Wren the mathematician

1960 ◽  
Vol 15 (1) ◽  
pp. 107-111 ◽  
Keyword(s):  
Seventeenth Century ◽  
Present State ◽  
Mathematical Achievement ◽  
Mathematical Work ◽  
Christiaan Huygens ◽  
John Wallis ◽  
Century Thought

Today Wren’s fame rests solidly on his architectural achievement, and deservedly so. Yet in his own time, and especially before his thoughts had turned towards architecture, he was acclaimed equally for his mathematical brilliance. In a famous passage of the Principia, Newton, master mathematician himself but no flatterer, paid Wren the compliment of ranking him with John Wallis and Christiaan Huygens as a leading geometer of his day, while his supreme mathematical achievement, the rectification of the general cycloid arc, made his name known throughout Europe, earning even Pascal’s approval. It is unfortunately difficult for us to begin to justify this reputation. Wren’s mathematical work now exists, if at all, in detached fragments rescued from oblivion, some in print, and a little more in bare outline in the published work of contemporaries, especially Wallis. Collecting these scattered remains is but a necessary preliminary to any evaluation. Doubts of authorship, uncertainty as to how far existing fragments are typical of his mathematical output and the problem of assessing their importance in the context of seventeenth-century thought, all introduce their further difficulties, and in the present state of knowledge no more than a reasoned reconstruction is possible.

The Indivisibles of the Continuum

2020 ◽  
pp. 104-122
Author(s):  
Douglas M. Jesseph
Keyword(s):  
Seventeenth Century ◽  
Internal Structure ◽  
Original Formulation ◽  
Infinitesimal Calculus ◽  
History Of ◽  
John Wallis ◽  
The Continuum

This chapter considers some significant developments in seventeenth-century mathematics which are part of the pre-history of the infinitesimal calculus. In particular, I examine the “method of indivisibles” proposed by Bonaventura Cavalieri and various developments of this method by Evangelista Torricelli, Gilles Personne de Roberval, and John Wallis. From the beginning, the method of indivisibles faced objections that aimed to show that it was either conceptually ill-founded (in supposing that the continuum could be composed of dimensionless points) or that its application would lead to error. I show that Cavalieri’s original formulation of the method attempted to sidestep the question of whether a continuous magnitude could be composed of indivisibles, while Torricelli proposed to avoid paradox by taking indivisibles to have both non-zero (yet infinitesimal) magnitude and internal structure. In contrast, Roberval and Wallis showed significantly less interest in addressing foundational issues and were content to maintain that the method could (at least in principle) be reduced to Archimedean exhaustion techniques.

Practices of reasoning: persuasion and refutation in a seventeenth-century Chinese mathematical treatise of “linear algebra”

2020 ◽  
Vol 33 (1) ◽  
pp. 65-93
Author(s):  
Jiang-Ping Jeff Chen
Keyword(s):  
Seventeenth Century ◽  
Linear Algebra ◽  
Mathematical Work ◽  
Traditional Practices ◽  
Systematic Treatment ◽  
Mathematical Content ◽  
Mathematical Treatise ◽  
Traditional Approaches

ArgumentThis article documents the reasoning in a mathematical work by Mei Wending, one of the most prolific mathematicians in seventeenth-century China. Based on an analysis of the mathematical content, we present Mei’s systematic treatment of this particular genre of problems, fangcheng, and his efforts to refute the traditional practices in works that appeared earlier. His arguments were supported by the epistemological values he utilized to establish his system and refute the flaws in the traditional approaches. Moreover, in the context of the competition between the Chinese and Western approaches to mathematics, Mei was motivated to demonstrate that the genre of fangcheng problems was purely a “Chinese” achievement, not discussed by the Jesuits. Mei’s motivations were mostly expressed primarily in the prefaces to his works, in his correspondence with other scholars, in synopses of his poems, and in biographical records of some of his contemporaries.

