discorsi e dimostrazioni matematiche (1638), while the latter planned to produce an edition of Galileo's works edited by Viviani, although this project was never realised.
This article argues that the Renaissance rediscovery of Greek mathematics functioned both as a stimulus to renewal and as a powerful constraint. The classical paradigm was not simply revived: it had to be reorganized and reinterpreted, yet its internal grammar-marked by tensions between form and extension, number and magnitude-continued to shape what could count as an admissible object and a legitimate proof. Francesco Maurolico provides the central case study, through his effort to construct a renewed framework for Archimedean geometry of measure-an effort that did not culminate in a stable synthesis, but instead exposed internal tensions within the classical framework. Galileo is used as a stress test: his attempt to mobilize the Euclidean theory of proportions for the description of motion reveals both the productivity and the limits of that inherited structure.
The paper provides a long-run overview of how the development of what we may term "proto-symbolic algebra" was profoundly shaped by the tradition of practical arithmetic, particularly as it evolved through abacus mathematics. Within this milieu, algebraic problem-solving techniques became increasingly sophisticated, and symbolic representations began to emerge. While the recovery of classical mathematical works provided an ideal of mathematical generality and abstraction, the mathematics practiced in abacus schools supplied computational techniques that were essential for the operationalization of algebra. Key figures such as Tartaglia, Cardano and Bombelli displayed influences of abacus mathematics in their algebraic works. The persistence of practical arithmetic techniques within these works suggests that the evolution of algebra was not a linear progression from classical to modern mathematics but rather a complex synthesis of diverse traditions.
The French historian & Eacute;lisabeth Labrousse dedicated a monograph to the solar eclipse of 1654, an event that sparked widespread debate and panic across Europe, including in Poland and the Grand Duchy of Lithuania. This study examines predictions related to the eclipse in: the work of Andrea Argoli, the European almanacs and calendars, the prognostication by the German astrologer Stefan Furman as well as the contemporary discussions in Poland and the Grand Duchy of Lithuania. Special attention is given to the role of astrology in elite society, particularly its connection to war prophecies. The eclipse became a focal point for clergy, nobility, and astrologers, whose interpretations varied dramatically. Forecasts of imminent wars and epidemics exacerbated apocalyptic fears, with many perceiving war as a literal apocalypse.
The sixteenth-century revival of Greek mathematics followed multiple-often divergent-paths. This paper explores the distinct yet complementary approaches of Francesco Maurolico and Federico Commandino to Apollonius' Conics, focusing on the editorial strategies and innovations each introduced in their Latin editions. Special attention is paid to how each mathematician engaged with both the textual content and the geometrical diagrams, revealing two modes of Renaissance mathematical humanism that would later shape the seventeenth-century reception ofApollonius.
Who compares Euler's algebra with that of al-Khw & amacr;rizmi will see more differences than kinship. Al-Khw & amacr;rizmi uses natural language, while Euler calculates within the syntax of algebraic symbolism. Al-Khw & amacr;rizmi has a single unknown (a word), Euler as many as he needs, represented by non-linguistic signs. Al-Khw & amacr;rizmi deals with the unknown and its second power, Euler knows no limits. Al-Khw & amacr;rizmi's coefficients are numerically fixed, those of Euler may have undetermined values. When al-Khw & amacr;rizmi operates on a composite expression, he needs roundabout ways; Euler has the parenthesis. The parenthesis mostly goes unmentioned when the characteristics of the "new algebra" are discussed. The rest is familiar. However, the unfolding of the various characteristics is largely left in the dark. The whole seems to have emerged fully grown from the minds of Vi & egrave;te and Descartes. The aim of the paper is to trace the emergence of the various characteristic features of the New Algebra from the 14th-century beginnings of abbacus algebra. The process is far from linear-- before the arrival of German co ss we cannot even speak of "stops and goes" on the road toward some aim. After Christoph Rudolff we probably can; in this final phase, the mostly neglected roles of Michael Stifel and Valentin Mennher are taken up.
Federico Cesi's Museum, whose inventory is transcribed here in its entirety for the first time, is in constant dialogue with the Library. Through the study of the Lincean sources, which attribute so much importance to the ars pingendi, the writing contextualizes the various inventory items, by analizying the events that influence the history of the Academia and by proposing some new documents on the legacy of the Cesi family.
This project examines the life and experimental/ domestic writing of Lady Venetia Digby (n & eacute;e Stanley; 1600-1633), including the context ofher marriage to Sir Kenelm Digby, an original member of the Royal Society. Lady Digby has largely been lost to history beyond her social and familial roles. She is remembered for her beauty and possible adultery, but rarely as a medical practitioner, or as a participant in the developing scientific world of seventeenth-century London. This article will seek to reattribute Wellcome MS. 7391 to Lady Digby, and use that manuscript (in the context of a larger primary archive and social network mapping) to reconstruct her role as an experimenter and medical practitioner. By undertaking this analysis, the study aims to demonstrate that women like Lady Digby were not only present but actively engaged in the scientific, cultural, and institutional networks of seventeenth-century England.
Galileo's interest in the nature and composition of wine, summarised in the saying "wine is a compound of humour and light" that is often ascribed to him, provided the basis for the research of the subsequent generation of scientists. These scientists had learned from their master how to approach the physics of wine in mechanistic and corpuscularian terms. Lorenzo Magalotti, Francesco Redi and Giuseppe Del Papa further developed this theme through a reflection and detailed analysis of the particulate structure of matter, the corporeal nature of light and the innumerable unsolved questions concerning the study of the apparati and organic functions ofbodies, as well as good dietetic and therapeutic practices.
InAstronomia Danica, Longomontanus provides a method for calculating the terrestrial longitude for a given location on Earth. To do so, he relies on precise calculations of the lunar position so that he can know when he is observing it without any parallax in longitude. As I will show, this method has a fatal flaw that renders it unusable. However, Longomontanus also provides a simple observational method that indicates, via the disposition of the lunar spot and/or horns, the time when the Moon shows no parallax in longitude. This last method, though it does not need any use of tables, also has some problems. In this paper Iwill explain in detail these methods provided by Longomontanus, together with the problems they carry.
Despite being the first woman to attend a meeting of the Royal Society, Margaret Cavendish (1623-1673) was denied membership. Her exclusion from these inner circles prevented her from participating in rigorous debates about her work and the work of her contemporaries. Although she was not invited into these conversations, she nevertheless entered them by imagining the kinds of objections her opponents would raise and publishing her responses in the form of an inner discourse. Inner discourse, here, describes a written dialogue where an author argues with themselves. This paper explores Cavendish’s use of inner discourse across three genres: philosophical prose, letter writing, and science-fiction. Ultimately, I argue that inner discourse as a literary device, for Cavendish, serves not only as a way to overcome social barriers, but also as an argument, by demonstration, against members of the Royal Society who believed that natural philosophy should be done primarily through experiments.
