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  Subjects -> HISTORY (Total: 1508 journals)
    - HISTORY (908 journals)
    - History (General) (58 journals)
    - HISTORY OF AFRICA (59 journals)
    - HISTORY OF ASIA (61 journals)
    - HISTORY OF AUSTRALASIA AREAS (9 journals)
    - HISTORY OF EUROPE (204 journals)
    - HISTORY OF THE AMERICAS (158 journals)
    - HISTORY OF THE NEAR EAST (51 journals)

HISTORY (908 journals)                  1 2 3 4 5 | Last

Showing 1 - 200 of 452 Journals sorted alphabetically
40 [degrees] South     Full-text available via subscription   (Followers: 3)
Aboriginal History     Full-text available via subscription   (Followers: 10)
Abstracta Iranica     Open Access   (Followers: 14)
Acadiensis : Journal of the History of the Atlantic Region / Acadiensis : revue d'histoire de la region Atlantique     Full-text available via subscription   (Followers: 4)
Accounting History Review     Hybrid Journal   (Followers: 21)
Acta Amazonica     Open Access   (Followers: 6)
Acta Historiae Artium     Full-text available via subscription   (Followers: 4)
Acta Musei Nationalis Pragae ? Historia litterarum     Open Access  
Acta Orientalia     Full-text available via subscription   (Followers: 19)
Actes d'Història de la Ciència i de la Tècnica     Open Access   (Followers: 1)
Advances in Historical Studies     Open Access   (Followers: 7)
Advances in Software Engineering     Open Access   (Followers: 10)
Africa Confidential     Hybrid Journal   (Followers: 22)
Africa Research Bulletin: Political, Social and Cultural Series     Hybrid Journal   (Followers: 13)
Africa Today     Full-text available via subscription   (Followers: 18)
African and Asian Studies     Hybrid Journal   (Followers: 25)
African Diaspora     Open Access   (Followers: 9)
African Historical Review     Hybrid Journal   (Followers: 17)
African Natural History     Open Access   (Followers: 2)
Agora     Full-text available via subscription   (Followers: 5)
Agricultural History Review     Full-text available via subscription   (Followers: 12)
Akroterion     Full-text available via subscription   (Followers: 6)
Al-Masaq: Islam and the Medieval Mediterranean     Hybrid Journal   (Followers: 28)
albuquerque : revista de história     Open Access  
Almagest     Full-text available via subscription  
Altorientalische Forschungen     Hybrid Journal   (Followers: 7)
American Archivist     Hybrid Journal   (Followers: 197)
American Communist History     Hybrid Journal   (Followers: 19)
American Jewish History     Full-text available via subscription   (Followers: 17)
American Nineteenth Century History     Hybrid Journal   (Followers: 25)
American Periodicals : A Journal of History, Criticism, and Bibliography     Full-text available via subscription   (Followers: 8)
American Review of Canadian Studies     Hybrid Journal   (Followers: 7)
American Studies     Full-text available via subscription   (Followers: 21)
Amérique Latine Histoire et Mémoire     Open Access   (Followers: 2)
Amsterdamer Beitrage zur alteren Germanistik     Full-text available via subscription   (Followers: 3)
Anadolu Araştırmaları     Open Access  
Anais do Museu Paulista : História e Cultura Material     Open Access  
Analecta Bollandiana     Full-text available via subscription   (Followers: 2)
Anales de Historia del Arte     Open Access   (Followers: 6)
Anatolica     Full-text available via subscription   (Followers: 13)
Ancient Civilizations from Scythia to Siberia     Hybrid Journal   (Followers: 12)
Ancient History : Resources for Teachers     Full-text available via subscription   (Followers: 6)
Ancient Mesoamerica     Hybrid Journal   (Followers: 10)
Anglican Historical Society Journal     Full-text available via subscription   (Followers: 3)
Anglo-Saxon England     Hybrid Journal   (Followers: 33)
Annales historiques de la Révolution française     Open Access   (Followers: 9)
Annali dell'Istituto e Museo di storia della scienza di Firenze     Hybrid Journal  
Annuaire de l'Ecole pratique des hautes etudes. Section des sciences historiques et philologiques     Open Access   (Followers: 6)
Annual Bulletin of Historical Literature     Hybrid Journal   (Followers: 12)
ANQ: A Quarterly Journal of Short Articles, Notes, and Reviews     Hybrid Journal   (Followers: 1)
Antike und Abendland     Hybrid Journal   (Followers: 10)
Antiteses     Open Access  
Anuario de Estudios Atlánticos     Open Access   (Followers: 1)
Anuario de Historia de la Iglesia     Open Access   (Followers: 2)
Anuario de la Escuela de Historia     Open Access  
Anuario del Departamento de Historia y Teoría del Arte     Open Access  
Arabian Humanities     Open Access   (Followers: 4)
Arabica     Hybrid Journal   (Followers: 11)
ARAM Periodical     Full-text available via subscription   (Followers: 3)
Araucaria. Revista Iberoamericana de Filosofía, Política y Humanidades     Open Access   (Followers: 1)
Archeion     Full-text available via subscription  
ArcheoArte. Rivista Elettronica di Archeologia e Arte     Open Access   (Followers: 8)
