conic sections

2019 ◽  
Author(s):  
Michael N. Fried
Keyword(s):  
Conic Sections ◽  
General Development ◽  
The Subject ◽  
Greek Mathematics ◽  
Doubling The Cube ◽  
Apollonius Of Perga

The curves known as conic sections, the ellipse, hyperbola, and parabola, were investigated intensely in Greek mathematics. The most famous work on the subject was the Conics, in eight books by Apollonius of Perga, but conics were also studied earlier by Euclid and Archimedes, among others. Conic sections were important not only for purely mathematical endeavors such as the problem of doubling the cube, but also in other scientific matters such as burning mirrors and sundials. How the ancient theory of conics is to be understood also played a role in the general development of the historiography of Greek mathematics.

Homeomeric Lines in Greek Mathematics

2010 ◽  
Vol 23 (1) ◽  
pp. 1-37 ◽  
Author(s):  
Fabio Acerbi
Keyword(s):  
Companion Paper ◽  
Future Issue ◽  
Property A ◽  
Straight Line ◽  
Key Issues ◽  
The Subject ◽  
Cosmological Debate ◽  
Greek Mathematics ◽  
Definition Of ◽  
Cylindrical Helix

ArgumentThis article presents ancient documents on the subject of homeomeric lines. On the basis of such documents, the article reconstructs a definition of the notion as well as a proof of the result, which is left unproved in extant sources, that there are only three homeomeric lines: the straight line, the circumference, and the cylindrical helix. A point of particular historiographic interest is that homeomeric lines were the only class of lines defined directly as the extension of a mathematical property, a move that is unparalleled in Greek mathematics. The far-reaching connections between mathematical homeomery and key issues in the ancient cosmological debate are extensively discussed here. An analysis of its relevance as a foundational theme will be presented in a companion paper in a future issue of Science in Context.

scholarly journals VI. The post-embryonic development of julus terrestris

1888 ◽  
Vol 179 ◽  
pp. 157-179 ◽  
Keyword(s):  
Embryonic Development ◽  
Young Animal ◽  
Full Description ◽  
Larval Life ◽  
General Development ◽  
History Of ◽  
The Subject

In a former paper I traced the development of Julus terrestris from the ovum within the ovary up to the bursting of the shell and the liberation of the young animal on the twelfth day. In the present paper I propose to take the different organs one by one, and to describe their development. This different way of treating the subject seemed to me to be the best: firstly, on account of the difficulty of describing a long and complicated development like that undergone by Julus in its larval life by dividing the history of its growth into periods of time; and, secondly, on account of the nature of the work which has hitherto been done upon this subject. The two most important works bearing on the subject of my paper are those of Newport (13)* and Metschnikoff (12). The former has observed the general development of Julus terrestris , and has given us a most accurate and full description of the external features of the young animals at various stages, from the time of hatching almost up to the adult condition.

scholarly journals Proclus’ division of the mathematical proposition into parts: how and why was it formulated?

1999 ◽  
Vol 49 (1) ◽  
pp. 282-303 ◽  
Author(s):  
Reviel Netz
Keyword(s):  
Logical Form ◽  
Conic Sections ◽  
Mathematical Proposition ◽  
Single Author ◽  
Communication Situation ◽  
Greek Mathematics

There are a number of ways in which Greek mathematics can be seen to be radically original. First, at the level of mathematical contents: many objects and results were first discovered by Greek mathematicians (e.g. the theory of conic sections). Second, Greek mathematics was original at the level of logical form: it is arguable that no form of mathematics was ever axiomatic independently of the influence of Greek mathematics. Finally, third, Greek mathematics was original at the level of form, of presentation: Greek mathematics is written in its own specific, original style. This style may vary from author to author, as well as within the works of a single author, but it is still always recognizable as the Greek mathematical style. This style is characterized (to mention a few outstanding features) by (i) the use of the lettered diagram, (ii) a specific technical terminology, and (iii) a system of short phrases (‘formulae’). I believe this third aspect of the originality—the style—was responsible, indirectly, for the two other aspects of the originality. The style was a tool, with which Greek mathematicians were able to produce results of a given kind (the first aspect of the originality), and to produce them in a special, compelling way (the second aspect of the originality). This tool, I claim, emerged organically, and reflected the communication-situation in which Greek mathematics was conducted. For all this I have argued elsewhere.

Transnational Radicalism and the Connected Lives of Tom Mann and Robert Samuel Ross

2017 ◽  
Author(s):  
Neville Kirk
Keyword(s):  
South Africa ◽  
Original Study ◽  
Transnational History ◽  
Radical Politics ◽  
General Development ◽  
Social Scientists ◽  
Methodological Nationalism ◽  
In Trans ◽  
The Subject ◽  
Anglophone World

This book explores the general development of transnational radicalism between the 1850s and 1940s. This is achieved by means of a new and original study of the connected transnational lives and wider radical worlds of two important socialists, British-born Tom Mann (1856-1941) and Australian-born Robert Samuel Ross (1873-1941). Mann and Ross were very active, as labour organisers, editors and educators, in socialist and labour movements in the Anglophone world and beyond. They met in Australia in 1903, worked individually and together in trans-Tasman radical circles in Australia and New Zealand, and developed strong connections with radicals in the wider world. They kept in close touch after Mann’s departure for Britain, via South Africa, in 1910. They helped to build radical transnational movements and networks that sought to create a socialist alternative to capitalism and capitalist globalisation. These have been largely neglected in the literature. Based upon extensive primary- and secondary-based research, this book seeks to recapture this partly hidden world of transnational radicalism. In so doing it also makes a case in favour of transnational history against the ‘methodological nationalism’ which has dominated the subject of history for so long. It attempts to make a new and useful contribution to the literature on transnationalism, globalisation and social movements. It will appeal not only to historians but social scientists in general and all those interested in radical politics, especially those seeking radical alternatives to today’s neo-liberal globalisation and capitalism.

