Euler's contribution to number theory

2007 ◽  
Vol 91 (522) ◽  
pp. 453-461 ◽  
Author(s):  
Peter Shiu
Keyword(s):  
Eighteenth Century ◽  
Number Theory ◽  
Scientific Output ◽  
Scholarly Work ◽  
Long Period ◽  
Peter The Great ◽  
Complete Work ◽  
Leonhard Euler ◽  
The Subject ◽  
Historic Background

Individuals who excel in mathematics have always enjoyed a well deserved high reputation. Nevertheless, a few hundred years back, as an honourable occupation with means to social advancement, such an individual would need a patron in order to sustain the creative activities over a long period. Leonhard Euler (1707-1783) had the fortune of being supported successively by Peter the Great (1672-1725), Frederich the Great (1712-1786) and the Great Empress Catherine (1729-1791), enabling him to become the leading mathematician who dominated much of the eighteenth century. In this note celebrating his tercentenary, I shall mention his work in number theory which extended over some fifty years. Although it makes up only a small part of his immense scientific output (it occupies only four volumes out of more than seventy of his complete work) it is mostly through his research in number theory that he will be remembered as a mathematician, and it is clear that arithmetic gave him the most satisfaction and also much frustration. Gazette readers will be familiar with many of his results which are very well explained in H. Davenport's famous text [1], and those who want to know more about the historic background, together with the rest of the subject matter itself, should consult A. Weil's definitive scholarly work [2], on which much of what I write is based. Some of the topics being mentioned here are also set out in Euler's own Introductio in analysin infinitorum (1748), which has now been translated into English [3].

Oswald Spengler and the Theory of Historical Cycles

Antiquity ◽  
1927 ◽  
Vol 1 (3) ◽  
pp. 311-325 ◽  
Author(s):  
R. G. Collingwood
Keyword(s):  
Eighteenth Century ◽  
General Theory ◽  
The West ◽  
Long Period ◽  
History Of ◽  
The Subject ◽  
Early Eighteenth Century ◽  
Historical Cycles ◽  
European Thought ◽  
Complete History

Since Plato announced that the course of history returned upon itself in 72,000 years, since Polybius discerned a “circular movement” by which the history of states came back, over and over again, to the same point, the theory of historical cycles has been a commonplace of European thought. Familiar to the thinkers of the Renaissance, it was modified by Vico in the early eighteenth century and again by Hegel in the early nineteenth; and a complete history of the idea would show many curious transformations and cover a long period of time. Here no attempt will be made to summarize this story; the subject of the present paper is the latest and, to ourselves, most striking exposition of the general theory, contained in Dr Oswald Spengler’s Decline of the West.

Isabeau of Bavaria, Queen of France (1385–1422): The Creations of an Historical Villainess (The Alexander Prize Essay)

1996 ◽  
Vol 6 ◽  
pp. 51-73 ◽  
Author(s):  
Rachel Gibbons
Keyword(s):  
Internal Conflict ◽  
Scholarly Work ◽  
First Line ◽  
Research Papers ◽  
The Past ◽  
Personal Profile ◽  
Complete Work ◽  
History Of ◽  
The Subject ◽  
Historical Tradition

Considering the high personal profile and influence of Isabeau of Bavaria during her time as queen of France between 1385 and 1422, it is extraordinary that she has not been the subject of more sustained serious academic study in the past, and that so little is known about her. The woman at the centre of such a turbulent period of Anglo-French war and internal conflict is far too often dismissed in the space of a few paragraphs; even then, what is written about her is often one-sided, two-dimensional and, in many cases, plain wrong. The history of Isabeau of Bavaria so far has largely been a fabricated mixture of gossip and propaganda which has been absorbed into historical tradition and repeated so often that, to many, legend has become indistinguishable from fact. For a mere two decades it has been accepted that: ‘Isabeau ne mérite point la réputation qui lui fut faite’, and it cannot be a coincidence that the few historians who have devoted any time to research on Isabeau all have come to the conclusion that her infamous legacy is not deserved. Yet, the movement for Isabeau of Bavaria's rehabilitation has not been as prominent as it might have been: Vallet de Viriville only wrote a few articles about her, Marcel Thibault never produced the promised second part of his biography and Yann Grandeau sadly died before his research papers could be developed into a complete work. The very first line that Thibault wrote in 1901 makes the claim that: ‘L'histoire vraie et complète d'Isabeau de Bavière n'a jamais été ecrite’ and, despite recent scholarly work, this still seems to be die case almost a century later.

scholarly journals Modernisation of the Russian state’s political elite in the context of peter the great’s transformations