Architectural Heritage     Hybrid Journal   (Followers: 25)
Archive for History of Exact Sciences     Hybrid Journal   (Followers: 7)
Archives Internationales d'Histoire des Sciences     Partially Free   (Followers: 6)
Archives of Natural History     Hybrid Journal   (Followers: 7)
Area     Hybrid Journal   (Followers: 13)
Arenal. Revista de historia de las mujeres     Open Access   (Followers: 1)
Aristotelian Society Supplementary Volume     Hybrid Journal   (Followers: 3)
Arizona Journal of Hispanic Cultural Studies     Full-text available via subscription   (Followers: 3)
Armstrong Undergraduate Journal of History     Open Access  
Art History     Hybrid Journal   (Followers: 298)
Art History & Criticism     Open Access   (Followers: 3)
Arthuriana     Full-text available via subscription   (Followers: 6)
Arys: Antigüedad, Religiones y Sociedades     Open Access   (Followers: 1)
Aschkenas     Hybrid Journal   (Followers: 3)
Asia Pacific Business Review     Hybrid Journal   (Followers: 10)
Asia Pacific Journal of Education     Hybrid Journal   (Followers: 21)
Asia-Pacific Journal : Japan Focus     Open Access   (Followers: 10)
Asian Journal of Social Psychology     Hybrid Journal   (Followers: 6)
Asian Perspectives     Full-text available via subscription   (Followers: 9)
Asian Philosophy: An International Journal of the Philosophical Traditions of the East     Hybrid Journal   (Followers: 8)
Asian Review of World Histories     Hybrid Journal   (Followers: 2)
Asian Studies Review     Hybrid Journal   (Followers: 19)
Aspasia     Full-text available via subscription  
Astérion     Open Access   (Followers: 1)
Aurora Journal     Full-text available via subscription  
Austral Ecology     Hybrid Journal   (Followers: 16)
Australasian Journal of Irish Studies, The     Full-text available via subscription   (Followers: 8)
Australasian Review of African Studies, The     Full-text available via subscription   (Followers: 2)
Australian Antarctic Magazine     Free   (Followers: 4)
Australian Cultural History     Hybrid Journal   (Followers: 10)
Australian Historical Studies     Hybrid Journal   (Followers: 13)
Australian Journal of Legal History     Full-text available via subscription   (Followers: 15)
Australian Journal of Politics & History     Hybrid Journal   (Followers: 15)
Australian Slavonic and East European Studies     Open Access   (Followers: 6)
Austrian History Yearbook     Full-text available via subscription   (Followers: 9)
Balkanologie : Revue d'Études Pluridisciplinaires     Open Access   (Followers: 3)
Baltic-Pontic Studies     Open Access   (Followers: 1)
Baroque     Open Access   (Followers: 1)
Behemoth     Open Access   (Followers: 3)
Berichte Zur Wissenschaftsgeschichte     Hybrid Journal   (Followers: 10)
BIBLOS - Revista do Departamento de Biblioteconomia e História     Open Access   (Followers: 7)
BibNum     Open Access  
Biographical Memoirs of Fellows of the Royal Society     Full-text available via subscription   (Followers: 1)
Biography     Full-text available via subscription   (Followers: 18)
Bochumer Philosophisches Jahrbuch für Antike und Mittelalter     Hybrid Journal   (Followers: 2)
Body & Society     Hybrid Journal   (Followers: 26)
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim do Arquivo da Universidade de Coimbra     Open Access  
Book History     Full-text available via subscription   (Followers: 142)
Boom : A Journal of California     Full-text available via subscription   (Followers: 1)
Britain and the World     Hybrid Journal   (Followers: 6)
British Catholic History     Hybrid Journal   (Followers: 1)
British Journal for Military History     Open Access   (Followers: 27)
British Journal for the History of Science     Hybrid Journal   (Followers: 24)
British Journal of Canadian Studies     Hybrid Journal   (Followers: 12)
British Journal of Middle Eastern Studies     Hybrid Journal   (Followers: 29)
British Mycological Society Symposia Series     Full-text available via subscription   (Followers: 1)
British Review of New Zealand Studies     Full-text available via subscription   (Followers: 4)
Bryn Mawr Classical Review     Open Access   (Followers: 44)
BSHM Bulletin: Journal of the British Society for the History of Mathematics     Hybrid Journal   (Followers: 5)
Buildings & Landscapes: Journal of the Vernacular Architecture Forum     Full-text available via subscription   (Followers: 14)
Bulletin d'histoire politique     Full-text available via subscription   (Followers: 3)
Bulletin de la Sabix     Open Access  
Bulletin de Philosophie Medievale     Full-text available via subscription   (Followers: 3)
Bulletin du centre d’études médiévales d’Auxerre     Open Access   (Followers: 4)
Bulletin d’études Orientales     Open Access   (Followers: 9)
Bulletin of Hispanic Studies     Hybrid Journal   (Followers: 11)
Bulletin of Latin American Research     Hybrid Journal   (Followers: 16)
Bulletin of Spanish Studies: Hispanic Studies and Researches on Spain, Portugal and Latin America     Hybrid Journal   (Followers: 31)
