Search

Aristarchus's De magnitudinis et distantiis solis et lunae was translated into Latin and printed by Federico Commandino in 1572. All subsequent editions of Aristarchus' treatise, published by John Wallis (1688), Fortia d' Urban (1823) and Thomas Heath (1913), followed Commandino's work. In this article, through a philological approach to the geometric diagrams, I tracked down one of the Greek sources used by Commandino for preparing his Latin version. Commandino pays particular attention to drawing figures. This article sheds light on the interaction between mathematical skills and the drawing of geometric diagrams implemented in his Latin edition of Aristarchus' book. [ABSTRACT FROM AUTHOR]

This paper discusses how John Wallis (1616–1703), Savilian Professor of Geometry at Oxford, used biblical evidence to support his ideas about natural philosophy and mathematics. Examples from Wallis's long career include his calculation of the age of the Earth, his critique of Robert Hooke's theory concerning the origin of fossils, and his debate with Edward Tyson about whether humans are naturally herbivorous or carnivorous. My analysis shows that Wallis's use of biblical history did not necessarily commit him to an intellectually conservative position, but neither did it always encourage him to embrace new ideas. In fact, the truth is somewhere in the middle: I argue that biblical history provided a useful way for Wallis to negotiate between tradition and innovation, to determine which new ideas represented important advances and which were unsubstantiated follies. [ABSTRACT FROM AUTHOR]

John Wallis, a founding member of the Royal Society, theologian and churchman, participated in the leading ecclesiastical conferences in England from the beginning of the English Civil War to the Restoration. His allegiance across governments, both civil and ecclesiastical, has provoked criticism. Close investigation into his position on key church issues, however, reveals a deeper philosophical unity binding together his natural philosophy, mathematics and views on church polity and liturgy. [ABSTRACT FROM AUTHOR]

The dispute that raged between Thomas Hobbes and John Wallis from 1655 until Hobbes's death in 1679 was one of the most intense of the 'battles of the books' in seventeenth-century intellectual life. The dispute was principally centered on geometric questions (most notably Hobbes's many failed attempts to square the circle), but it also involved questions of religion and politics. This paper investigates the origins of the dispute and argues that Wallis's primary motivation was not so much to refute Hobbes's geometry as to demolish his reputation as an authority in political, philosophical, and religious matters. It also highlights the very different conceptions of geometrical methodology employed by the two disputants. In the end, I argue that, although Wallis was successful in showing the inadequacies of Hobbes's geometric endeavours, he failed in his quest to discredit the Hobbesian philosophy in toto. [ABSTRACT FROM AUTHOR]

Emulating the Greek geometers, Newton used synthetic demonstration to present the groundbreaking arguments of the Principia. This paper argues that we can better understand Newton's reasons for using geometry by considering John Wallis's interpretation of synthetic demonstration. Wallis condemned demonstration for failing to explain the mathematical truths it presented. He opposed to it a presentation that combined symbolic analysis with a documented account of discovery. In preferring symbols, Wallis was motivated both by the nascent tradition of symbolic analysis and by contemporary interest in artificial languages. Newton maintained Wallis's characterization of Greek demonstration as adapted to common understanding rather than as strictly elucidating, but he inverted the values Wallis associated with synthesis and analysis. In Newton's new account, synthetic demonstration was preferable precisely because it could address inexpert readers without exposing them to the complications of symbols-based analysis. Newton advanced his arguments on behalf of geometry through portraits of ancient mathematicians: Archimedes and Pythagoras. [ABSTRACT FROM AUTHOR]

John Wallis's encyclopaedic endeavours were built on a mountain of ink and paper. To consider Wallis's work in the making, this article will draw his portrait as a reader and book collector. Keeper of the University of Oxford archives, he secured donations for the Bodleian and Savilian libraries and obsessively consulted old and new publications, manuscript and printed texts to build and defend his own work. Revealing interconnections between his contributions to theology, cryptography, linguistics, music and mathematics, this paper will focus on Wallis's methodical construction of his personal 'inkscape'. His passionate obsession with the preservation and dissemination of his thought in print will be considered alongside the research he only consigned in manuscript form, through correspondence and notes. This reconstruction of John Wallis's libraries will therefore provide us with an overview of the érudit's contested achievements, as well as a panorama of contemporary scholarly practices. [ABSTRACT FROM AUTHOR]

