Viète's Controversy with Clavius Over the Truly Gregorian Calendar

Some twenty years after the Gregorian calendar reform, towards the end of his life, François Viète published his own calendar proposal. This treatise contains a sharp attack against the Jesuit scholar Clavius, the mathematical mind behind the reform. Understandably enough, Clavius prepared a negative reply. Viète heard of it and exploded in a fit of rage, ``I demonstrated that you are a false mathematician [ . . . ], and a false theologian.'' Sadly, Clavius' rejection, added as a chapter to his monumental apology of the Gregorian reform, appeared when Viète had already passed away.Viète seriously believed that the true aim of the Gregorian reform has been betrayed and he was furious about some logical inconsistencies which he claimed to have found in Clavius' calendar. Clavius apparently confused solar day and epactal day (or ``tithi''), the thirtieth part of a lunar month. This is the very core of Viète's attack against Clavius whom he accused of having introduced a false lunar period (``falsa periodus lunaris''). But his own work has some logical inconsistencies too. For instance, he reproaches Clavius for having introduced lunar months of 31 days which, indeed, are unrealistic. Grievously, his own rules can likewise give rise to lunations of unnatural lengths.In order to understand these subtle twists reader and author must work largely through both Clavius and Viète's methods of Easter reckoning. The fruit of all those efforts might be an insight into Viète's clear mathematical thinking. His calendar, however, was never considered.     

The Science of Magnetism Before Gilbert Leonardo Garzoni's Treatise on the Loadstone

This paper presents the main features of the treatise on magnetism written by the Jesuit Leonardo Garzoni (1543–92). The treatise was believed to be lost, but a copy of it has been recently recovered. The treatise is briefly described and analysed. The results of a comparison between Garzoni's treatise, Della Porta's Magia Naturalis (1589), and Gilbert's De Magnete (1600) are also summarized. As claimed in the seventeenth century by Niccolò Cabeo and Niccolò Zucchi, the treatise contains quite a lot of the material to be found subsequently in the Magia Naturalis and in the De Magnete. Most importantly, the treatise presents so many interesting features, well before Gilbert's work, which make it the first example of a modern treatment of magnetic phenomena.     

Between Viète and Descartes: Adriaan van Roomen and the <Emphasis Type="Italic">Mathesis Universalis</Emphasis>

Adriaan van Roomen published an outline of what he called a Mathesis Universalis in 1597. This earned him a well-deserved place in the history of early modern ideas about a universal mathematics which was intended to encompass both geometry and arithmetic and to provide general rules valid for operations involving numbers, geometrical magnitudes, and all other quantities amenable to measurement and calculation. ‘Mathesis Universalis’ (MU) became the most common (though not the only) term for mathematical theories developed with that aim. At some time around 1600 van Roomen composed a new version of his MU, considerably different from the earlier one. This second version was never effectively published and it has not been discussed in detail in the secondary literature before. The text has, however, survived and the two versions are presented and compared in the present article. Sections 1–6 are about the first version of van Roomen’s MU the occasion of its publication (a controversy about Archimedes’ treatise on the circle, Sect. 2), its conceptual context (Sect. 3), its structure (with an overview of its definitions, axioms, and theorems) and its dependence on Clavius’ use of numbers in dealing with both rational and irrational ratios (Sect. 4), the geometrical interpretation of arithmetical operations multiplication and division (Sect. 5), and an analysis of its content in modern terms. In his second version of a MU van Roomen took algebra into account, inspired by Viète’s early treatises; he planned to publish it as part of a new edition of Al-Khwarizmi’s treatise on algebra (Sect. 7). Section 8 describes the conceptual background and the difficulties involved in the merging of algebra and geometry; Sect. 9 summarizes and analyzes the definitions, axioms and theorems of the second version, noting the differences with the first version and tracing the influence of Viète. Section 10 deals with the influence of van Roomen on later discussions of MU, and briefly sketches Descartes’ ideas about MU as expressed in the latter’s Regulae.     