Applications of Quadratic Equations

1945 ◽  
Vol 38 (3) ◽  
pp. 120-125
Author(s):  
William A. Cordrey
Keyword(s):  
Fourth Century ◽  
Conic Sections ◽  
Quadratic Equations ◽  
The Subject

The advent of quadratic equations antedates the dawn of the Christian era by about two millennia. The study of conics, however, did not get under way until the fourth century prior to the birth of Christ. The first writer on this subject, Menaechmus, used the parabola and hyperbola in duplicating the cube. Several years later Euclid wrote a treatise on conic sections. This work was continued by Apollonius, whose investigations added much to the existing knowdedge of the subject.

Toward Caribbean Self-Help

Worldview ◽  
1982 ◽  
Vol 25 (1) ◽  
pp. 19-21
Author(s):  
Francis X. Gannon
Keyword(s):  
Economic Growth ◽  
Costa Rica ◽  
Central America ◽  
Caribbean Basin ◽  
General Development ◽  
Financial Policies ◽  
International Assistance ◽  
Island States ◽  
Self Help ◽  
The Subject

World attention now rivets on a troubled Central America — from Guatemala to Costa Rica — and on surrounding island states of the larger Caribbean basin. In many international forums the question is asked: Can an international assistance effort, with financial, technical, and market components, be mounted to assist the hemispheric subregion in achieving a more stable, secure, and peaceful ground for economic growth and general development? The subject is not a new one by any means. In fact, since 1945 it has found its way again and again onto the Hemisphere's geopolitical and economic agenda.Skeptics argue the futility of any effort to transfer resources from the wealthier to the poorer countries, maintaining that “official transfers cannot significantly promote development,” since they have too many adverse consequences on recipient nations, including encouragement of “imprudent financial policies.”

Ein Leben Mohammeds

Millennium ◽  
2018 ◽  
Vol 15 (1) ◽  
pp. 177-232
Author(s):  
Paul Dräger
Keyword(s):  
Subject Matter ◽  
Latin Text ◽  
General Development ◽  
12Th Century ◽  
The Subject ◽  
Guibert Of Nogent ◽  
The City ◽  
Annotated Translation

AbstractThe principal purpose and nucleus of the article is the publication of a Latin text of highly demanding qualities in terms of philological principles which, in connection with its first abundantly annotated translation into German, has hitherto scarcely been noticed by researchers. The only literary collection which bears witness to the existence of the manuscript is a folio edition which presumably came into being in the middle of the 12th century, i. e. during the time of the crusades (conquest of Jerusalem in 1099) and is kept in the municipal library of the city of Treves. The dialogue between the anonymous author and a Greek, who hates the Saracens, forms the content. When, in the centre of the text, the author asks about Mohammed, the ‘monster’ (monstrum), the Greek relates the life of the hater of all Christians in the darkest colours. He begins wit Mohammed’s youth when he was a swineherd, continues with his devil-initiated encounter with the heretic Nestorius and the general development of a new common ‘faith’ as well as its spreading among the desert tribes by means of sorcery and deceipt and the student’s treacherous murder of his teacher. The assassin is then married to a Babylonian royal widow and, finally, meets his contumelious death caused by a pigs’ attack. The repeated comparison of our text with poetical ‘western’ scripts of the 11th and 12th centuries (Embricho of Mayence, Guibert of Nogent, Walter of Compiègne) as regards the subject matter leads us to the conclusion that our manuscript is likely to be of a most Islam critical tendency.

scholarly journals РЕАЛИЗАЦИЯ НАВЫКОВ АВТОКОРРЕКЦИИ ЦЕННОСТНОЙ СФЕРЫ ЛИЧНОСТИ С ПОМОЩЬЮ АРТ-ТЕРАПЕВТИЧЕСКОЙ МЕТОДИКИ «EIDEALING»

World Science ◽  
2019 ◽  
Vol 3 (3(43)) ◽  
pp. 29-33
Author(s):  
Shugalei Elena Viktorovna
Keyword(s):  
Cognitive Strategies ◽  
Reference Points ◽  
Personal Meaning ◽  
Psychological State ◽  
Social Aspects ◽  
General Development ◽  
Skill Formation ◽  
The Past ◽  
Autonomous Search ◽  
The Subject

The subject of the research is the assessment of effectiveness of the art- therapeutic method “Eidealing”, which is aimed at mastering the strategy and skills of structural self-analysis of the value sphere and the value images transformation, reference points, their hierarchy and event scenarios. The study revealed the important value inquiries at the participants of the method, both in personal and social aspects, and their transformation over the past 2 years. The result of eidling as a process is a picture harmoniously composed and having a personal meaning, which contributes to the correction of psychological state and to motivation for the autonomous search for sustainable personal decisions, to the extension of mindfulness zones and to the psychological auto-correction skill formation. The personal interpretation of the symbols received allows a person to move into the field of informed decisions. The method helps to develop individual cognitive and sensory mechanisms, the natural synesthesia capabilities, and consolidate them using cognitive strategies acquired at the Eidealing. As a result of applying the Eidealing method, the skills have sustainable auto-correctional character and contribute to the general development of cognitive and creative abilities.

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