Bulletin of the Ecological Society of America     Open Access   (Followers: 4)
Bulletin of the John Rylands Library     Hybrid Journal   (Followers: 17)
Bulletin of the School of Oriental and African Studies     Hybrid Journal   (Followers: 21)
Bustan     Hybrid Journal  
Byzantine and Modern Greek Studies     Hybrid Journal   (Followers: 12)
Byzantinische Zeitschrift     Hybrid Journal   (Followers: 14)
Byzantion Nea Hellás     Open Access   (Followers: 2)
C@hiers du CRHIDI     Open Access  
Cabo     Full-text available via subscription  
Cadernos de História     Open Access  
Cadernos de História UFPE     Open Access  
CADUS - Revista de Estudos de Política, História e Cultura     Open Access  
Cahiers d'histoire     Full-text available via subscription   (Followers: 2)
Cahiers d'histoire. Revue d'histoire critique     Open Access   (Followers: 13)
Cahiers de l'Urmis     Open Access   (Followers: 1)
Cahiers des études anciennes     Open Access   (Followers: 7)
Cahiers du Centre de recherches historiques     Open Access   (Followers: 6)
Cahiers du Monde Russe     Open Access   (Followers: 11)
Cahiers d’études africaines     Open Access   (Followers: 9)
Cahiers « Mondes anciens »     Open Access   (Followers: 4)
California Italian Studies Journal     Full-text available via subscription   (Followers: 6)
Cambridge Journal of Regions, Economy and Society     Hybrid Journal   (Followers: 12)
Camden Fifth Series     Full-text available via subscription   (Followers: 3)
Canadian Historical Review     Full-text available via subscription   (Followers: 12)
Canadian Journal of History     Full-text available via subscription   (Followers: 10)
Canadian Journal of Linguistics / La revue canadienne de linguistique     Full-text available via subscription   (Followers: 9)
Canadian Review of American Studies     Full-text available via subscription   (Followers: 2)
Canadian-American Slavic Studies     Hybrid Journal   (Followers: 6)
Caribbean Studies     Full-text available via subscription   (Followers: 11)
Catholic Historical Review     Full-text available via subscription   (Followers: 15)
Cemoti, Cahiers d'études sur la méditerranée orientale et le monde turco-iranien     Open Access   (Followers: 3)
Central Asian Survey     Hybrid Journal   (Followers: 11)
Central Europe     Hybrid Journal   (Followers: 6)
Central European History     Full-text available via subscription   (Followers: 32)
Chaucer Review     Full-text available via subscription   (Followers: 7)
Childhood in the Past : An International Journal     Hybrid Journal   (Followers: 5)
Chinese Studies in History     Full-text available via subscription   (Followers: 10)
Chronica Nova. Revista de Historia Moderna de la Universidad de Granada     Open Access   (Followers: 2)
Chronique d'Egypte     Full-text available via subscription   (Followers: 5)
Church History and Religious Culture     Hybrid Journal   (Followers: 51)
Church History: Studies in Christianity and Culture     Full-text available via subscription   (Followers: 69)
Cihannuma : Journal of History and Geography Studies     Open Access  
Circe de clásicos y modernos     Open Access  
Civil War History     Full-text available via subscription   (Followers: 19)
Cleveland Studies in the History of Art     Full-text available via subscription   (Followers: 2)
CLIO : Revista de Pesquisa Histórica     Open Access  
Clio y Asociados     Open Access  
Clio. Femmes, Genre, Histoire - Articles     Open Access   (Followers: 8)
Clio. Women, Gender, History     Open Access   (Followers: 4)
Cliodynamics     Open Access   (Followers: 1)
Collections électroniques de l'INHA     Open Access   (Followers: 1)
Collingwood and British Idealism Studies     Full-text available via subscription  
Colonial Latin American Review     Hybrid Journal   (Followers: 10)
Comitatus : A Journal of Medieval and Renaissance Studies     Full-text available via subscription   (Followers: 16)
Comparative Legal History     Full-text available via subscription   (Followers: 8)
Comparative Studies of South Asia, Africa and the Middle East     Full-text available via subscription   (Followers: 27)
Comptabilités     Open Access  
Concorso. Arti e lettere     Open Access  
Conservative Judaism     Full-text available via subscription   (Followers: 4)
Conserveries mémorielles     Open Access  
Contemporaneity : Historical Presence in Visual Culture     Open Access   (Followers: 4)
Contemporary Arab Affairs     Hybrid Journal   (Followers: 4)
Contemporary British History     Hybrid Journal   (Followers: 26)
Contemporary European History     Hybrid Journal   (Followers: 26)
Contemporary French and Francophone Studies     Hybrid Journal   (Followers: 12)
Convivium     Full-text available via subscription  
Creativity Studies     Open Access   (Followers: 3)
Crime, Histoire & Sociétés     Open Access   (Followers: 6)
Critical Historical Studies     Full-text available via subscription   (Followers: 8)