Radical mathematical Thomism: beings of reason and divine decrees in Torricelli’s philosophy of mathematics

Evangelista Torricelli (1608-1647) is perhaps best known for being the most gifted of Galileo’s pupils, and for his works based on indivisibles, especially his stunning cubature of an infinite hyperboloid. Scattered among Torricelli’s writings, we find numerous traces of the philosophy of mathematics underlying his mathematical practice. Though virtually neglected by historians and philosophers alike, these traces reveal that Torricelli’s mathematical practice was informed by an original philosophy of mathematics. The latter was dashed with strains of Thomistic metaphysics and theology. Torricelli’s philosophy of mathematics emphasized mathematical constructs as human-made beings of reason, yet mathematical truths as divine decrees, which upon being discovered by the mathematician ‘appropriate eternity’. In this paper, I reconstruct Torricelli’s philosophy of mathematics—which I label radical mathematical Thomism—placing it in the context of Thomistic patterns of thought.     

John case on art and nature

John Case (d. 1600), the most important English Aristotelian of the Renaissance period, has not yet received the attention he deserves. In his Lapis philosophicus (Oxford, 1599), an exposition of Aristotle's Physics, is found a discussion of the relation of nature to art which parallels in many ways that formulated a few years later in the writings of Francis Bacon. Case argues, in a way more reminiscent of the works of Giambattista della Porta than of those of Aristotle, that the natural philosopher can legitimately apply the productive arts in helping nature to fulfill her function. Moreover, while rejecting the excessive claims of the Paracelsians, Case does accept the transmutational claims of the alchemists. In the final analysis, his ‘Aristotelianism’ has been tempered by the tradition of Renaissance natural magic. Like many other Peripatetic thinkers of the period, Case shows himself to be an eclectic, drawing materials from a wide variety of sources and open to many of the new scientific tendencies then developing.     

Interprétation chymique de la création et origine corpusculaire de la vie chez Athanasius Kircher

The famous Jesuit father Athanasius Kircher (1602–1680) tried to interpret the Creation of the world and to explain the origin of life in the last book of his geocosmic encyclopedia, Mundus subterraneus (Amsterdam, 1664–1665). His interpretation largely depended on the ‘concept of seeds’ which was derived from the tradition of Renaissance ‘chymical’ (chemical and alchemical) philosophy. The impact of Paracelsianism on his vision of the world is also undeniable. Through this undertaking, Kircher namely developed a corpuscular theory for the spontaneous generation of living beings. The present study examines this theory and its relationship with Kircher's chymical interpretation of the Creation in order to place it in its own intellectual and historical context and will uncover one of its most important sources.     

Chu Shih-chieh's Suan-hsüeh ch'i-meng (introduction to mathematical studies)

Conclusion The multi-faceted content of the SHCM and its collection of rules and tables made it an important mathematical work not only in China, but also in Korea and Japan. This book clearly demonstrated Chu's predominant interest in the field of algebra and his contribution to the solution of numerical equations of higher degree, which was a prelude to his famous treatise the Ssu-yüan yü-chien.     

The Lighthouse and the Observatory: Islam,Science, and Empire in Late Ottoman Egypt

Well-known in his day, but overlooked since, Erasmus King lectured in natural and experimental philosophy from the 1730s until 1756 at his Westminster home and twenty other venues, publicizing his frequent courses exclusively in the Daily Advertiser. In 1739 he escorted Desaguliers's youngest son to Russia, hoping to demonstrate experimental philosophy to the Russian empress. En route, he conducted trials with a sea-guage in the Baltic which were reported by Stephen Hales in his Statical Essays. Various sources testify to King's subsequent experimental research for Hales in the fields of anatomy, respiration and electricity. There is recorded evidence for the exceptional range and quality of King's scientific apparatus and models.     

