tomus I. Physica generalis. (2 v) -- tomus II. Physica specialis. (2 v.).

Vydání Galileova Hvězdného posla vyvolalo okamžitou reakci mnoha evropských učenců, s jednou důležitou výjimkou, kterou tvořili jezuitští matematici Římské koleje pod vedením uznávaného matematika Christophora Clavia. Cílem článku je prozkoumat možné důvody opožděné reakce římských jezuitů, kteří se k nebeským objevům vyjádřili více než rok po vydání Galileovy knihy. Existují důkazy nasvědčující tomu, že i když byli římští matematici nakloněni uznání novinek odhalených teleskopem, nástrojem, který ještě musel dokázat svou důvěryhodnost, byli omezeni přísnými pravidly, která měla za úkol udržet jednotu (...) jezuitského řádu. (shrink)

I discuss two questions: (1) would Duhem have accepted the thesis of the continuity of scientific methodology? and (2) to what extent is the Oxford tradition of classification/subalternation of sciences continuous with early modern science? I argue that Duhem would have been surprised by the claim that scientific methodology is continuous; he expected at best only a continuity of physical theories, which he was trying to isolate from the perpetual fluctuations of methods and metaphysics. I also argue that the evidence (...) does not support the conclusion that early modern doctrines about mathematics and physics are continuous with the subalternation of sciences from Grosseteste, Bacon, and the theologians of fourteenth-century Oxford. The official and dominant context for early modern scientific methodology seems to have been progressive Thomism, and early modern thinkers seem to have pitted themselves against it. (shrink)

I discuss two questions: (1) would Duhem have accepted the thesis of the continuity of scientific methodology? and (2) to what extent is the Oxford tradition of classification/subalternation of sciences continuous with early modern science? I argue that Duhem would have been surprised by the claim that scientific methodology is continuous; he expected at best only a continuity of physical theories, which he was trying to isolate from the perpetual fluctuations of methods and metaphysics. I also argue that the evidence (...) does not support the conclusion that early modern doctrines about mathematics and physics are continuous with the subalternation of sciences from Grosseteste, Bacon, and the theologians of fourteenth-century Oxford. The official and dominant context for early modern scientific methodology seems to have been progressive Thomism, and early modern thinkers seem to have pitted themselves against it. (shrink)

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. (shrink)

ABSTRACT In 1588 Tycho Brahe proposed a new cosmological system keeping a motionless Earth at the centre of the world. In the first half of the following century the reception of Tycho’s model within the Society of Jesus was characterized by a strong resistance at the beginning, followed by a long and winding path, and then a good fortune, whereas heliocentric models were increasingly investigated in European observatories. In 1651 a Jesuit astronomer, Giovan Battista Riccioli, published the Almagestum novum, an (...) encyclopaedic synthesis of astronomical knowledge where the Earth’s motions or rest were extensively discussed in order to prove the Earth's immobility. However, through the period 1650–1687 the Almagestum novum did not entirely fulfil its aims, rather seeming like the dying swan’s song of Tychonic or semi-Tychonic models. Contemporary scholars appreciated the encyclopaedic effort by Riccioli, but many were critical of his proofs. Even influential Jesuit astronomers showed a remarkable interest in the Copernican model, accepting geocentric models only on the basis of Holy Scripture’s authority. This conduct and the tacitly allowed circulation in Catholic Europe of openly Copernican books, indicate that Catholic science tolerated heliocentric theory, when presented as a computational device rather than a representation of reality, more frequently than we usually think. (shrink)

We consider the Geometria Practica of Christopher Clavius, S.J., a surprisingly eclectic and comprehensive practical geometry text, whose first edition appeared in 1604. Our focus is on four particular sections from Books IV and VI where Clavius has either used his sources in an interesting way or where he has been uncharacteristically reticent about them. These include the treatments of Heron’s Formula, Archimedes’ Measurement of the Circle, four methods for constructing two mean proportionals between two lines, and finally (...) an algorithm for computing nth roots of numbers. (shrink)

The article deals with the Arabic sources of Chr. Clavius in Rome and the six different ways they were used by him in mathematics and astronomy. It inquires especially into his attitude towards al-Farghani, Thabit ibn Qurra, al-Bi[tdotu]ruji, Ibn Rushd, Mu[hdotu]ammad al-Baghdadi, Pseudo-Ibn al-Haytham, Jabir ibn Afla[hdotu], and Pseudo-al-[Tuotu]usi.