In his posthumously published work Chartham News (1669), the antiquary William Somner tentatively sought to link the discovery of fossilized remains near Canterbury to the prehistoric existence of an isthmus connecting Britain and France, before calling on natural philosophers to pursue his explanation further. This call was eventually heeded by the Oxford mathematician John Wallis, but only after more than thirty years had elapsed. The arrival in England of a catalogue of questions concerning the geology of the Channel led to the republication of Chartham News in the Philosophical Transactions, prompting Wallis to develop a physical explanation based on his intimate knowledge of the Kent coastline. Unbeknown to Wallis at the time, that catalogue had been sent by G. W. Leibniz, who had in turn received it from G. D. Schmidt, the former Resident of Brunswick-Lüneburg in Sweden. Wallis's explanation, based on the principle of establishing physical causes both for the rupturing of the isthmus and for the origin of fossils, placed him in a camp opposed by Newtonian authors such as John Harris at a time when the priority dispute over the discovery of the calculus led to the severing of his ties with the German mathematician and philosopher Leibniz. [ABSTRACT FROM AUTHOR]

The article explores the pervasiveness of the culture of combination in 17th-century England. It examines early modern permutational systems by analyzing mathematician and cryptographer John Wallis' calculation and his use of letters and anagrams and bells to explain permutations. The combinatorial, anagrammatical extrapolations of change-ringing and church bells are also discussed.

The article offers information on the video game "Who Wears the Crown: An Entire New Game" that was published between 1814 and 1818 by John and Edward Wallis. It mentions about the symbol of the King instead of the King himself, the Wallises give victory a metaphorical gloss; the player's goal should not be to become King, a radical suggestion but to get closer to his milieu.

In 1668–1669 William Neile and John Wallis engaged in a protracted correspondence regarding the nature of motion. Neile was unhappy with the laws of motion that had been established by the Royal Society in three papers published in 1668, deeming them not explanations of motion at all, but mere descriptions. Neile insisted that science could not be informative without a discussion of causes, meaning that Wallis's purely kinematic account of collision could not be complete. Wallis, however, did not consider Neile’s objections to his work to be serious. Rather than engage in a discussion of the proper place of natural philosophy in science, Wallis decided to show how Neile's preferred treatment of motion lead to absurd conclusions. This dispute is offered as a case study of dispute resolution within the early Royal Society. [ABSTRACT FROM AUTHOR]

This paper explores Shakespeare's use of wh-relative pronouns with personal antecedents, particularly the personal use of which, which had started to be marginalised before Shakespeare's period and replaced by who and whom. The present survey of Shakespeare's plays reveals a significant fact with relation to the second person pronouns thou and you (including their inflected case forms) as antecedents: which is common with thou but extremely rare with singular you; on the other hand, who(m) shows no preference for either form and occurs with them equally. The association of which with thou and its avoidance of you suggests that Shakespeare may have exploited personal which in contexts where thou is generally preferred - when the speaker is superior in social status to the referent or the speaker is highly emotional. Evidence is presented from close examination of three plays ( Romeo and Juliet, King Richard II, and King Lear), demonstrating that characters of high status may use which if the referents are social inferiors but not vice versa. In addition, personal which is associated with heightened emotion and dramatic tension. In fact, fellow, knave, and similar insulting words are commonly used as antecedents of which. On the other hand, social status or emotional states of characters are not relevant to the use of who(m). Hence in Shakespeare's English, who(m) is the unmarked form as a personal relative pronoun, while which is the marked form, usually used, just like thou, to refer to social inferiors or to mark strong emotions. [ABSTRACT FROM AUTHOR]

The article focuses on the controversy between Isaac Newton and Gottfried Wilhelm von Leibniz in relation to the invention of calculus in the late 17th century. An evidence that Newton had some ideas about the calculus as early as his famous annus mirabilis in 1666, and hints of calculus in the work of his predecessors in England, in particular the writings of John Wallis and Isaac Barrow, is mentioned.

