Niccolo Guicciardini
- Published in print:
- 2009
- Published Online:
- August 2013
- ISBN:
- 9780262013178
- eISBN:
- 9780262258869
- Item type:
- book
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262013178.001.0001
- Subject:
- History, History of Science, Technology, and Medicine
Historians of mathematics have devoted considerable attention to Isaac Newton’s work on algebra, series, fluxions, quadratures, and geometry. This book examines a critical aspect of Newton’s work ...
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Historians of mathematics have devoted considerable attention to Isaac Newton’s work on algebra, series, fluxions, quadratures, and geometry. This book examines a critical aspect of Newton’s work that has not been tightly connected to his actual practice: His philosophy of mathematics. Newton aimed to inject certainty into natural philosophy by deploying mathematical reasoning (titling his main work The Mathematical Principles of Natural Philosophy most probably to highlight a stark contrast to Descartes’ Principles of Philosophy). To that end he paid concerted attention to method, particularly in relation to the issue of certainty, participating in contemporary debates on the subject and elaborating his own answers. The author shows how Newton carefully positioned himself against two giants in the “common” and “new” analysis, Descartes and Leibniz. Although his work was in many ways disconnected from the traditions of Greek geometry, Newton portrayed himself as antiquity’s legitimate heir, thereby distancing himself from the moderns. The author reconstructs Newton’s own method by extracting it from his concrete practice and not solely by examining his broader statements about such matters. He examines the full range of Newton’s works, from his early treatises on series and fluxions to the late writings, which were produced in direct opposition to Leibniz. The complex interactions between Newton’s understanding of method and his mathematical work then reveal themselves through the author’s analysis of selected examples. The book uncovers what mathematics was for Newton, and what being a mathematician meant to him.Less
Historians of mathematics have devoted considerable attention to Isaac Newton’s work on algebra, series, fluxions, quadratures, and geometry. This book examines a critical aspect of Newton’s work that has not been tightly connected to his actual practice: His philosophy of mathematics. Newton aimed to inject certainty into natural philosophy by deploying mathematical reasoning (titling his main work The Mathematical Principles of Natural Philosophy most probably to highlight a stark contrast to Descartes’ Principles of Philosophy). To that end he paid concerted attention to method, particularly in relation to the issue of certainty, participating in contemporary debates on the subject and elaborating his own answers. The author shows how Newton carefully positioned himself against two giants in the “common” and “new” analysis, Descartes and Leibniz. Although his work was in many ways disconnected from the traditions of Greek geometry, Newton portrayed himself as antiquity’s legitimate heir, thereby distancing himself from the moderns. The author reconstructs Newton’s own method by extracting it from his concrete practice and not solely by examining his broader statements about such matters. He examines the full range of Newton’s works, from his early treatises on series and fluxions to the late writings, which were produced in direct opposition to Leibniz. The complex interactions between Newton’s understanding of method and his mathematical work then reveal themselves through the author’s analysis of selected examples. The book uncovers what mathematics was for Newton, and what being a mathematician meant to him.
John M. Dixon
- Published in print:
- 2016
- Published Online:
- August 2016
- ISBN:
- 9780801448034
- eISBN:
- 9781501703515
- Item type:
- chapter
- Publisher:
- Cornell University Press
- DOI:
- 10.7591/cornell/9780801448034.003.0007
- Subject:
- History, American History: early to 18th Century
This chapter examines Cadwallader Colden's colonial philosophy and how it served to integrate European and American scientific thought. The Anglo-Irish philosopher, Bishop George Berkeley, questioned ...
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This chapter examines Cadwallader Colden's colonial philosophy and how it served to integrate European and American scientific thought. The Anglo-Irish philosopher, Bishop George Berkeley, questioned the intellectual credibility of new scientific knowledge. He rejected calculus on the basis that it invoked confusing and philosophically unsustainable terms and claimed that matter was imperceptible and therefore unknowable. These arguments were rejected by Colden, insisting that they threatened the eighteenth century's historic opportunity to create an enlightened age of useful knowledge. This chapter discusses Colden's efforts to defeat Berkleyan philosophy by writing an essay on fluxions in 1743 and introducing a theory of active matter that was published in 1746. It also considers how Colden became embroiled in religious as well as philosophical controversy in his attempt to answer Berkeley. Finally, it explores how Colden combined his investigations into natural philosophy with a revived interest in medicine and physiology during the 1740s.Less
This chapter examines Cadwallader Colden's colonial philosophy and how it served to integrate European and American scientific thought. The Anglo-Irish philosopher, Bishop George Berkeley, questioned the intellectual credibility of new scientific knowledge. He rejected calculus on the basis that it invoked confusing and philosophically unsustainable terms and claimed that matter was imperceptible and therefore unknowable. These arguments were rejected by Colden, insisting that they threatened the eighteenth century's historic opportunity to create an enlightened age of useful knowledge. This chapter discusses Colden's efforts to defeat Berkleyan philosophy by writing an essay on fluxions in 1743 and introducing a theory of active matter that was published in 1746. It also considers how Colden became embroiled in religious as well as philosophical controversy in his attempt to answer Berkeley. Finally, it explores how Colden combined his investigations into natural philosophy with a revived interest in medicine and physiology during the 1740s.
Joseph Mazur
- Published in print:
- 2016
- Published Online:
- January 2018
- ISBN:
- 9780691173375
- eISBN:
- 9781400850112
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691173375.003.0019
- Subject:
- Mathematics, History of Mathematics
This chapter discusses Isaac Newton's contributions to algebra and mathematics, and particularly in terms of using symbols. It first examines Newton's idea of unknown variables as quantities flowing ...