The article deals with the Arabic sources of Chr. Clavius in Rome and the six different ways they were used by him in mathematics and astronomy. It inquires especially into his attitude towards al-Farghānī, Thābit ibn Qurra, al-Bi[tdotu]rūjī, Ibn Rushd, Mu[hdotu]ammad al-Baghdādī, Pseudo-Ibn al-Haytham, Jābir ibn Afla[hdotu], and Pseudo-al-[Tuotu]ūsī.

La notion de dénomination d’un rapport domine la théorie de la proportionnalité au Moyen Âge et à la Renaissance. Elle apparaît dans des contextes différents, traités d’arithmétique, éditions des Éléments, traités sur la théorie des proportions, etc. L’exposé le plus complet sur cette notion se trouve dans le commentaire de Clavius à la définition 4 du livre V des Éléments d’Euclide. Clavius se fait ici l’écho des travaux de ses prédécesseurs en particulier de Jordanus et de Campanus, mais (...) ne rapporte pas la théorie des rapports irrationnels initiée par Bradwardine et développée par Oresme. (shrink)

This paper analyses the questions on the science of the soul and on the immortality of the soul in two commentaries on Aristotle’s De anima that subsist in the manuscripts of the teaching of philosophy in Coimbra in the sixteenth-century. The paper shows that the positions of the two commentators – Petrus Fonsecae (attr.) and Christophorus Gilli – are in total opposition, concerning either the commentary tradition on Aristotle’s De anima or the theories on the soul they assume. Focused (...) on unpublished and less studied sources this research brings to light some innovative aspects of the teaching of philosophy in Coimbra. We thus suggest that the manuscript sources of the period be reassessed and studied in comparison to the published works. (shrink)

No single text could be considered more important in the history of philosophy than Descartes' Meditations. This unique collection of background material to this magisterial philosophical text has been translated from the original French and Latin. The texts gathered here illustrate the kinds of principles, assumptions, and philosophical methods that were commonplace when Descartes was growing up. The selections are from: Francisco Sanches, Christopher Clavius, Pierre de la Ramee, Francisco Suárez, Pierre Charron, Eustachius a Sancto Paulo, Scipion Dupleix, Marin (...) Mersenne, Pierre Gassendi, Jean de Silhon, François de la Mothe le Vayer, Charles Sorel, and Jean-Baptiste Morin. (shrink)

Este artículo analiza las condiciones a través de las cuales las matemáticas pasan de un estado de subordinación a desempeñar un papel rector frente a la filosofía natural. Esta transformación se manifestó esencialmente en un cambio de actitud frente al pensamiento tradicional, mediante la sustitución de la explicación cualitativa de los fenómenos naturales por una explicación cuantitativa. En el texto se abordarán los aspectos epistemológicos e institucionales que están implicados en el debate sobre la cientificidad de las matemáticas. A su (...) vez, se hará un recorrido historiográfico señalando las diferentes posturas que tuvieron lugar en la polémica, para ofrecer elementos históricos y conceptuales de análisis respecto de las matemáticas como herramienta de la ciencia moderna. (shrink)

This article examines Hobbes’s conception of mathematical method, situating his methodological writings in the context of disputed mathematical issues of the seventeenth century. After a brief exposition of the Hobbesian philosophy of mathematics, it investigates Hobbes’s attempts to resolve three important mathematical controversies of the seventeenth century: the debates over the status of analytic geometry, disputes over the nature of ratios, and the problem of the “angle of contact” between a curve and tangent. In the course of these investigations, Hobbes’s (...) account of mathematics and its method is contrasted with the those of Descartes, Isaac Barrow, John Wallis, and Christopher Clavius. (shrink)

The paper shows that, contrary to what has been held since the sixteenth-century mathematician Christoph Clavius, there is no application of consequentia mirabilis (CM) in Greek mathematical works. This is shown by means of a detailed discussion of the logical structure of the proofs where CM is allegedly employed. The point is further enlarged to a critical assessment of the unsound methodology applied by many interpreters in seeking for specific logical rules at work in ancient mathematical texts.