‘Philosophical’ grammar in John Wilkins’s ‘Essay’

1975 ◽  
Vol 20 (2) ◽  
pp. 131-160 ◽  
Author(s):  
Vivian Salmon
Keyword(s):  
Twentieth Century ◽  
Seventeenth Century ◽  
Royal Society ◽  
Natural Philosophy ◽  
Real Character ◽  
Philosophical Language ◽  
John Wilkins ◽  
Century Thought ◽  
Insight Into

Recent studies of John Wilkins, author ofAn essay towards a real character, and a philosophical language(1668) have examined aspects of his life and work which illustrate the modernity of his attitudes, both as a theologian, sympathetic to the ecumenical ideals of seventeenth-century reformers like John Amos Comenius (DeMott 1955, 1958), and as an amateur scientist enthusiastically engaged in forwarding the interests of natural philosophy in his involvement with the Royal Society. His linguistic work has, accordingly, been examined for its relevance to seventeenth-century thought and for evidence of its modernity; described by a twentieth-century scientist as “impressive” and as “a prodigious piece of work” (Andrade 1936:6, 7), theEssayhas been highly praised for its classification of reality (Vickery 1953:326, 342) and for its insight into phonetics and semantics (Linsky 1966:60). It has also, incidentally, been examined for the evidence it offers on seventeenth-century pronunciation (Dobson 1968).

Freedom of Speech in Seventeenth-Century Thought

1999 ◽  
Vol 57 (2) ◽  
pp. 165
Author(s):  
Leonard W. Levy
Keyword(s):  
Seventeenth Century ◽  
Freedom Of Speech ◽  
Century Thought

MUSIC, MORALITY AND SYMPATHY IN THE EIGHTEENTH-CENTURY ENGLISH SERMON

2020 ◽  
Vol 17 (1) ◽  
pp. 9-35
Author(s):  
JONATHAN RHODES LEE
Keyword(s):  
Eighteenth Century ◽  
Seventeenth Century ◽  
Adam Smith ◽  
Musical Life ◽  
Moral Sentiments ◽  
Religious Writing ◽  
Aesthetic Concepts ◽  
Century Thought ◽  
Scholarly Attention ◽  
Theory Of Moral Sentiments

ABSTRACTWhile the furrows of sixteenth- and seventeenth-century religious writing on music have been deeply ploughed, eighteenth-century English sermons about music have received relatively slight scholarly attention. This article demonstrates that the ideas of sympathy and sensibility characteristic of so much eighteenth-century thought are vital to understanding these sermons. There is an evolution in this literature of the notion of sympathy and its link to musical morality, a development in the attitude towards music among clergy, with this art of sympathetic vibrations receiving ever higher approbation during the century's middle decades. By the time that Adam Smith was articulating his Theory of Moral Sentiments (1759) and Handel's oratorios stood as a fixture of English musical life, religious thinkers had cast off old concerns about music's sensuality. They came to embrace a philosophy that accepted music as moral simply because it made humankind feel, and in turn accepted feeling as the root of all sociable experience. This understanding places the music sermon of the eighteenth century within the context of some of the most discussed philosophical, social, literary, musical and moral-aesthetic concepts of the time.

ALHACEN’S APPROACH TO ‘‘ALHAZEN’S PROBLEM’’

2008 ◽  
Vol 18 (2) ◽  
pp. 143-163 ◽  
Author(s):  
A. MARK SMITH
Keyword(s):  
Seventeenth Century ◽  
Medieval Latin ◽  
Absolute Sense ◽  
Christiaan Huygens ◽  
Spherical Mirrors ◽  
Latin Version ◽  
Current Standards

In the fifth book of his De aspectibus, the medieval Latin version of Ibn al-Haytham’s Kitāb al-Manāẓir, Alhacen undertakes to determine precisely where a given ray of light will reflect to a given center of sight from a variety of convex and concave mirrors based on circular sections. As applied specifically to convex and concave spherical mirrors, this problem exercised several seventeenth-century thinkers, Christiaan Huygens foremost among them, and in that context it soon became known as ‘‘Alhazen’s Problem.’’ By current standards, Alhacen’s solution (or solutions) of this problem is deficient in comparison to that of Huygens and later mathematicians. It is my purpose in this paper to show by reconstruction that in fact, far from deficient in any absolute sense, Alhacen’s approach to this problem was remarkably ingenious and elegant in its conceptual simplicity.

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