        1 2 3 4 5 | Last

Similar Journals
Journal Cover
Archive for History of Exact Sciences
Journal Prestige (SJR): 0.186
Citation Impact (citeScore): 1
Number of Followers: 7  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1432-0657 - ISSN (Online) 0003-9519
Published by Springer-Verlag Homepage  [2352 journals]
  • Jost Bürgi’s methods of calculating sines, and possible
           transmission from India
    • Abstract: A few years ago, a manuscript by Jost Bürgi (1552–1632) was brought to scholarly attention, which included an ingenious sine calculation method. The purpose of this paper is to discuss two aspects of this manuscript. First, we wish to improve the current understanding of Bürgi’s method of sine calculation, especially with respect to the calculation of sines at a resolution of 1 min. Second, we wish to suggest a possible transfer of knowledge between India’s Kerala School of mathematical astronomy and Bürgi. The evidence for the latter seems to be stronger than the evidence for other available case studies, but still revolves mainly around analogies, and can therefore not be considered as conclusive proof of transmission. We also append a translation of the relevant chapter of Bürgi’s treatise.
      PubDate: 2019-03-14
       
  • Correction to: “The etherealization of common sense'” Arithmetical
           and algebraic modes of intelligibility in late Victorian mathematics of
           measurement
    • Abstract: The original version of this article unfortunately contained mistakes.
      PubDate: 2019-03-01
       
  • “The Etherealization of Common Sense'” Arithmetical and Algebraic
           Modes of Intelligibility in Late Victorian Mathematics of Measurement
    • Abstract: The late nineteenth century gradually witnessed a liberalization of the kinds of mathematical object and forms of mathematical reasoning permissible in physical argumentation. The construction of theories of units illustrates the slow and difficult spread of new “algebraic” modes of mathematical intelligibility, developed by leading mathematicians from the 1830s onwards, into elementary arithmetical pedagogy, experimental physics, and fields of physical practice like telegraphic engineering. A watershed event in this process was a clash that took place during 1878 between J. D. Everett and James Thomson over the meaning and algebraic manipulation of dimensional formulae. This precipitated the emergence of rival “Maxwellian” and “Thomsonian” approaches towards interpreting and applying “dimensional” equations, which expressed the relationship between derived and fundamental units in an absolute system of measurement. What at first looks like a dispute over a seemingly esoteric mathematical tool for unit conversion turns out to concern Everett’s break with arithmetical algebra in the representation and manipulation of physical quantities. This move prompted a vigorous rebuttal from Thomsonian defenders of an orthodox “arithmetical empiricism” on epistemological, semantic, or pedagogical grounds. Their resistance in Victorian Britain to a shift in mathematical intelligibility is suggestive of the difficult birth of theoretical physics, in which the intermediate steps of a mathematical argument need have no direct physical meaning.
      PubDate: 2019-03-01
       
  • Three thousand years of sexagesimal numbers in Mesopotamian mathematical
           texts
    • Abstract: The Mesopotamian system of sexagesimal counting numbers was based on the progressive series of units 1, 10, 1·60, 10·60, …. It may have been in use already before the invention of writing, with the mentioned units represented by various kinds of small clay tokens. After the invention of proto-cuneiform writing, c. 3300 BC, it continued to be used, with the successive units of the system represented by distinctive impressed cup- and disk-shaped number signs. Other kinds of “metrological” number systems in the proto-cuneiform script, with similar number signs, were used to denote area numbers, capacity numbers, etc. In a handful of known mathematical cuneiform texts from the latter half of the third millennium BC, the ancient systems of sexagesimal counting numbers and area numbers were still in use, alongside new kinds of systems of capacity numbers and weight numbers. Large area numbers, capacity numbers, and weight numbers were counted sexagesimally, while each metrological number system had its own kind of fractional units. In the system of counting numbers itself, fractions could be expressed as sixtieths, sixtieths of sixtieths, and so on, but also in terms of small units borrowed from the system of weight numbers. Among them were the “basic fractions” which we would understand as 1/3, 1/2, and 2/3. In a very early series of metro-mathematical division exercises and an equally early metro-mathematical table of squares (Early Dynastic III, c. 2400 BC), “quasi-integers” of the form “integer plus basic fraction” play a prominent role. Quasi-integers play an essential role also in a recently found atypical cuneiform table of reciprocals. The invention of sexagesimal numbers in place-value notation, in the Neo-Sumerian period c. 2000 BC, was based on a series of innovations. The range of the system of sexagesimal counting numbers was extended indefinitely both upward and downward, and the use of quasi-integers was abolished. Sexagesimal place-value numbers were used for all kinds of calculations in Old Babylonian mathematical cuneiform texts, c. 1700 BC, while traditional metrological numbers were retained in both questions and answers of the exercises. Examples of impressive computations of reciprocals of many-place regular sexagesimal place-value numbers, with no practical applications whatsoever, are known from the Old Babylonian period. In the Late Babylonian period (the latter half of the first millennium BC), such computations were still popular, performed by the same persons who constructed the many-place sexagesimal tables that make up the corpus of Late Babylonian mathematical astronomy.
      PubDate: 2019-03-01
       
