Πτολεμαίου Πρόχειροι Κανόνεϲ. Les «Tables Faciles» de Ptolémée/Ptolemy’s Handy Tables. Tables A1–A2 (original) (raw)
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Displaced tables in Latin: The Tables for the Seven Planets for 1340
2013
The anonymous set of astronomical tables preserved in Paris, Bibliothèque nationale de France, MS lat. 10262, is the first set of displaced tables to be found in a medieval Latin text. These tables are a reworking of the standard Alfonsine tables and yield the same results. However, the mean motions are defined differently, the presentation of the tables is unprecedented, and some new functions are introduced for computing true planetary longitudes. The absence of any instructions as well as unusual technical terms in the headings make it difficult to appreciate the cleverness that went into the construction of these tables that are extant in a unique copy. In this article we provide a detailed analysis of these tables and their underlying parameters. The displaced tables are typical of a pervasive tendency in Islamic science to provide extensive and elegant numerical tables for the convenience of practitioners. The underlying astronomical theory is neither questioned nor affected.
Surveying the Types of Tables in Ancient Greek Texts [Apeiron]
Apeiron, 2024
We may take tables for granted. However, due to a variety of factors, tables were a rarity in the history of ancient Greek culture, used only limitedly in very special contexts and generally in a non-systematic way, except in astronomy. In this paper I present the main types of tables that can be found in ancient Greek texts: non-ruled columnar lists (accounts and other types of informal tables), ruled columnar lists (mostly astronomical tables), and symmetric tables (mainly Pythagorean displays of numbers).
The oldest known mathematical table was found in the ancient Sumerian city of Shuruppag in southern Iraq. Since then, tables have been an important feature of mathematical activity; table making and printed tabular matter are important precursors to modern computing and information processing. This book contains a series of articles summarising the technical, institutional and intellectual history of mathematical tables from earliest times until the late twentieth century. It covers mathematical tables (the most important computing aid for several hundred years until the 1960s), data tables (eg. Census tables), professional tables (eg. insurance tables), and spreadsheets - the most recent tabular innovation. The book is presented in a scholarly yet accessible way, making appropriate use of text boxes and illustrations. Each chapter has a frontispiece featuring a table along with a small illustration of the source where the table was first displayed. Most chapters have sidebars telling a short "story" or history relating to the chapter. The aim of this edited volume is to capture the history of tables through eleven chapters written by subject specialists. The contributors describe the various information processing techniques and artefacts whose unifying concept is "the mathematical table".
Mini-Workshop: History of Numerical and Graphical Tables
Oberwolfach Reports, 8 (2011), 639-689
Numerical tables were one of the most commonly used instruments of calculation from the earliest periods for which we have evidence of mathematical activity until the appearance of computing machines. Such tables (including graphical tables) are interesting both as tools of calculation and insofar as traces for certain social and scientific activities of the practitioners by, and for, whom they were produced. Nevertheless, despite the fact that the historical record has preserved thousands of tables from a broad range of civilizations, these tables have themselves received relatively little critical study. Hence, it has seemed to us both useful and innovative to consider the problem of tables in general by bringing together specialists of the different mathematical traditions and of the various professional milieus in which numerical tables have been developed. The workshop allowed us therefore to make significant breakthroughs in our understanding of the places and roles of tables in the history of science, and should bring us to publish a collective book on this subject.
The Stars in the Classical and Medieval Traditions, ed. by Alena Hadravová, Petr Hadrava, and Kristen Lippincott, 2019
The study of ancient astronomy calls to arms a number of disciplines: philology, codicology, algebra, geometry, illumination and art history, astrology, and of course astronomy itself. This book admirably succeeds in bringing together outstanding specialists from these different fields and in addressing several questions: How many are the fixed stars? How can astronomy help discover the geographical coordinates of a city? How do you construct an Aratean sphere? How is the representation of the sky rendered in illustrations ranging from medieval manuscripts to 18th-century sculpture gardens? How does the ancient mechanism of catasterism work? How are pagan constellations interpreted in Christian settings? This collection of essays provides new editions and new interpretations of astronomical texts from such diverse authors as Eratosthenes and Manilius, Aratus, Germanicus and al-Sūfī, Ptolemy and Carolingian scholars. Readers with diverse interests will benefit from this book.
Survey of Graphical and Numerical Tables in Egypt
Oberwolfach Reports, 2011
Numerical tables were one of the most commonly used instruments of calculation from the earliest periods for which we have evidence of mathematical activity until the appearance of computing machines. Such tables (including graphical tables) are interesting both as tools of calculation and insofar as traces for certain social and scientific activities of the practitioners by, and for, whom they were produced. Nevertheless, despite the fact that the historical record has preserved thousands of tables from a broad range of civilizations, these tables have themselves received relatively little critical study. Hence, it has seemed to us both useful and innovative to consider the problem of tables in general by bringing together specialists of the different mathematical traditions and of the various professional milieus in which numerical tables have been developed. The workshop allowed us therefore to make significant breakthroughs in our understanding of the places and roles of tables in the history of science, and should bring us to publish a collective book on this subject.
The Most Obscure and Inconvenient Tables that have ever been Constructed?
With an Oxford degree and close ties to both François Vìète and Thomas Harriot, Nathaniel Torporley was perhaps one of the most enigmatic contributors to the mathematics of the late sixteenth and early seventeenth-centuries. John Aubrey, in his Brief Lives, states that:"Mr. Hooke affirms to me that Torporley was amanuensis to Vieta; but from whom he had that information he haz now forgot, but he had good and credible authority for it, and bids me tell you that he was certainly so . . . [and that] Mr Nicholas Mercator assures me that the earle of Northumberland who was prisoner in the Tower gave also a pension to one Mr Torporley, Salopiensis, a learned man; and that in the library of that family at Petworth, are some papers of his."Torporley published only one mathematical work: Diclides Coelometricae, seu valvae astronomicae universale, frequently described as barely comprehensible, in which he develops two lengthly sets of tables relating to spherical trigonometry and astrology. With reference to these tables, named Quadrans and Quncunx, Delambre writes:<<Cette dernière est composée de cinq parties différentes. Ces deux tables peuvent passer à bon droit pour les plus obscures and les plus incommodes qui aient jamais été construites.>> De Morgan abandoned his attempt to untangle the structure of the Qunicnux saying, “Those who like such questions may find out the meaning of the other parts of the table.” To my knowledge, no one yet has done so, nor does there exist a translation of Dicilides into any other language, nor has anyone commented on or explained the theorems developed by Torporley in order to produce his tables. In this presentation we focus on the means by which this table was generated, based upon evidence within Torporley’s work itself.
Adaptations of the Oxford Tables to Paris, Mantua, and Louvain
Journal for the History of Astronomy, 2018
The Oxford Tables of 1348, also called Tabule anglicane, were computed for the meridian of Oxford in the framework of Alfonsine astronomy. They had a remarkable success, for they are extant in a good number of Latin manuscripts, and they were adapted repeatedly. This paper focuses on these adaptations: the Tabule Parisiensis, with radices for the year 1368 complete and the meridian of Paris, extant in Hebrew and Latin manuscripts; the version made by Mordecai Finzi, with radices for 1443 complete and the meridian of Mantua, preserved in a unique Hebrew manuscript; and the partial adaptation by Henry Baers printed in Latin in Louvain in 1528.