The introduction of the differential notation to Great Britain

In the history of chemistry, the Danish chemist Julius Thomsen (1826–1909) is best known for his contributions to thermochemistry. Throughout his life, he was a pronounced atomist and a tireless advocate of neo-Proutian views as to the constitution of matter. On many occasions, especially in his later years, he engaged in speculations concerning the unity of matter and the complexity of atoms. In this engagement, Thomsen was alone in Danish chemistry, but his works were representative of a large number of 19th-century chemists, particularly in England and Germany. Thomsen's ideas as to the constitution of matter, the periodic system and the noble gases, may be seen as typical of this vigorous trend in fin de siècle chemistry.     

The genesis of a mediaeval historian: Pierre Duhem and the origins of statics

Contrary to what might be expected given a religious or other motivation, Pierre Duhem's interest in mediaeval science was the result of his surprise encounter with Jordanus de Nemore while working on Les origines de la statique in the late autumn of 1903. Historical assumptions common among physicists at that time may explain this surprise, which occasioned a frantic search for more mediaeval precursors for Renaissance mechanics. It also raised serious historiographical problems that threatened even his methodological views, until they were resolved in his To save the phenomena of 1908.     

The Instrument That Never Was: Inventing,Manufacturing, and Branding Réaumur's Thermometer During the Enlightenment

At the beginning of the 1730s René Antoine Ferchault de Réaumur published two long memoirs on a new type of thermometer equipped with a specially calibrated scale — known ever since as the Réaumur scale. It became one of the most common ‘standardized’ thermometers in Europe until the late nineteenth century. What made this thermometer so successful? What was it specifically? I will first argue that the real Réaumur thermometer as an instrument was a fiction, a ghost — an idealized instrument. On paper, it was theoretically flawless. In reality, the standardized Réaumur thermometer was most likely never achieved. This article shows that its success was essentially due to a recontextualisation from theoretical natural philosophy — Réaumur's principle of uniformity — to: 1) the context of artisanal knowledge and practices and 2) the context of making and reporting in the Mémoires de l'Académie royale des sciences actual measurements done in the field (in Paris at the Observatory, in Provincial France, in the Colonies, and in the rest of Europe). Réaumur's thermometer was essentially a theoretical method to which was associated a particular scale. It was the instrument's reification for market consumption and fieldwork that gave this specific type of thermometer materiality and authority. Although most Réaumur thermometers ever made were strikingly different from one another, over time the thermomètre de Réaumur designation became a brand, a seal of approval born from customary artisanal practices and cultural habitudes.     

The Definitions of Fundamental Geometric Entities Contained in Book I of Euclids Elements

OElig;he thesis is sustained that the definitions of fundamental geometric entities which open Euclids Elements actually are excerpts from the Definitions by Heron of Alexandria, interpolated in late antiquity into Euclids treatise. As a consequence, one of the main bases of the traditional Platonist interpretation of Euclid is refuted. Arguments about the constructivist nature of Euclids mathematical philosophy are given. (Received June 6, 1997)     

Theophrastus on Lyngurium: Medieval and Early Modern Lore from the Classical Lapidary Tradition

The ancient philosopher Theophrastus (c. 371-285 BC) described a gemstone called lyngurium, purported to be solidified lynx urine, in his work De lapidibus ('On Stones'). Knowledge of the stone passed from him to other classical authors and into the medieval lapidary tradition, but there it was almost always linked to the 'learned master Theophrastus'. Although no physical example of the stone appears to have been seen or touched in ancient, medieval, or early modern times, its physical and medicinal properties were continually reiterated and elaborated as if it did 'exist'. By the seventeenth century, it began to disappear from lapidaries, but with no attempt to explain previous authors' errors since it had never 'existed' anyway. In tracing the career of lyngurium, this study sheds some light on the transmission of knowledge from the classical world to the Renaissance and the changing criteria by which such knowledge was judged.