The Symbol Master

2016 ◽  
Author(s):  
Joseph Mazur
Keyword(s):  
Seventeenth Century ◽  
Rene Descartes ◽  
Integral Calculus ◽  
Isaac Newton ◽  
René Descartes

This chapter focuses on the symbols created by Gottfried Leibniz. Alert to the advantages of proper symbols, Leibniz worked them, altered them, and tossed them whenever he felt the looming possibility that some poorly devised symbol might someday unnecessarily complicate mathematical exposition. He foresaw how symbols for polynomials could not possibly continue into algebra's generalizations at the turn of the seventeenth century. He knew how inconvenient symbols trapped the advancement of algebra in the fifteenth and sixteenth centuries. By the last half of the seventeenth century, symbols were pervasive in mathematics manuscripts, largely due to Leibniz, along with others such as William Oughtred, René Descartes, and Isaac Newton. Among the more than 200 new symbols invented by Leibniz are his symbols for the differential and integral calculus.

Passionate souls: Elisabeth of Bohemia and René Descartes

2021 ◽  
Vol 105 (563) ◽  
pp. 193-200
Author(s):  
Tomoko L. Kitagawa
Keyword(s):  
Seventeenth Century ◽  
Rene Descartes ◽  
History Of Mathematics ◽  
Intellectual Ability ◽  
Natural Phenomena ◽  
Her Family ◽  
Isaac Newton ◽  
René Descartes ◽  
History Of ◽  
Natural Philosophers

The mathematical investigations of natural phenomena in the seventeenth century led to the inventions of calculus and probability. While we know the works of eminent natural philosophers and mathematicians such as Isaac Newton (1643-1727), we know little about the learned women who made important contributions in the seventeenth century. This article features Princess Elisabeth of Bohemia (1618-1680), whose intellectual ability and curiosity left a unique mark in the history of mathematics. While some of her family members were deeply involved in politics, Elisabeth led an independent, scholarly life, and she was a close correspondent of René Descartes (1596-1650) and Gottfried Leibniz (1646-1716).

Analysis, philosophical issues in

2018 ◽  
Author(s):  
I. Grattan-Guinness
Keyword(s):  
Eighteenth Century ◽  
Seventeenth Century ◽  
Set Theory ◽  
Integral Calculus ◽  
Analytic Proof ◽  
Isaac Newton ◽  
The Status ◽  
Point Set ◽  
Convergence And Divergence ◽  
Major Branch

The term ‘mathematical analysis’ refers to the major branch of mathematics which is concerned with the theory of functions and includes the differential and integral calculus. Analysis and the calculus began as the study of curves, calculus being concerned with tangents to and areas under curves. The focus was shifted to functions following the insight, due to Leibniz and Isaac Newton in the second half of the seventeenth century, that a curve is the graph of a function. Algebraic foundations were proposed by Lagrange in the late eighteenth century; assuming that any function always took an expansion in a power series, he defined the derivatives from the coefficients of the terms. In the 1820s his assumption was refuted by Cauchy, who had already launched a fourth approach, like Newton’s based on limits, but formulated much more carefully. It was refined further by Weierstrass, by means which helped to create set theory. Analysis also encompasses the theory of limits and of the convergence and divergence of infinite series; modern versions also use point set topology. It has taken various forms over the centuries, of which the older ones are still represented in some notations and terms. Philosophical issues include the status of infinitesimals, the place of logic in the articulation of proofs, types of definition, and the (non-) relationship to analytic proof methods.

Understandings of Colors: Varieties of Theories in the Color Worlds of the Early Seventeenth Century

2015 ◽  
Vol 20 (4-6) ◽  
pp. 515-535 ◽  
Author(s):  
Fokko Jan Dijksterhuis
Keyword(s):  
Seventeenth Century ◽  
Crucial Role ◽  
Intellectual Development ◽  
Rene Descartes ◽  
The Status ◽  
René Descartes

In the early seventeenth century, there existed a myriad of theories to account for color phenomena. The status, goal, and content of such accounts differed as well as the range of phenomena they explained. Starting with the journal of Isaac Beeckman (1588–1637), this essay inquires into the features and functions of conceptual reflections upon color experiences. Beeckman played a crucial role in the intellectual development of René Descartes (1596–1650), while at the same time their ideas differed crucially. Early corpuscular conceptions of colors cannot be reduced to the mechanistic variety of Descartes. Moreover, the optical rather than corpuscular features of Descartes’s understanding of colors were essential. A stratification of conceptualizations is proposed that is grounded in various problem contexts rather than philosophical doctrines, thus opening a way to interpret the philosophical parts of color worlds in a more diverse way.