  • There is no consequentia mirabilis in Greek mathematics
    • Abstract: The paper shows that, contrary to what has been held since the sixteenth-century mathematician Christoph Clavius, there is no application of consequentia mirabilis (CM) in Greek mathematical works. This is shown by means of a detailed discussion of the logical structure of the proofs where CM is allegedly employed. The point is further enlarged to a critical assessment of the unsound methodology applied by many interpreters in seeking for specific logical rules at work in ancient mathematical texts.
      PubDate: 2019-02-22
       
  • Michel Chasles’ foundational programme for geometry until the
           publication of his Aperçu historique
    • Abstract: In this paper, I propose the idea that the French mathematician Michel Chasles developed a foundational programme for geometry in the period 1827–1837. The basic concept behind the programme was to show that projective geometry is the foundation of the whole of geometry. In particular, the metric properties can be reduced to specific graphic properties. In the attempt to prove the validity of his conception, Chasles made fundamental contributions to the theory of polarity and also understood that a satisfactory development of projective geometry has to overcome the specificity of that theory itself. In this perspective, he developed his ideas on duality and homography, showing their dependence on the concept that he was going to pose at the basis of geometry: the anharmonic ratio, today called cross-ratio. The conceptual itinerary that starts from Chasles’ studies on polarity and ends with his results based on the cross-ratio represents the itinerary of his foundational programme. I will follow this complex and interesting line of thought, place it in the context of what was then called descriptive geometry, and outline a connection with the later great results of Von Staudt, Cayley, and Klein.
      PubDate: 2019-02-19
       
  • A study of Babylonian planetary theory I. The outer planets
    • Abstract: In this study I attempt to provide an answer to the question how the Babylonian scholars arrived at their mathematical theory of planetary motion. Although no texts are preserved in which the Babylonians tell us how they did it, from the surviving Astronomical Diaries we have a fairly complete picture of the nature of the observational material on which the scholars must have based their theory and from which they must have derived the values of the defining parameters. Limiting the discussion to system A theory of the outer planets Saturn, Jupiter and Mars, I will argue that the development of Babylonian planetary theory was a gradual process of more than a century, starting sometime in the fifth century BC and finally resulting in the appearance of the first full-fledged astronomical ephemeris around 300 BC. The process of theory formation involved the derivation of long “exact” periods by linear combination of “Goal–Year” periods, the invention of a 360° zodiac, the discovery of the variable motion of the planets and the development of the numerical method to model this as a step function. Longitudes of the planets in the Babylonian zodiac could be determined by the scholars with an accuracy of 1° to 2° from observations of angular distances to Normal Stars with known positions. However, since the sky is too bright at first and last appearances of the planets and at acronychal rising for nearby stars to be visible, accurate longitudes as input for theoretical work could only be determined when the planets were near the stationary points in their orbits. In this study I show that the Babylonian scholars indeed based their system A modeling of the outer planets on planetary longitudes near stations, that their system A models of Saturn and Jupiter provided satisfactory results for all synodic phenomena, that they realized that their system A model of Mars did not produce satisfactory results for the second station so that separate numerical schemes were constructed to predict the positions of Mars at second station from the model at first station, and finally that their system A model for Mars provided quite poor predictions of the longitude of Mars at first and last appearances over large stretches of the zodiac. I further discuss ways in which the parameters of the system A models may have been derived from observations of the outer planets. By analyzing contemporaneous ephemerides from Uruk of four synodic phenomena of Jupiter from the second century BC, I finally illustrate how the Babylonian scholars may have used observations of Normal Star passages of planets to choose the initial conditions for their ephemerides.
      PubDate: 2019-01-01
       
  • Ptolemaic planetary models and Kepler’s laws
    • Abstract: In this article, we aim at presenting a thorough and comprehensive explanation of the mathematical and theoretical relation between all the aspects of Ptolemaic planetary models and their counterparts which are built according to Kepler’s first two laws (with optimized parameters). Our article also analyzes the predictive differences which arise from comparing Ptolemaic and these ideal Keplerian models, making clear distinctions between those differences which must be attributed to the structural variations between the models, and those which are due to the specific parameters Ptolemy determined in the Almagest. We expect that our work will be a contribution for a better understanding not only of the Ptolemaic theories for planetary longitudes through a clearer perception of the way in which Keplerian features are present—or absent—in Ptolemy’s models, but also for a more balanced judgement of different aspects of the contribution of the first two laws of Kepler to the modern astronomical revolution.
      PubDate: 2019-01-01
       