The article discusses a letter contained in archives of the Bodleian Library related to a proposal by bookseller and publisher Jacob Tonson, the Elder, to Cambridge University Press for an edition of Euclid printed in both Greek and Latin. Other topics include Tonson's membership n the Whig Kit-Cat Club, his relationship with his business partner and nephew Jacob Tonson, the Younger, and scholars including classicist Arthur Charlett as well as mathematicians John Wallis and David Gregory.

In 1695, in his Opera Mathematica, John Wallis (Savilian Professor of Geometry at the University of Oxford) published an analysis of the forces in a reciprocal grillage structure. The structure itself was an extended version of a famous design often attributed to Serlio, but first sketched much earlier by Villard de Honnecourt. The extended structure was also sketched by Leonardo da Vinci. Wallis's analysis is remarkable for the fact that he systematically (and correctly) solved a set of 25 simultaneous equations to obtain the required forces. The main steps in the analysis closely parallel the essential stages in modern Finite Element Analysis, and Wallis's calculations can be seen as a key step in the development of structural analysis techniques. [ABSTRACT FROM AUTHOR]

John Bulwer's (1606-1656) work was unknown in 17th-18th century France. In 1827 when Joseph-Marie Degérando (1772-1842) became curious about the relation between the methods respectively of Bulwer and John Wallis (1616-1703), the pioneer oral instructor of the deaf in Britain, he had to query Charles Orpen, M.D. (1791-1856) in Dublin because no copy of Bulwer's Philocophus (1648) could be found in Paris. In fact, Theodore Haak (1605-1690) had sent a copy of this book from London to Père Marin Mersenne (1588-1648) in Paris in July 1648, but none of Mersenne's circle could read English, an Mersenne died several weeks later. In that context, this paper presents a comparison of Bulwer's views with those of the Cartesians and Port-Royalists. Wallis claimed he knew of no work on speech for the deaf prior to his own, but he must have known about the Philocophus from the time of its publication, five years before his De Loquela (1653) and nearly 14 years before he began teaching the deaf. [ABSTRACT FROM AUTHOR]

The article discusses formulas for gamma function introduced by Scottish mathematician James Stirling, named Stirling's formula and Stirling's formula for the Gamma function. It mentions the approach in the first case which relies upon analysis of Wallis formula given by English mathematician John Wallis. It states that the approach that provides estimation to the factorial used in probability and statistical physics.

This paper aims first and foremost to unravel and clarify an interesting 17th century controversy around superposition in projectiles, which allegedly existed between the French Jesuit Honoré Fabri and the Italian physicist and astronomer Giovanni Alfonso Borelli. This conflict – initially described by the English mathematician John Wallis in a letter from 1670 to the secretary of the Royal Society – has been erroneously identified with Fabri's Dialogi physici (1669), a work written in response to Borelli's De vi percussionis (1669). In fact, this “conflict” was nothing but Wallis's account of a contradiction between Borelli's above mentioned work and Fabri's Tractatus physicus de motu locali from 1646, while Fabri's 1669 work expressed views very different from those contained in his Tractatus physicus. I will try here to reconstruct Fabri's change of heart between 1646 and 1669 concerning projectiles and superposition, while tracing the real bone of contention between (the later) Fabri and Borelli – superimposing contrary motions – to its Aristotelian origins. My analysis will lead me to problematize the way modern historians usually interpret the relation between Aristotle's physical thinking and projectile theories of early modern theoreticians (e.g. Nicollò Tartaglia's). [ABSTRACT FROM PUBLISHER]

Abstract: John Wallis, Savilian professor of geometry at Oxford from 1649 to 1703, engaged in a number of disputes with French mathematicians: with Fermat (in 1657–1658), with Pascal (in 1658–1659), with Dulaurens (in 1667–1668), and against Descartes (in the early 1670s). This paper examines not only the mathematical content of the arguments but also Wallis’s various strategies of response. Wallis’s opinion of French mathematicians became increasingly bitter, but at the same time he was able to use the confrontations to promote his own reputation. [Copyright &y& Elsevier]

The article profiles English mathematician John Wallis who was credited for discovering a formula for approximating the value of pi. He also introduced the symbol for infinity and the term 'continued fraction,' and published a treatise on conic sections. As Savilian Professor of Geometry at Oxford University, Wallis debated with philosopher Thomas Hobbes and argued for the inclusion of logic in the curriculum. A Wallis Professorship was created at the Oxford Mathematical Institute in 1969.