Richard Baxter as Philosophical Theologian

2017 ◽  
Author(s):  
David S. Sytsma
Keyword(s):  
Seventeenth Century ◽  
Rene Descartes ◽  
Thomas Hobbes ◽  
Modern Science ◽  
Robert Boyle ◽  
Mechanical Philosophy ◽  
René Descartes ◽  
Pierre Gassendi ◽  
The Way

This chapter argues for Baxter’s importance as a theologian engaged with philosophy. Although Baxter is largely known today as a practical theologian, he also excelled in knowledge of the scholastics and was known in the seventeenth century also for his scholastic theology. He followed philosophical trends closely, was connected with many people involved in mechanical philosophy, and responded directly to the ideas of René Descartes, Pierre Gassendi, Robert Boyle, Thomas Willis, Thomas Hobbes, and Benedict de Spinoza. As a leading Puritan and nonconformist, his views are especially relevant to the question of the relation of the Puritan tradition to the beginnings of modern science and philosophy. The chapter introduces the way in which “mechanical philosophy” will be used, and concludes with a brief synopsis of the argument of the book.

scholarly journals PAPPUS DE ALEXANDRIA

2020 ◽  
Vol 7 (20) ◽  
pp. 08-17
Author(s):  
Lucicleia Chagas Magno ◽  
Miguel Chaquiam ◽  
Ruan Wenderson De Oliveira Sousa ◽  
Ruan Wenderson De Oliveira Sousa
Keyword(s):  
Rene Descartes ◽  
Blaise Pascal ◽  
Isaac Newton ◽  
René Descartes

Este trabalho tem como objetivo presentar vida e obra de Pappus de Alexandria, com destaque em seu teorema, e teve como base a seguinte questão de pesquisa: Qual a contribuição de Pappus de Alexandria à Matemática? Os caminhos foram percorridos tensdo como objetivo apresentar vida e obra de Pappus de Alexandria, com destaque em seu teorema. Neste sentido, a pesquisa, de cunho qualitativo, foi amparada em métodos bibliográficos, durante a qual foram revisados estudos de Chaquiam, (2017); Chaves (2013); Estrada, Sá et al (2000); Gillispie e Pereira (2007); Garnica e Souza (2012); Jones (s/d); Miguel e Miorim, (2002) e Roque (2012). Desse modo, com a execução dessa pesquisa foi possível observar que os trabalhos produzidos por Pappus de Alexandria, apresentam grandes contribuições à Matemática, em particular á Geometria, e também, a outras áreas de conhecimento, como na geografia, música, hidrostática, alquimia e na astronomia, além disso, sua principal obra, a Coletânea, e seu famoso teorema serviram como fonte de informação e inspiração para outros matemáticos, os quais contribuíram para a construção e aprimoramento de novos conhecimentos matemáticos, dentre eles, podemos citar René Descartes, Pierre de Fermat, Blaise Pascal, Isaac Newton e G. W Leibniz. Por conseguinte, percebeu-se que a História da Matemática é um ramo que estuda a evolução dos conteúdos matemáticos dentro do processo histórico-cultural, sendo um importante instrumento para o ensino de Matemática, principalmente, para a construção de conceitos, por isso torna-se essencial, também, o estudo e a utilização de biografias de personagens que contribuíram de alguma forma á Matemática, além de ser uma forma interessante de despertar o interesse dos estudantes pela Matemática e pela História da Matemática e, muito mais, fazer uso da história da matemática como recurso didático no processo de ensino e aprendizagem da matemática.

Physics and Metaphysics in Descartes and Newton

2019 ◽  
pp. 803-815
Author(s):  
Andrew Janiak
Keyword(s):  
Twentieth Century ◽  
Natural Philosophy ◽  
Rene Descartes ◽  
Space Time ◽  
First Line ◽  
Unpublished Manuscript ◽  
Isaac Newton ◽  
Time And Motion ◽  
René Descartes

Isaac Newton had a vexed relationship with his most important immediate predecessor in mathematics and philosophy, René Descartes. He was typically loath to admit the importance of Cartesian ideas for the development of his own thinking in mathematics and natural philosophy. For this reason, generations of students and scholars relying on Newton’s published work had little inkling of Descartes’s significance. This unfortunate fact was compounded by the tendency of philosophers to focus on the Meditations or the Regulae in their scholarship, for it was Descartes’s Principles above all that influenced Newton’s thinking as a young man. With the discovery of a previously unpublished manuscript amongst Newton’s papers by two famous historians of science in the middle of the twentieth century, everything changed. The manuscript, now known as De Gravitatione after its first line, illustrates the astonishing care with which Newton read the Principles, focusing his critical acumen on Descartes’s understanding of space, time, and motion. These criticisms of Descartes, in turn, shine light on otherwise opaque passages in Newton’s most significant published discussion of space, time, and motion, the Scholium in Principia mathematica. Indeed, the very title of the latter work represents both an homage to, and a swipe at, Descartes’s work: Newton would offer mathematical principles of natural philosophy to replace Descartes’s qualitative account. It is not a stretch to say that Newton saw further because he stood on Descartes’s shoulders, even if he wouldn’t admit it publicly.