  • François Viète’s revolution in algebra
    • Authors: Jeffrey A. Oaks
      Pages: 245 - 302
      Abstract: Françios Viète (1540–1603) was a geometer in search of better techniques for astronomical calculation. Through his theorem on angular sections he found a use for higher-dimensional geometric magnitudes which allowed him to create an algebra for geometry. We show that unlike traditional numerical algebra, the knowns and unknowns in Viète’s logistice speciosa are the relative sizes of non-arithmetized magnitudes in which the “calculations” must respect dimension. Along with this foundational shift Viète adopted a radically new notation based in Greek geometric equalities. His letters stand for values rather than types, and his given values are undetermined. Where previously algebra was founded in polynomials as aggregations, Viète became the first modern algebraist in working with polynomials built from operations, and the notations reflect these conceptions. Viète’s innovations are situated in the context of sixteenth-century practice, and we examine the interpretation of Jacob Klein, the only historian to have conducted a serious inquiry into the ontology of Viète’s “species”.
      PubDate: 2018-05-01
      DOI: 10.1007/s00407-018-0208-0
      Issue No: Vol. 72, No. 3 (2018)
       
  • A further analysis of Cardano’s main tool in the De Regula Aliza : on
           the origins of the splittings
    • Authors: Sara Confalonieri
      Pages: 303 - 352
      Abstract: In the framework of the De Regula Aliza (1570), Cardano paid much attention to the so-called splittings for the family of equations \(x^3 = a_1x + a_0\) ; my previous article (Confalonieri in Arch Hist Exact Sci 69:257–289, 2015a) deals at length with them and, especially, with their role in the Ars Magna in relation to the solution methods for cubic equations. Significantly, the method of the splittings in the De Regula Aliza helps to account for how Cardano dealt with equations, which cannot be inferred from his other algebraic treatises. In the present paper, this topic is further developed, the focus now being directed to the origins of the splittings. First, we investigate Cardano’s research in the Ars Magna Arithmeticae on the shapes for irrational solutions of cubic equations with rational coefficients and on the general shapes for the solutions of any cubic equation. It turns out that these inquiries pre-exist Cardano’s research on substitutions and cubic formulae, which will later be the privileged methods for dealing with cubic equations; at an earlier time, Cardano had hoped to gather information on the general case by exploiting analogies with the particular case of irrational solutions. Accordingly, the Ars Magna Arithmeticae is revealed to be truly a treatise on the shapes of solutions of cubic equations. Afterwards, we consider the temporary patch given by Cardano in the Ars Magna to overcome the problem entailed by the casus irreducibilis as it emerges once the complete picture of the solution methods for all families of cubic equations has been outlined. When Cardano had to face the difficulty that appears if one deals with cubic equations using the brand-new methods of substitutions and cubic formulae, he reverted back to the well-known inquiries on the shape of solutions. In this way, the relation between the splittings and the older inquiries on the shape of solutions comes to light; furthermore, this enables the splittings to be dated 1542 or later. The last section of the present paper then expounds the passages from the Aliza that allow us to trace back the origins of the substitution \(x = y + z\) , which is fundamental not only to the method of the splittings but also to the discovery of the cubic formulae. In this way, an insight into Cardano’s way of dealing with equations using quadratic irrational numbers and other selected kinds of binomials and trinomials will be provided; moreover, this will display the role of the analysis of the shapes of solutions in the framework of Cardano’s algebraic works.
      PubDate: 2018-05-01
      DOI: 10.1007/s00407-018-0209-z
      Issue No: Vol. 72, No. 3 (2018)
       
  • Bisecting the trapezoid: tracing the origins of a Babylonian computation
           of Jupiter’s motion
    • Authors: Mathieu Ossendrijver
      Pages: 145 - 189
      Abstract: Between ca. 400 and 50 BCE, Babylonian astronomers used mathematical methods for predicting ecliptical positions, times and other phenomena of the moon and the planets. Until recently these methods were thought to be of a purely arithmetic nature. A new interpretation of four Babylonian astronomical procedure texts with geometric computations has challenged this view. On these tablets, Jupiter’s total distance travelled along the ecliptic during a certain interval of time is computed from the area of a trapezoidal figure representing the planet’s changing daily displacement along the ecliptic. Moreover, the time when Jupiter reaches half the total distance is computed by bisecting the trapezoid into two smaller ones of equal area. In the present paper these procedures are traced back to precursors from Old Babylonian mathematics (1900–1700 BCE). Some implications of the use of geometric methods by Babylonian astronomers are also explored.
      PubDate: 2018-03-01
      DOI: 10.1007/s00407-018-0204-4
      Issue No: Vol. 72, No. 2 (2018)
       