Drawing on archival material in Utrecht and Rotterdam, we examine the geophysical surveys of Indonesia and Brazil carried out by Elie van Rijckevorsel during the period 1870 to 1890. We pay special attention to the complex interactions among university academics, government administrators and ministers of state, and private, ‘gentlemanly’ specialists. Making an appearance, in addition to Van Rijckevorsel, are the Utrecht polymath Christophorus Hendricus Diedericus Buys Ballot , the colonial and metropolitan astronomer Jean Abraham Chrétien Oudemans , colonial geophysicist (...) Pieter Adriaan Bergsma , French-Brazilian astronomer Emmanuel Liais , Colonial Minister Isaac Dignus Fransen van de Putte , and others. The decision of Van Rijckevorsel, an independently wealthy man of learning, to carry out a magnetic survey of the Malay archipelago spurred colonial authorities at The Hague to endow the finest geomagnetic observatory in the tropics. Van Rijckevorsel's interactions with academia and government suggest the extent to which wealthy Dutch patricians readily accepted government patronage for their scientific undertakings. A late-nineteenth-century Dutch ‘gentleman of science’ is seen to differ rather widely from his English counterpart of an earlier generation. An appendix reproduces, in English translation, correspondence from the early 1870s. (shrink)

On the origin of the cinematic odyssey Kubrick remarks: 'I do not remember when I got the idea to do the film. I became interested in extraterrestrial intelligence in the universe, and was convinced that the universe was *full* of intelligent life, and so it seemed time to make a film'. But as to the confusion surrounding the film upon its release, and in particular many thinking Floyd had gone to the 'planet' Clavius he said: 'Why they think there's (...) a planet Clavius I'll never know. But they hear him [Floyd] asked, 'Where are you going?', and he says, 'I'm going to Clavius'. With many people -- *boom* -- that one word registers in their heads and they don't look at fifteen shots of the moon; they don't see he's going to the Moon'. At the same time he rhetorically asked: 'How could we possibly appreciate the Mona Lisa if Leonardo had written at the bottom of the canvas: 'The lady is smiling because she is hiding a secret from her lover'. This would shackle the viewer to reality, and I don't want this to happen to _2001_'. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Descartes’ Meditations: Background Source Materials ed. by Roger Ariew, John Cottingham, and Tom SorellRichard A. WatsonRoger Ariew, John Cottingham, and Tom Sorell, editors. Descartes’ Meditations: Background Source Materials. Cambridge: Cambridge University Press, 1998. Pp. xviii + 170. Cloth, $54.95. Paper, $18.95.This volume includes primarily source materials from authors who were contemporary to Descartes’s composition of the Meditations. Thus there are no selections from Augustine, Aquinas, and Montaigne, for (...) example, who were more influential on the Meditations than some of the authors excerpted. Of course their influence is already amply documented by such scholars as Gilson and Gouhier. Probably the most important source included is Suárez, whose role is championed by Jean-Luc Marion in several works. Readers should look for the forthcoming Index Augustino-Cartèsian: Textes et Commentaire by Zbigniew Janowski (Paris: J. Vrin) for a startling challenge to the view that Descartes is Suárezian.In the volume under review, Eustachius a Sancto Paulo is of special interest because Descartes thought of refuting him item by item (but decided exposition of his own view would be adequate). In his youth Descartes had a definite interest in Petrus Ramus, although Beeckman told him his method consisted of tired old tricks. Francisco Sanches and Pierre Charron are important for their expositions of sceptical arguments and attitudes. Christopher Clavius is Descartes’s direct predecessor in mathematical analysis, and none of Descartes’s protests that he never read the man has convinced anyone. Scipion Dupleix is a fine example of how the Old Philosophy appeared to the New Philosophers, and Marin Mersenne, of course, compiled material on every subject Descartes ever had an interest in. Pierre Gassendi exercised Descartes’s ire more than any other commentator on the Meditations, and Descartes again probably read Gassendi’s continuing criticisms even though he claimed he wouldn’t. [End Page 366]Of special interest is Jean de Silhon, an old friend of Descartes’s who published a book containing a proto-cogito three years before the Meditations appeared. François de la Mothe le Vayer represents the libertine strain many detect in Descartes’s writings, while Jean-Baptiste Morin provides fodder for those who detect Descartes’s piety, although Descartes asserts that the man is an idiot for defending the immobility of the earth. Finally, Charles Sorel provides an example of the deductive mode of exposition in a text that shows that the notion of a unified science was more than Cartesian. One contemporary who was left out and should have been included was the Augustinian Guillaume Gibieuf.But overall, this is an interesting and useful collection of works Descartes doubtless knew. [End Page 367]Richard A. WatsonWashington UniversityCopyright © 1999 Johns Hopkins University Press... (shrink)