2021 ◽  
pp. 32-38
Author(s):  
D. A. Filimonov
Keyword(s):  
Eighteenth Century ◽  
Seventeenth Century ◽  
Political Elite ◽  
The Other ◽  
The Political ◽  
Russian Society ◽  
Long Period ◽  
Peter The Great ◽  
Russian State ◽  
The One

Early eighteenth century was the age of Peter the Great’s transformations, which affected many spheres of life of Russian society, and, in particular, caused the restructuring of the highest political elite. The reforms were, on the one hand, conditioned by the processes of the late seventeenth century, on the other hand, by the specificity of Peter’s absolutism and the long period of warfare. The article analyses the features of Peter’s reforms of the higher political elite. The background to the reforms has been examined, and Peter the Great’s personnel policy, approaches and principles have been analysed. Particular attention has been paid to institutional change, looking at the mechanisms used by Peter the Great in replacing obsolete institutions with new ones. An analysis of the qualitative composition of the elite made it possible to establish a continuity between the political elite of Peter the Great and the aristocracy of the earlier period, with a change in the principles of interaction. The post-reform Russian state is no longer built on the principles of the “servant state”, but on absolutism with a rationalist approach and the principle of “suitability”. 

C. S. Lewis and the Truth about Angels

2013 ◽  
Vol 3 (2) ◽  
pp. 97-110
Author(s):  
Janice Brown
Keyword(s):  
Renaissance Literature ◽  
Scholarly Work ◽  
Deep Space ◽  
The Subject

Lewis’s perspective on angels is apparent in The Discarded Image, his scholarly work on medieval and Renaissance literature. His preface to The Screwtape Letters reveals the seriousness with which he approaches the subject: it proposes that a mistaken view of angelic beings is more dangerous than ignorance of them. The space trilogy seeks to avert that danger. In it we are confronted by angelic eldila—inscrutable and holy beings inhabiting “deep space” who relentlessly accomplish the purposes of the Almighty. Characterized by absolute goodness and archetypal charity, they are serene yet they pulsate with energy. Lewis’s intense interest in angels is further apparent in a number of his poems. Throughout his work he depicts angels as real beings, inhabiting an actual universe, who actually participate our lives. They represent mysterious eternal realities, yet they are part of God’s daily providence.

Rights, Authority, and Workability: An Examination of Universal Jurisdiction

2019 ◽  
Vol 3 ◽  
pp. 7-17
Author(s):  
Srdan Durica
Keyword(s):  
Universal Jurisdiction ◽  
Scholarly Work ◽  
Contemporary State ◽  
The Core ◽  
Core Areas ◽  
The Subject

In this paper, I conceptualize ‘universal jurisdiction’ along three axes: rights, authority, and workability to reduce the compendium of scholarly work on the subject into three prominent focus areas. I then review the longstanding debates between critics and supports, and ultimately show the vitality of this debate and persuasiveness of each side’s sets of arguments. By using these three axes as a sort of methodological filter, one can develop a richer understanding of universal jurisdiction, its theoretical pillars, practical barriers, and the core areas of contention that form the contemporary state of knowledge.

Statistical Evaluation for claims and disputes in construction contracts

2017 ◽  
Vol 5 (2) ◽  
pp. 80-96
Author(s):  
Raid Saleem Abd Ali ◽  
Nooran kanaan Yassin
Keyword(s):  
Construction Projects ◽  
Statistical Evaluation ◽  
Relative Importance ◽  
Minimum Level ◽  
Construction Contracts ◽  
Long Period ◽  
Price Schedule ◽  
Questionnaire Form ◽  
The Subject ◽  
The Cost

This research aims to diagnose and identify the causes of claims and disputes between the contractor and the employer, also review the methods used to resolve disputes in construction contracts. In order to achieve the goal of the research, scientific methodology is followed to collect information and data on the subject of claims and disputes in construction projects in Iraq through personal interviews and questionnaire form. The most important results in this research are: the price schedule contract as a kind of competitive contracts is the most important and guarantee for the completion of minimum level of claims and disputes with relative importance of (84.1), compared with the (cost plus a percentage of the cost contract) as a kind of negotiating contracts is the most relative importance of (79.6), and the turnkey contract as a kind of special contracts is the most relative importance of (74.2). The  contractor and  his agents are one of the most influence sources in occurring claims and disputes in construction contracts with relative importance of (77.4) followed by the contract documents with relative importance of (74.2) and then the employer with relative importance of (73.2). In addition to the long period of litigation and the multiplicity of veto grades are most negative when contractual disputes have resolved by it, and with relative importance of (86), followed by the large number of issues and lack of efficiency and specialty of Judges with relative importance (78.4). Finally, the direct negotiation method (relative importance of 77) is one of the most friendly settlement ways favored by conflicted parties, while the resolution of disputes and claims board (relative importance of 10) occupied the last rank in the friendly settlement ways.