  • An analysis of medieval solar theories
    • Authors: S. Mohammad Mozaffari
      Pages: 191 - 243
      Abstract: From Antiquity through the early modern period, the apparent motion of the Sun in longitude was simulated by the eccentric model set forth in Ptolemy’s Almagest III, with the fundamental parameters including the two orbital elements, the eccentricity e and the longitude of the apogee λA, the mean motion ω, and the radix of the mean longitude \( \bar{\lambda }_{0} \) . In this article we investigate the accuracy of 11 solar theories established across the Middle East from 800 to 1600 as well as Ptolemy’s and Tycho Brahe’s, with respect to the precision of the parameter values and of the solar longitudes λ that they produce. The theoretical deviation due to the mismatch between the eccentric model with uniform motion and the elliptical model with Keplerian motion is taken into account in order to determine the precision of e and λA in the theories whose observational basis is available. The smallest errors in the eccentricity are found in these theories: the Mumtaḥan (830): − 0.1 × 10−4, Bīrūnī (1016): + 0.4 × 10−4, Ulugh Beg (1437): − 0.9 × 10−4, and Taqī al-Dīn (1579): − 1.1 × 10−4. Except for al-Khāzinī (1100, error of ~ + 21.9 × 10−4, comparable to Ptolemy’s error of ~ + 33.8 × 10−4), the errors in the medieval determinations of the solar eccentricity do not exceed 7.7 × 10−4 in absolute value (Ibn al-Shāṭir, 1331), with a mean error μ = + 2.57 × 10−4 and standard deviation σ = 3.02 × 10−4. Their precision is remarkable not only in comparison with the errors of Copernicus (− 7.8 × 10−4) and Tycho (+ 10.2 × 10−4), but also with the seventeenth-century measurements by Cassini–Flamsteed (− 2.4 × 10−4) and Riccioli (+ 5.5 × 10−4). The absolute error in λA varies from 0.1° (Taqī al-Dīn) to 1.9° (al-Khāzinī) with the mean absolute error MAE = 0.87°, μ = −0.71° and σ = 0.65°. The errors in λ for the 13,000-day ephemerides show MAE < 6′ and the periodic variations mostly remaining within ± 10′ (except for al-Khāzinī), closely correlated with the accuracy of e and λA.
      PubDate: 2018-03-01
      DOI: 10.1007/s00407-018-0207-1
      Issue No: Vol. 72, No. 2 (2018)
       
  • Astronomical observations at the Maragha observatory in the
           1260s–1270s
    • Abstract: This paper presents an analysis of the systematic astronomical observations performed by Muḥyī al-Dīn al-Maghribī (d. 1283 AD) at the Maragha observatory (northwestern Iran, ca. 1260–1320 AD) between 1262 and 1274 AD. In a treatise entitled Talkhīṣ al-majisṭī (Compendium of the Almagest), preserved in a unique copy at Leiden, Universiteitsbibliotheek (Or. 110), Muḥyī al-Dīn explains his observations and measurements of the Sun, the Moon, the superior planets, and eight reference stars. His measurements of the meridian altitudes of the Sun, the superior planets, and the eight bright stars were made using the mural quadrant of the observatory, and the times of their meridian transit using a water clock. The mean absolute error in the meridian altitudes of the Sun is ~ 3.1′, of the superior planets  ~ 4.6′, and of the eight fixed stars ~ 6.2′. The clepsydras used by Muḥyī al-Dīn could apparently fix time intervals with a precision of ± 5 min. His estimation of the magnitudes of three lunar eclipses observed in Maragha in 1262, 1270, and 1274 AD is in close agreement with modern data.
      PubDate: 2018-11-01
       
  • The astronomical orientation of the historical Grand mosques in Anatolia
           (Turkey)
    • Abstract: In the ancient civilizations, the sky has been observed in order to understand the motions of the celestial bodies above the horizon. The study of faiths and practices dealing with the sky in the past has been attributed to the sun, the moon, and the prominent stars. The alignment and orientation of constructions to significant celestial objects were a common practice. The orientation was an important component of the religious structure design. Religious buildings often have an intentional orientation to fix the praying direction. In Islam, a sacred direction (Qibla) towards Kaaba located in the courtyard in the Sacred Mosque in Mecca has been used for praying and fulfilling varied ritual tasks. Therefore, the mosques had then to orientate towards the Qibla direction, being designated by a focal niche in the Qibla-wall, wherever they were built on Earth. In this study, the orientations of the historical Grand mosques in Turkey are surveyed with regard to the folk astronomy derived from pre-Islamic Arabian sources, early traditions of the Islamic period, and geometric-trigonometric computation in mathematical astronomy inherited and developed mostly from Greek sources according to the Islamic view of the World geography.
      PubDate: 2018-11-01
       