This paper explores Wallis's role as editor of Newton's mathematical work. My objective is to understand how two mathematicians who held different views concerning mathematical method could nonetheless cooperate with one another quite effectively. Most notably, Wallis and Newton pursued different policies as far as the printing of algebra is concerned. In the 1690s Newton held the view that algebra is a heuristic method 'not worthy of publication™. Wallis, instead, for all his life was keen on making algebraic methods explicit in print. As the analysis of the correspondence between Wallis, Collins and Newton reveals, the methodological tension between Wallis and Newton was resolved in such a way that Newton agreed to print his heuristic methods in Wallis's English Algebra (1685) and Latin Opera (1693-99). Newton wished to guarantee his priority rights on discoveries in algebra and calculus, yet he also sought to avoid any tight authorial commitment towards them. Wallis, in contrast, received from Newton material that turned out to be useful for the fulfilment of a nationalistic programme aimed at eulogizing British mathematicians as well as his own work. [ABSTRACT FROM AUTHOR]

Historical studies on the development of mathematical concepts will help mathematics teachers to relate their students' difficulties in understanding to conceptual problems in the history of mathematics. We argue that one popular tool for teaching about numbers, the number line, may not be fit for early teaching of operations involving negative numbers. Our arguments are drawn from the many discussions on negative numbers during the seventeenth and eighteenth centuries from philosophers and mathematicians such as Arnauld, Leibniz, Wallis, Euler and d'Alembert. Not only does division by negative numbers pose problems for the number line, but even the very idea of quantities smaller than nothing has been challenged. Drawing lessons from the history of mathematics, we argue for the introduction of negative numbers in education within the context of symbolic operations. [ABSTRACT FROM AUTHOR]

In Galileo's opinion, his most important argument for the Earth's motion was based on his theory of the tides that combined the Earth's rotation with its orbital motion so that it alternately accelerates and decelerates the sea. His theory deliberately ignored the Moon's influence, which at that time was generally regarded as occult. Galileo's confidence in his theory was strongly reinforced by its providing a mechanical model. That a theory that ignored the Moon's influence could seem plausible is confirmed by comparison with the theories of Bacon and Wallis. That Galileo's theory could seem plausible despite encountering difficulties is confirmed by comparison with Newton's theory, which is deeply flawed by its inclusion of a vertical response to the total tidal force. That many people now regard Galileo's theory as wrong is due to our having absorbed as natural Newton's idea of lunar attraction. [ABSTRACT FROM AUTHOR]

The article informs about theorems propounded by doctor in philosophy William Brouncker of England. It also mention the book "Arithematica Infinitorium," by John Wallis who referred to arithmetic of infinites. Wallis had planned to obtain the new formula using method of interpolation assisted by Brouncker. It mentions how Wallis convinced Brouncker hard to publish the proof but all in vain. It also reveals how proof of Brouncker's formula is the starting point of Stieltjes's theory.

During the Renaissance there was an explosion of interest in secret communication when political intrigue and war intersected with new scientific developments. This article shows how leaders of the Scientific Revolution who espoused openness in science, reconciled that ethos with the need for secrecy in affairs of state. [ABSTRACT FROM AUTHOR]

'Lord Brouncker's continued fraction for π' is a well-known result. In this article, we show that Brouncker found not only this one continued fraction, but an entire infinite sequence of related continued fractions for π. These were recorded in the Arithmetica Infinitorum by John Wallis, but appear to have been ignored and forgotten by modern mathematicians. We identify these continued fractions and give a modern derivation. [ABSTRACT FROM AUTHOR]

The article discusses the evaluation of the probability integral using the product formula for π of mathematician John Wallis. It explores the standard one-variable calculus method for evaluating the probability integral and functions using the approximation theory. It states that to approximate the integrand in the probability integral can yield a simpler evaluation of integrals. It proves that calculating the limits of the expression can be done using the Wallis product formula for π.