Historical Fragments’ Mobile Echo

Transfers ◽  
2017 ◽  
Vol 7 (2) ◽  
pp. 115-119 ◽  
Author(s):  
Susan E. Bell ◽  
Kathy Davis
Keyword(s):  
Nineteenth Century ◽  
Twentieth Century ◽  
Eighteenth Century ◽  
Cultural Revolution ◽  
Ming Dynasty ◽  
Third Century ◽  
Refugee Crisis ◽  
The Third ◽  
Opium War ◽  
The Subject

Translocation – Transformation is an ambitious contribution to the subject of mobility. Materially, it interlinks seemingly disparate objects into a surprisingly unified exhibition on mobile histories and heritages: twelve bronze zodiac heads, silk and bamboo creatures, worn life vests, pressed Pu-erh tea, thousands of broken antique teapot spouts, and an ancestral wooden temple from the Ming dynasty (1368–1644) used by a tea-trading family. Historically and politically, the exhibition engages Chinese stories from the third century BCE, empires in eighteenth-century Austria and China, the Second Opium War in the nineteenth century, the Chinese Cultural Revolution of the mid-twentieth century, and today’s global refugee crisis.

The Laws of Hammurabi

2020 ◽  
Author(s):  
Pamela Barmash
Keyword(s):  
Eighteenth Century ◽  
Roman Law ◽  
Intellectual Culture ◽  
Biblical Law ◽  
Intellectual Tradition ◽  
Legal Principles ◽  
Copernican Revolution ◽  
The Subject ◽  
The Law

The Laws of Hammurabi is one of the earliest law codes, dating from the eighteenth century BCE Mesopotamia (ancient Iraq). It is the culmination of a tradition in which scribes would demonstrate their legal flair by composing statutes on a repertoire of traditional cases, articulating what they deemed just and fair. The book describes how the scribe of the Laws of Hammurabi advanced beyond earlier scribes in composing statutes that manifest systematization and implicit legal principles. The scribe inserted the statutes into the structure of a royal inscription, skillfully reshaping the genre. This approach allowed the king to use the law code to demonstrate that Hammurabi had fulfilled the mandate to guarantee justice enjoined upon him by the gods, affirming his authority as king. This tradition of scribal improvisation on a set of traditional cases continued outside of Mesopotamia, influencing biblical law and the law of the Hittite Empire and perhaps shaping Greek and Roman law. The Laws of Hammurabi is also a witness to the start of another stream of intellectual tradition. It became a classic text and the subject of formal commentaries, marking a Copernican revolution in intellectual culture.

Clausewitz and the Eighteenth-Century Context of Partisan Warfare

2018 ◽  
Author(s):  
Sibylle Scheipers
Keyword(s):  
Eighteenth Century ◽  
Intellectual Development ◽  
Small Wars ◽  
System P ◽  
The Subject ◽  
Partisan Warfare

Clausewitz was an ardent analyst of partisan warfare. In 1810 and 1811, he lectured at the Berlin Kriegsschule, the war academy, on the subject of small wars. Clausewitz’s lectures focused on the tactical nature of small wars. However, the eighteenth-century context was by no means irrelevant for Clausewitz’s further intellectual development. On the contrary, he extrapolated from his analysis of the tactical nature of small wars their strategic potential, as well as their exemplary nature for the study of war as such. The partisan, in Clausewitz’s eyes, possessed exemplary qualities in that he acted autonomously and, in doing so, had to draw upon all his human faculties. As such, he was the paradigmatic antagonist to the regular soldier who displayed a ‘cog mentality’ fostered by the Frederickian military system.

On the Shoulders of Giants

2018 ◽  
Author(s):  
David D. Nolte
Keyword(s):  
Eighteenth Century ◽  
Robert Hooke ◽  
New Approach ◽  
Isaac Newton ◽  
Least Action ◽  
New Science ◽  
Principle Of Least Action ◽  
Parabolic Trajectory ◽  
Leonhard Euler ◽  
New Generation

Galileo’s parabolic trajectory launched a new approach to physics that was taken up by a new generation of scientists like Isaac Newton, Robert Hooke and Edmund Halley. The English Newtonian tradition was adopted by ambitious French iconoclasts who championed Newton over their own Descartes. Chief among these was Pierre Maupertuis, whose principle of least action was developed by Leonhard Euler and Joseph Lagrange into a rigorous new science of dynamics. Along the way, Maupertuis became embroiled in a famous dispute that entangled the King of Prussia as well as the volatile Voltaire who was mourning the death of his mistress Emilie du Chatelet, the lone female French physicist of the eighteenth century.

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