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.

Verse Miscellanies in the Eighteenth Century

2016 ◽  
Author(s):  
Carly Watson
Keyword(s):  
Eighteenth Century ◽  
Seventeenth Century ◽  
Significant Contribution ◽  
Literary Culture ◽  
Literary Canon ◽  
The Status ◽  
Critical Understanding ◽  
Distinct Kind

The eighteenth century was an age of miscellanies; thousands of miscellaneous collections containing verse appeared in print over the course of the century. This article considers miscellanies as a distinct kind of verse collection; whereas anthologies promote authorship as a category of literary definition, miscellanies invite readers to sample a variety of poetic forms and genres and often include poems without authorial attribution. The eighteenth-century tradition of miscellanies devoted exclusively to poetry has its roots in the late seventeenth century, and many aspects of seventeenth-century miscellany culture persisted well into the next century. This article looks at a number of ways in which verse miscellanies offer fresh perspectives on eighteenth-century literary culture. The popularity and reception of particular poems and poets, the formation of the English literary canon, and the status of authorship are all areas in which miscellanies make a significant contribution to critical understanding.

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.

From Toleration to Verbesserung: German and English Debates on the Jews in the Eighteenth Century

1989 ◽  
Vol 22 (1) ◽  
pp. 3-32 ◽  
Author(s):  
Robert Liberles
Keyword(s):  
Eighteenth Century ◽  
Seventeenth Century ◽  
Jewish Population ◽  
Civil Servant ◽  
Public Debate ◽  
Moses Mendelssohn ◽  
General Utility ◽  
The Status ◽  
Jewish Immigrants ◽  
Council Of State

In 1780 Christian Dohm, a ranking Prussian civil servant, collaborated with the Berlin Jewish philosopher Moses Mendelssohn on a memorandum submitted on behalf of the Jews of Alsace to the French Council of State. A year later Dohm issued his Über die bürgerliche Verbesserung der Juden, a treatise on the civil improvement of the Jews, which contained a comprehensive program for increasing the general utility of the Jewish population. By that time, the European debate over the Jews was already long in progress. The seventeenth century had dealt with the question of readmission and the first half of the eighteenth century less successfully with naturalization. Both debates had centered in England, although the issues involved were pertinent to Holland, France, and to some extent Italy as well. Both debates had also produced a considerable number of polemics. Most recently, a 1753 bill sponsored by the Pelham government sought to facilitate the process of naturalization for Jewish immigrants. The so-called Jew Bill precipitated a wide-ranging public debate on the status of the Jews in England.

Essay review. Robert Hooke under the microscope

2004 ◽  
Vol 58 (3) ◽  
pp. 299-302
Author(s):  
J. Friesen
Keyword(s):  
Seventeenth Century ◽  
Royal Society ◽  
Scientific Revolution ◽  
Essay Review ◽  
Founding Father ◽  
Robert Hooke ◽  
Isaac Newton ◽  
The Status ◽  
Four Books ◽  
Century Thought

Three centuries after Hooke's death his contributions to late seventeenth–century thought are only beginning to be examined in their totality. Hooke's reputation as a leading experimentalist and founding father of The Royal Society has been obscured by the success of his rival Isaac Newton and pro–Newtonian historiography that has portrayed him as the man who thought of the grand idea second, an innovative figure who vindictively accused Newton and others of plagiarism despite his own failures to publicize his discoveries or to carry his many projects to completion. These four books attempt to rescue Hooke from historical neglect. As Jardine in her biography explains, the goal is ‘to retrieve Hooke and his genius, and give him back the status he undoubtedly deserves today, as a groundbreaking thinker and brilliant experimentalist, a founding figure in the European scientific revolution’.

Acoustics in the early Royal Society 1660-1680

1982 ◽  
Vol 36 (2) ◽  
pp. 155-175 ◽  
Keyword(s):  
Eighteenth Century ◽  
Seventeenth Century ◽  
Detailed Analysis ◽  
Music Theory ◽  
Royal Society ◽  
Scientific Discipline ◽  
Isaac Newton ◽  
Collective Interest ◽  
The Subject