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This chapter discusses Isaac Newton's contributions to algebra and mathematics, and particularly in terms of using symbols. It first examines Newton's idea of unknown variables as quantities flowing along a curve. Fluents, as he called them (from the Latin fluxus, which means “fluid”), were very close to the things that we now call dependent variables, our x's, but limited by their dependence on time. Newton thought of curves as “flows of points” that represented quantities. According to Newton, the fundamental task of calculus was to find the fluxions of given fluents and the fluents of given fluxions. The chapter also considers Newton's work on infinitesimals and how his invention of calculus advanced a wide range of fields such as architecture, astronomy, chemistry, optics, and thermodynamics. It also describes some of the major developments that occurred in the fifty years following Newton's death.Less
This chapter discusses Isaac Newton's contributions to algebra and mathematics, and particularly in terms of using symbols. It first examines Newton's idea of unknown variables as quantities flowing along a curve. Fluents, as he called them (from the Latin fluxus, which means “fluid”), were very close to the things that we now call dependent variables, our x's, but limited by their dependence on time. Newton thought of curves as “flows of points” that represented quantities. According to Newton, the fundamental task of calculus was to find the fluxions of given fluents and the fluents of given fluxions. The chapter also considers Newton's work on infinitesimals and how his invention of calculus advanced a wide range of fields such as architecture, astronomy, chemistry, optics, and thermodynamics. It also describes some of the major developments that occurred in the fifty years following Newton's death.
Niccolò Guicciardini
- Published in print:
- 2009
- Published Online:
- August 2013
- ISBN:
- 9780262013178
- eISBN:
- 9780262258869
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262013178.003.0001
- Subject:
- History, History of Science, Technology, and Medicine
This chapter presents a survey of Isaac Newton’s mathematical work and the development of his theories on the mathematical method that began to mature. It explores Newton’s early influences in the ...
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This chapter presents a survey of Isaac Newton’s mathematical work and the development of his theories on the mathematical method that began to mature. It explores Newton’s early influences in the field of mathematics, such as Isaac Barrow and Descartes, and then outlines the first steps in his quest for mathematical mastery. The chapter also details Newton’s encounter with the problem of drawing tangents to plane curves and explores his discovery of the fluxions in the mid-1600s. It also briefly explores Newton’s mathematical maturity when he was elected as the Lucasian Professor at Cambridge University, succeeding Isaac Barrow, in which he discussed and claimed that certainty in natural philosophy can be attained through the use of geometry.Less
This chapter presents a survey of Isaac Newton’s mathematical work and the development of his theories on the mathematical method that began to mature. It explores Newton’s early influences in the field of mathematics, such as Isaac Barrow and Descartes, and then outlines the first steps in his quest for mathematical mastery. The chapter also details Newton’s encounter with the problem of drawing tangents to plane curves and explores his discovery of the fluxions in the mid-1600s. It also briefly explores Newton’s mathematical maturity when he was elected as the Lucasian Professor at Cambridge University, succeeding Isaac Barrow, in which he discussed and claimed that certainty in natural philosophy can be attained through the use of geometry.
Niccolò Guicciardini
- Published in print:
- 2009
- Published Online:
- August 2013
- ISBN:
- 9780262013178
- eISBN:
- 9780262258869
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262013178.003.0008
- Subject:
- History, History of Science, Technology, and Medicine
This chapter explores the analytical method of fluxions, as stated in De Methodis. Newton’s method of fluxions can be divided into two parts: The direct and the inverse. Newton considered the ...
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This chapter explores the analytical method of fluxions, as stated in De Methodis. Newton’s method of fluxions can be divided into two parts: The direct and the inverse. Newton considered the techniques of the direct method to be perfected, as presented in his treatise De Methodis. After making his De Methodis treatise, he also sought to develop his inverse method algorithm, while also creating a better conceptual foundation to the direct method. The chapter notes that Newton continued in improving the two methods until he composed the De Quadratura, a work which explains the most advanced refinement of his method of fluxions.Less
This chapter explores the analytical method of fluxions, as stated in De Methodis. Newton’s method of fluxions can be divided into two parts: The direct and the inverse. Newton considered the techniques of the direct method to be perfected, as presented in his treatise De Methodis. After making his De Methodis treatise, he also sought to develop his inverse method algorithm, while also creating a better conceptual foundation to the direct method. The chapter notes that Newton continued in improving the two methods until he composed the De Quadratura, a work which explains the most advanced refinement of his method of fluxions.
Thomas Nail
- Published in print:
- 2018
- Published Online:
- December 2018
- ISBN:
- 9780190908904
- eISBN:
- 9780190908942
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780190908904.003.0012
- Subject:
- Political Science, Political Theory, International Relations and Politics
This chapter argues that being flows and folds, but is also distributed by a field. Flows join into stable folds, and folds are conjoined into things, but things are also arranged or ordered together ...
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This chapter argues that being flows and folds, but is also distributed by a field. Flows join into stable folds, and folds are conjoined into things, but things are also arranged or ordered together through a field of circulation. This is the third concept in the theory of motion. A field is a single continuous flow that has a kinetic vector for each period on its surface. If flows intersect and folds periodically cycle, fields organize them all in a continuous feedback loop. This chapter provides a kinetic theory of how conjoined flows become organized according to distinct regimes or fields of motion.Less
This chapter argues that being flows and folds, but is also distributed by a field. Flows join into stable folds, and folds are conjoined into things, but things are also arranged or ordered together through a field of circulation. This is the third concept in the theory of motion. A field is a single continuous flow that has a kinetic vector for each period on its surface. If flows intersect and folds periodically cycle, fields organize them all in a continuous feedback loop. This chapter provides a kinetic theory of how conjoined flows become organized according to distinct regimes or fields of motion.