  • The end of an error: Bianchini, Regiomontanus, and the tabulation of
           stellar coordinates
    • Abstract: Giovanni Bianchini’s fifteenth-century Tabulae primi mobilis is a collection of 50 pages of canons and 100 pages of tables of spherical astronomy and mathematical astrology, beginning with a treatment of the conversion of stellar coordinates from ecliptic to equatorial. His new method corrects a long-standing error made by a number of his antecedents, and with his tables the computations are much more efficient than in Ptolemy’s Almagest. The completely novel structure of Bianchini’s tables, here and in his Tabulae magistrales, was taken over by Regiomontanus in the latter’s Tabulae directionum. One of the tables Regiomontanus imported from Bianchini contains the first appearance of the tangent function in Latin Europe, which both used as an auxiliary quantity for the calculation of stellar coordinates.
      PubDate: 2018-09-01
       
  • “A masterly though neglected work”, Boscovich’s treatise
           on conic sections
    • Abstract: In this paper, we describe the genesis of Boscovich’s Sectionum Conicarum Elementa and discuss the motivations which led him to write this work. Moreover, by analysing the structure of this treatise in some depth, we show how he developed the completely new idea of “eccentric circle” and derived the whole theory of conic sections by starting from it. We also comment on the reception of this treatise in Italy, and abroad, especially in England, where—since the late eighteenth century—several authors found inspiration in Boscovich’s work to write their treatises on conic sections.
      PubDate: 2018-07-01
       
  • The concept of given in Greek mathematics
    • Abstract: This paper is a contribution to our understanding of the technical concept of given in Greek mathematical texts. By working through mathematical arguments by Menaechmus, Euclid, Apollonius, Heron and Ptolemy, I elucidate the meaning of given in various mathematical practices. I next show how the concept of given is related to the terms discussed by Marinus in his philosophical discussion of Euclid’s Data. I will argue that what is given does not simply exist, but can be unproblematically assumed or produced through some effective procedure. Arguments by givens are shown to be general claims about constructibility and computability. The claim that an object is given is related to our concept of an assignment—what is given is available in some uniquely determined, or determinable, way for future mathematical work.
      PubDate: 2018-07-01
       
  • Uses of construction in problems and theorems in Euclid’s Elements
           I–VI
    • Abstract: In this paper, I present an interpretation of the use of constructions in both the problems and theorems of Elements I–VI, in light of the concept of given as developed in the Data, that makes a distinction between the way that constructions are used in problems, problem-constructions, and the way that they are used in theorems and in the proofs of problems, proof-constructions. I begin by showing that the general structure of a problem is slightly different from that stated by Proclus in his commentary on the Elements. I then give a reading of all five postulates, Elem. I.post.1–5, in terms of the concept of given. This is followed by a detailed exhibition of the syntax of problem-constructions, which shows that these are not practical instructions for using a straightedge and compass, but rather demonstrations of the existence of an effective procedure for introducing geometric objects, which procedure is reducible to operations of the postulates but not directly stated in terms of the postulates. Finally, I argue that theorems and the proofs of problems employ a wider range of constructive and semi- and non-constructive assumptions that those made possible by problems.
      PubDate: 2018-07-01
       
  • Binocular vision and image location before Kepler
    • Authors: Robert Goulding
      Abstract: Kepler’s 1604 Optics (Ad Vitellionem Paralipomena) proposed among many other things a new way of locating the place of the image under reflection or refraction. He rejected the “perspectivist” method that had been used through antiquity and the Middle Ages, whereby the image was located on the perpendicular between the object and the mirror (the “cathetus”). Kepler faulted the method for requiring a metaphysical commitment to the action of final causes in optics: the notion that the image was at that place because it was best or appropriate for it to be there, and for no other discernible reason. Kepler’s new theory relied on binocular vision and depth perception to determine the location of the image. No final causes were required, and he showed that the image would in general not be found on the cathetus. According to modern scholarship, Kepler’s theory was part of his revolutionary transformation of the science of optics, and his abandonment of perspectivist optics; as a consequence, the theory of binocular vision is also thought to be original with him. This article demonstrates that the very same theory of binocular image location was set out by Giovanni Battista Benedetti some twenty years earlier, and his writings on this subject may have been Kepler’s unacknowledged source for his own theory. Furthermore, another mathematician, Simon Stevin, developed much the same theory at the same time as Kepler and, it seems, independently of either Benedetti or Kepler. The discovery of these other binocular theories, especially Benedetti’s, requires us to recognize that Kepler’s revolution (if it can be called that) emerged out of a wider dissatisfaction with the foundations of perspectivist optics, which other lesser-known opticians resolved in much the same way that Kepler did.
      PubDate: 2018-05-16
      DOI: 10.1007/s00407-018-0210-6
       
  • Correction to: The modernity of Dedekind’s anticipations contained in
           What are numbers and what are they good for'
    • Authors: J. Climent Vidal; J. Soliveres Tur
      Abstract: The original version of this article unfortunately contained a mistake: The equation on page 34 was incorrect. The corrected equation is given below.
      PubDate: 2018-02-07
      DOI: 10.1007/s00407-018-0203-5
       
 
 
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