The early Royal Society has been the focus of much attention by historians of science over many years, (1) but strangely enough there is no really detailed account to be found of the activities and discussions which took place in the weekly meetings, although there is ample information available on the subject. This study of the Royal Society’s collective interest in acoustics aims to provide a detailed analysis of an important subject that has not been dealt with elsewhere, at the same time as providing a case study of the way in which experiments were suggested and sometimes undertaken in meetings during the first twenty years of the Society’s existence. Apart from the article published forty years ago in this journal by Lloyd, in which the author is concerned only with articles in the Philosophical Transactions relating to music theory and acoustics in the years 1677—1698 (2), the contribution of members of the Royal Society to the topic of acoustics has been treated as subsidiary to that of more famous individuals in the seventeenth century; namely Galileo Galilei, Marin Mersenne, Isaac Newton and Joseph Sauveur. The comparative neglect of the activities of the Royal Society has arisen because writers have been concerned with tracing the ‘progress’ of acoustics as a scientific discipline, in which events in the seventeenth century merely set the scene for the triumphs of John and Daniel Bernoulli and Euler in the eighteenth century.

A wall to separate the barbarians from the Romans

2008 ◽  
Author(s):  
Richard Hingley
Keyword(s):  
Eighteenth Century ◽  
Seventeenth Century ◽  
Civic Virtue ◽  
Military Strategy ◽  
Ruling Elite ◽  
Classical Education ◽  
The Status ◽  
Roman Military ◽  
Hadrian's Wall ◽  
And Control

This chapter explores the ways in which Hadrian’s Wall and the Antonine Wall were interpreted from the late sixteenth to the end of the eighteenth centuries, while also addressing the discovery of the Roman military ‘stations’ of northern Britain. In the context of debates about the unification of England and Scotland, the Walls were commonly used to explore the differing identities of contemporary populations. Writing to a friend in 1739, Sir John Clerk reflected on the meaning of the Roman fortifications of northern England and southern Scotland, observing that: ‘’Tis true the Romans walled out humanity from us, but ’tis as certain they thought the Caledonians a very formidable people, when they, at so much labor and cost, built this wall . . .’ A Scot himself, Clerk’s musings on the purpose of the Picts’ Wall contains a basic interpretational dichotomy, contrasting the exclusion of civility with the scale of northern valour. This chapter assesses the way in which these two ideas were used to explore the contemporary significance of the Roman military fortifications, providing a justification for programmes of surveying and publication. It also assesses how the remains of Roman camps, forts, and military ways that were recognized and planned from the end of the seventeenth century, came to be used to inform eighteenth century military strategy, embodying knowledge relevant to the colonization and control of the Scottish Highland population. The associations with ancient Roman parallels drawn upon at this time derived from the nature of the classical education of the upper classes and the contemporary political context. Antiquity was familiar through the reading of classical texts, a staple element in the education of all gentlemen. The Roman parallel emphasized an idealized notion of virtue and civic patriotism but also stressed ideas of taste, learning, and civic virtue which validated the status of the aristocratic ruling elite. In this context, it was logical that Roman military monuments were seen as providing useful lessons for scholars, landed gentlemen, and military men.

In Support of Nagorno-Karabakh: Social Components of the Armenian Nationalist Movement

1990 ◽  
Vol 18 (2) ◽  
pp. 5-14 ◽  
Author(s):  
Henry R. Huttenbach
Keyword(s):  
Eighteenth Century ◽  
Seventeenth Century ◽  
Soviet Union ◽  
Nationalist Movement ◽  
Autonomous Region ◽  
The Soviet Union ◽  
The Status ◽  
Social Components

Without a thorough grounding in the pre- and post-1917 historical dimension of the Nagorno-Karabakh dispute, one will have difficulty comprehending the depth of sentiment, indeed passion, it arouses among the disputing parties, in this case among Armenians, whether inside or outside the Soviet Union.The roots of prying Nagorno-Karabakh from Muslim control via Russian intervention go back to the seventeenth century when Armenian emissaries contacted the Romanovs and urged them to liberate fellow Christians from Muslim domination. This, in part, led to the eighteenth century Russian campaign to conquer Transcaucasia, the Tsarist court encouraged by the possibility of local Christian support. Through Muslim eyes (a conviction held to this day), this was an act of political sabotage casting the Armenians in the role of political collaborators in collusion with the new Tsarist overlords, a suspicion that finds its modern echoes today as Armenia and Azerbaijan compete for Moscow's support in determining the status of the autonomous region.