The article focuses on the "General Scholium" of the "Principia Mathematica" by scientist Sir Isaac Newton. It explores the writings and ideas of his contemporary scientists and members of the Royal Society of London, England John Wallis, Christopher Wren, and Christiaan Huygens regarding the third law of motion from Book 1 of the "Principia Mathematica." The author argues that the "General Scholium," as added to the "Principia Mathematica" twenty-six years after it was first published, does not do justice to the remainder of the book's existing scientific and mathematical methodology. A discussion of Newton's use of logical reasoning and philosophical induction is also presented.

The article focuses on the contribution of professor John Wallis in examining the origin of the Royal Society in London, England. It is evident that Wallis devote his life in studying the natural philosophy in the country from 1645-49 with the purpose of examining popular subjects in astronomy, medicine and mechanics. He considers the discussion among physicians and scholars a great origin of the Royal Society. However, his main concern is to uphold and emphasize the intellectual focus of the society noting that it is established based on the social and environmental concerns of scholars and historians.

The article reports on John Wallis' attribution of the startling fact that a hole can be cut in one of two equal cubes large enough to permit that passage of the second cube to Prince Rupert. It has been showed in 1968 that a hole can be cut in one of two equal regular tetrahedra large enough to permit the passage of the second tetrahedron. A more precise notion of "plug" is considered. It shows that every such stopper has the Rupert property. An argument which shows generally that it is possible to cut a hole in any universal stopper through which every other multipurpose plug of the same diameter can be passed is presented.

The article examines geometrical problems encountered in locating or determining the normals to a parabola and the real roots of a cubic. In the book "Tractatus duo, prior de cycloide, posterior de cissoide," John Wallis made the first rectification of a algebraic curve. The transformation of any cubic equation through the horizontal translation do not alter the number of real roots of the equation. Key information about the Neil's parabola and envelope of the family of normals is further presented.

Discusses John Wallis's book 'Arithmetica Infinitorum.'

William Oughtred's Clavis mathematicae, first published in 1631, was regarded for the remainder of the seventeenth century as a classic text in algebra, reprinted, translated, and explained for over 70 years. Yet its content was limited, its style obscure and its notation old-fashioned even when it was first written, and it now seems extraordinary that it should have had such a long life. The early success of the book, and the great esteem in which Oughtred was held by contemporary and later mathematicians, can only be understood in the light of the general state of algebra teaching in England during the first half of the seventeenth century. In later years the book was kept alive by the efforts of one of its greatest admirers, John Wallis. The aim of this paper is to set the story of the Clavis into the wider context of English algebra, and the political background of the time. [ABSTRACT FROM AUTHOR]

Discusses the interpretation of the foundations of calculus by mathematician Gottfried Wilhelm von Leibniz. Details on Leibniz's formulation of calculus and the doctrine of conatus by mathematician Thomas Hobbes; Objections raised by mathematicians Bernard Nieuwentijt and Michel Rolle against calculus; Response of Leibniz to the criticisms; Examination of the correspondence between Leibniz and mathematician John Wallis.

Presents information on the contribution made by the work of mathematicians John Wallis and Isaac Barrow to the development of mathematics in early modern England. Reference to tension between algebraic techniques and traditional geometric mode of thought; Comparison of Wallis' and Barrow's mathematical styles; Examination of Wallis' and Barrow's views on ancient and modern mathematics.

An introduction is presented in which the editor discusses several articles published within issue on topics including working of the Cromwellian intelligence networks, prison writings of Henry Adis, and intellectual cross-currents that influenced the Mathematician John Wallis.

Information is provided on the British Society for the History of Mathematics (BSHM) meeting titled "John Wallis and the Parallel Postulate" held at the Mathematical Institute at Oxford University, England on June 11, 2013 and the meeting titled "Geometry from Euclid to Einstein" organized by BSHM and the Oxford University Department of Continuing Education (OUDCE) held at Oxford University June 22-June 23, 2013. Topics, including the British mathematician John Wallis, the relationship between geometry and art and 19th century non-Euclidean geometry, are discussed.

The article talks about a conference that focuses on the history of mathematician John Wallis dealing with his works on mathematics, music theory or canonics, and cryptography in the 17th century, views on Presbyterianism, and foundations of geometry and parallel postulate.

The article announces centenaries for 2016 including the birthday of English mathematician John Wallis, the publication of Nicolaus Mulerius' textbook "Institutionum astronomicarum libri duo," and the death of Italian geometer Antony Cagnoli.