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. (shrink)

This fascinating and expertly edited little volume brings to light some hitherto neglected works, illustrating Leibniz’s lifelong interest in the calculus of combinations, and in the problem of the progress of human culture. In fact both interests are united in these works in a characteristically Leibnizian way. Leibniz’s project in De l’Horizon de la Doctrine Humaine is well expressed in its lengthy subtitle: “Meditation on the number of all possible truths and falsities, enunciable by humanity such as we know it (...) to be; and on the number of feasible books. Wherein it is demonstrated that these numbers are finite, and that it is possible to write, and easy to conceive, a much greater number. To show the limits of the human spirit [l’esprit humain], and to know the extent of these limits”. Following in the tradition of the mathematical curiosities of Clavius, Mersenne, and Guldin, Leibniz offers a formula for the calculation of the number of possible words, significant or nonsignificant, pronounceable or unpronounceable, which can be generated from an alphabet of 23 letters. Even though the product of this calculation is prodigiously great, it is finite, and given a sufficiently lengthy lifespan of the species all truths would very likely be exhausted, and novelty give way to repetition. This observation yields the notion of a “horizon of human doctrine”, an extrinsic limit to the number of truths statable in language, and confirms the “vulgar expression that 'nothing is said which has not been said already’”. (shrink)

Anstatt die Herkunft von Leibniz' Monadenkonzept in rezeptionsgeschichtlicher Perspektive nachweisen zu wollen, erklärt die vorliegende Studie die offensichtliche Präsenz und Virulenz des Monadenbegriffs im 17. und 18. Jahrhundert selbst zu ihrem Untersuchungsgegenstand.Sie rekonstruiert den frühneuzeitlichen Bildungskanon zum Pythagoreismus, in dem der Monadenbegriff tradiert worden ist, und analysiert vor diesem Hintergrund die monadologischen Philosophien von Gottfried Wilhelm Leibniz, Christian Wolff und Andreas Clavius. An reichem Quellenmaterial zeigt sie, wie die ahistorisch argumentierenden Monadologien von Leibniz und Wolff von deren Zeitgenossen rehistorisiert (...) bzw. "repythagoreisiert", in das Raster des Antike-Moderne-Verhältnisses verortet und auf diese Weise evaluiert worden sind.Ein die Studie beschließender Ausblick fasst die Ergebnisse zusammen und weist selektiv auf die Wege der Monaden in die Moderne hin. (shrink)

In modern times the so?called consequentia mirabilis (if not-P, then P). then P) was first enthusiastically applied and commented upon by Cardano (1570) and Clavius (1574). Of later passages where it occurs Saccheri?s use (1697) has drawn a good deal of attention. It is less known that about the middle of the 17th century this remarkable mode of arguing became the subject of an interesting debate, in which the Belgian mathematician Andreas Tacquet and Christiaan Huygens were the main representatives (...) of opposite views concerning its probative force. In this article the several phases and moves of that debate are delineated. (shrink)

Dans cet article nous étudions le Trattato della sfera de Galilée, écrit avant 1600. C’est un traité d’astronomie géocentrique qui suit la structure du Tractatus de sphæra de Johannes de Sacrobosco. Nous analysons quelques particularités du traité, en le comparant à d’autres travaux astronomiques du xvie siècle, et nous discutons ses sources probables. Nous soutenons que l’influence du commentaire de Christoph Clavius sur la Sphæra de Sacrobosco ne peut pas être considérée comme son influence unique ou principale. Le traité (...) de Galilée était probablement inspiré par la Sfera del mondo de Piccolomini, un travail qui anticipait plusieurs particularités du Trattato della sfera. Cette influence est établie par de nombreuses annotations de Galilée trouvées dans un exemplaire du livre de Piccolomini. (shrink)

Ever since its foundation in 1540, the Society of Jesus had had one mission—to restore order where Luther, Calvin and the other instigators of the Reformation had brought chaos. To stop the hemorrhage of believers, the Jesuits needed to form a united front. No signs of internal disagreement could to be shown to the outside world, lest the congregation lose its credibility. But in 1570s two prominent Jesuits, Cristophorus Clavius and Benito Perera, had engaged in a bitter controversy. The (...) issue at stake had apparently nothing to do with the values on which Ignazio of Loyola had built the Society of Jesus. And yet the dispute between Clavius and Perera was matter of concern for the entire Jesuit community. They were... (shrink)