LIETUVOS RESPUBLIKONŲ SUVAŽIAVIMAI VILNIUJE 1701 M.: BANDYMAI ĮTVIRTINTI ANTISAPIEGINIO JUDĖJIMO IŠKOVOTĄ VALDŽIĄ

2018 ◽  
pp. 246-268
Author(s):  
Gintautas Sliesoriūnas
Keyword(s):  
Eighteenth Century ◽  
Seventeenth Century ◽  
State Power ◽  
Political Events ◽  
The Status ◽  
New Form ◽  
The Republic ◽  
Grand Duchy Of Lithuania ◽  
Great Northern War ◽  
Grand Duchy

The article analyses two conventions of the Grand Duchy of Lithuania republicans, aristocracy and nobility that won the power in Lithuania at the end of 1700, which took place in Vilnius in 1701. First of the conventions in Vilnius took place 0n May 2–14, 1701. The second convention in Vilnius started meetings in same year, from July 23 through to August 12, 1701. The article discusses documents that were approved in these conventions, location of the gatherings and their significance in the sequence of republican conventions in 1698–1703. The analysis is focused on the influence of the conventions in establishing a new form of republican confederate governance in the Grand Duchy of Lithuania, also assessing the international and military context of the conventions. The conventions of the republicans of the Grand Duchy of Lithuania, having gathered for two meetings in Vilnius in 1701, were the most important political events in the life of Lithuanian state. In the course of these conventions the supreme Lithuanian state power of the time, the nature of which was quite special – close to confederate, decided on the most important issues, facing the new authority, established after the victory by the republicans against the Sapiehas, the aristocrats of the Grand Duchy of Lithuania who by the end of the seventeenth century had reached the status of hegemons. These conventions at the capital of Lithuania were extraordinary events that attracted key politicians of the time and some active nobility, which would not participate in great numbers but still were more actively than at other forums, such as inaugurations and sessions of the Lithuanian Tribunal. Republican conventions were initiated in 1698 and ended in 1703. Both 1701 conventions held their meetings in Vilnius alongside the Vilnius sessions of the Lithuanian Tribunal. First of the conventions took place at the eve of the Sejm of the Republic, and the second one soon after the Sejm, thus problems discussed in the conventions were closely related to the agenda of the Sejm of the Polish and Lithuanian state. Keywords: Grand Duchy of Lithuania, eighteenth century, Great Northern War, Lithuanian Civil War, the Sapiehas, August II, confederation, republicans, Vilnius.

Common Law Constitutionalism

2018 ◽  
Author(s):  
William E. Nelson
Keyword(s):  
Eighteenth Century ◽  
Seventeenth Century ◽  
Common Law ◽  
Legal Profession ◽  
Legal Institutions ◽  
Law System ◽  
The Common ◽  
Common Law System

This chapter shows how common law pleading, the use of common law vocabulary, and substantive common law rules lay at the foundation of every colony’s law by the middle of the eighteenth century. There is some explanation of how this common law system functioned in practice. The chapter then discusses why colonials looked upon the common law as a repository of liberty. It also discusses in detail the development of the legal profession individually in each of the thirteen colonies. Finally, the chapter ends with a discussion of the role of legislation. It shows that, although legislation had played an important role in the development of law and legal institutions in the seventeenth century, eighteenth-century Americans were suspicious of legislation, with the result that the output of pre-Revolutionary legislatures was minimal.

The Musical Topic of the Mass in B Minor

2018 ◽  
Author(s):  
Daniel R. Melamed
Keyword(s):  
Eighteenth Century ◽  
Seventeenth Century ◽  
Sixteenth Century ◽  
Church Music ◽  
Sacred Music ◽  
The Other ◽  
Entire Spectrum ◽  
Giovanni Pierluigi Da Palestrina ◽  
Early Eighteenth Century

If there is a fundamental musical subject of Johann Sebastian Bach’s Mass in B Minor, a compositional problem the work explores, it is the tension between two styles cultivated in church music of Bach’s time. One style was modern and drew on up-to-date music such as the instrumental concerto and the opera aria. The other was old-fashioned and fundamentally vocal, borrowing and adapting the style of Giovanni Pierluigi da Palestrina, his sixteenth-century contemporaries, and his seventeenth-century imitators. The movements that make up Bach’s Mass can be read as exploring the entire spectrum of possibilities offered by these two styles (the modern and the antique), ranging from movements purely in one or the other to a dazzling variety of ways of combining the two. The work illustrates a fundamental opposition in early-eighteenth-century sacred music that Bach confronts and explores in the Mass.

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