Was There a Scientific Revolution?

2017 ◽  
Author(s):  
John L. Heilbron
Keyword(s):  
Seventeenth Century ◽  
Early Modern ◽  
Scientific Revolution ◽  
Early Modern Europe ◽  
Republic Of Letters ◽  
Isaac Newton ◽  
Natural Knowledge ◽  
René Descartes ◽  
Modern Europe ◽  
The Republic

This article asks whether there was a Scientific Revolution (SR) at anytime between 1550 and1800. The label ‘Scientific Revolution’ to indicate a period in the development of natural knowledge in early modern Europe has carved a place in historiography. This article suggests that there was SR, if SR signifies a period of time; perhaps, if it is taken as a metaphor. It illustrates how the deployment of the metaphor to seventeenth-century natural knowledge might be accomplished. It also considers the physics of René Descartes, the influence of Cartesianism throughout the Republic of Letters, and the academies. The metaphor can be useful if it is taken in analogy to a major political revolution. The analogy points to a later onset, and a swifter career, for the SR than is usually prescribed, and shows that Isaac Newton was its counter rather than its culmination.

scholarly journals As pesquisas de Newton sobre a luz: Uma visão histórica

2015 ◽  
Vol 37 (4) ◽  
pp. 4202-1-4202-32
Author(s):  
Roberto de Andrade Martins ◽  
Cibelle Celestino Silva
Keyword(s):  
Rene Descartes ◽  
Robert Hooke ◽  
Robert Boyle ◽  
Isaac Newton ◽  
Christiaan Huygens ◽  
René Descartes

Este artigo apresenta uma visão histórica geral sobre o desenvolvimento dos trabalhos de Isaac Newton a respeito da óptica, desde suas primeiras investigações em 1664 até o final de sua vida, quando publicou as várias edições de seu livro Opticks. Para permitir uma compreensão adequada do trabalho de Newton, são também apresentadas as contribuições de outros autores importantes do Século XVII, especialmente René Descartes, Walter Charleton, Robert Boyle, Robert Hooke e Christiaan Huygens. A análise dos trabalhos inéditos e publicados de Newton permite notar que ele jamais chegou a uma teoria definitiva a respeito da luz e das cores, adotando diversas hipóteses diferentes e mutuamente inconsistentes. O estudo aqui apresentado pode contribuir para complementar as visões simplificadas sobre a história da óptica e das contribuições de Newton sobre esse tema, bem como corrigir diversos equívocos presentes em obras didáticas e de divulgação científica sobre o assunto.

Embrace the Organisation Unconscious: The Next Steps for Change Leaders and Organisation Development Practitioners

2020 ◽  
Vol 13 (3) ◽  
pp. 340-351
Author(s):  
V. Kartikeyan
Keyword(s):  
Seventeenth Century ◽  
Rene Descartes ◽  
The Unconscious ◽  
Organisation Development ◽  
René Descartes ◽  
Change Leaders ◽  
Human Systems

The move from an ‘A-rational’ world to the rational can be traced to the seventeenth century, in particular to the contribution of Rene Descartes, who advocated what is now known as the Cartesian view, which deifies the rational, the objective and the measurable. The problem with this advocacy was that all aspects of what did not seem rational got marginalised. This marginalisation has led, over the last couple of centuries, to a sense of disenchantment, fragmentation and ‘exclusionary processes’ in society, organisations and in general all human systems. Carl Jung’s pioneering work on the unconscious offers us a way out of this by beckoning us to revisit and reimagine the ‘A-rational’ in a way that brings vibrancy and aliveness to organisations. By envisaging the ‘Organisation Psyche’ and by learning to work with aspects of the ‘Organisation Unconscious’, such as the ‘Organisation Shadow’ and ‘Symbolic Complexes’, it may be possible to discover new integrative paths for change leaders and organisation development (OD) practitioners alike, to adopt to bring in a new sense of endeavour, volition and adventure for organisations and their agents.

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