Contrary to astronomy, the early modern Chinese State did not systematically sponsor mathematics. However, early in his reign, the Kangxi Emperor studied this subject with the Jesuit missionaries in charge of the calendar. His first teacher, Ferdinand Verbiest relied on textbooks based on Christoph Clavius'. Those who succeeded Verbiest as imperial tutors in the 1690s produced lecture notes in Manchu and Chinese. Newly discovered manuscripts show Antoine Thomas wrote substantial treatises on arithmetic and algebra while teaching those subjects. In (...) 1713, the emperor commissioned a group of scholars and officials to compile a standard survey of mathematics. This work opened with the claim that mathematics had its roots in Chinese Antiquity. However, it can be shown that the Jesuits' lecture notes were the main source of the Shuli jingyun. The reconstruction of mathematics under Kangxi's patronage is thus best characterised as the imperial appropriation of Western learning. (shrink)

Johannes Kepler belonged to a long tradition of inquiring into nature with reference to God. This applies to Ptolemy, N. Copernicus, Chr. Clavius. Kepler's „new kind of poem” is analyzed in five sections which are based on Keplerian key words: Innovation, Hypothesis, Cause, Soul, Picture. Kepler consciously adhered to new questions, new answers, new methods. He relied on a new notion of hypothesis. His celestial dynamics included a celestial psychology whereby he used a visual conception of astronomy.

The anonimous scholiumOn all forms of syllogism was copied in 1884 from the Paris Codex 2064 by E. Richter. In 1899 M. Wallies published it in the preface to Ammonius' commentary on the Prior Analytics of Aristotle. There appear in that scholium, apart from the complex figure of Galenos, other characteristic forms of inference.Among these forms I found five so-called non-demonstrable stoic syllogisms, three modifications of the law of transposition of which the third is not mentioned by the authors of (...) Princ pia Mathematica, and a modification of the form of inference known as Euclid's law. This form of inference was applied by Euclid in mathematics and by Saccherius in syllogistics; it is mentioned for the first time by Cardan in a treatise of 1570 and later by Clavius in his commentary of 1574 on the Elements of Euclid and in the commentary on Theodosius'Sphaerica of the year 1586.In 1658 Erhard Weigel made the first attempt at refuting the logical law of Euclid as formulated by Cardan and Clavius and in 1686 James Bernoulli tried to prove it. (shrink)

This article analyzes the epistemological legitimation of mathematics in natural philosophy in the seventeenth century. In the Renaissance it was claimed that mathematics does not meet the Aristotelian criteria of scientificity, and that it did not explain the efficient and final causes. So, its critics, inspired by the Aristotelian tradition, rejected the first attempts to mathematize natural philosophy. The epistemological conditions involved in the debate are examined on the scientific nature of mathematics and its relevance to natural philosophy. A historiographical (...) tour of the mathematization of nature is made to provide new weighing elements with respect to a historically and philosophically more conceptual characterization of the emergence of modern science. (shrink)

This chapter contains section titled: Introduction Descartes's Early Engagement with Mathematics (up to 1623) Rules for the Direction of the Mind Discourse on the Method Geometry, Book I: The Algebra of Segments Geometry, Book I: Pappus' Problem Geometry, Book II: Descartes's Classification of Curves Conclusion Acknowledgments Note References.

Roger Ariew begins this book with the following sensible claim: “A philosophical system cannot be studied adequately apart from the intellectual context in which it is situated”. His book, naturally enough, attempts to demonstrate the way in which Descartes responded to and affected the philosophical world of late Scholasticism. The ten chapters themselves are all previously, or soon to be, published essays, unified by the view that our knowledge of late Scholasticism is deeply imperfect and that our resulting picture of (...) Descartes is also imperfect. Each chapter provides an example of how, with a proper understanding of Scholastic philosophy, we arrive at a slightly different and more refined picture of Descartes. Indeed, Ariew’s work is the product of an admirably broad and detailed knowledge of the works of the major thinkers of the sixteenth and seventeenth centuries; Toletus, Suarez, Eustachius, Basso, Clavius, Dupleix, Mersenne, Arnauld, and many others are the actors in this drama of the rise of Cartesianism. (shrink)