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Introduction To Arithmetic
The book ''Introduction to Arithmetic'' ( grc-gre, Ἀριθμητικὴ εἰσαγωγή, ''Arithmetike eisagoge'') is the only extant work on mathematics by Nicomachus (60–120 AD). Summary The work contains both philosophical prose and basic mathematical ideas. Nicomachus refers to Plato quite often, and writes that philosophy can only be possible if one knows enough about mathematics. Nicomachus also describes how natural numbers and basic mathematical ideas are eternal and unchanging, and in an abstract realm. It consists of two books, twenty-three and twenty-nine chapters, respectively. Although he was preceded by the Babylonians and the Chinese, Nicomachus provided one of the earliest Greco-Roman multiplication tables, whereas the oldest extant Greek multiplication table is found on a wax tablet dated to the 1st century AD (now found in the British Museum). Influence The ''Introduction to Arithmetic'' of Nicomachus was a standard textbook in Neoplatonic schools an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nicomachus Adad2
Nicomachus of Gerasa ( grc-gre, Νικόμαχος; c. 60 – c. 120 AD) was an important ancient mathematician and music theorist, best known for his works ''Introduction to Arithmetic'' and ''Manual of Harmonics'' in Greek. He was born in Gerasa, in the Roman province of Syria (now Jerash, Jordan). He was a Neopythagorean, who wrote about the mystical properties of numbers.Eric Temple Bell (1940), ''The development of mathematics'', page 83.Frank J. Swetz (2013), ''The European Mathematical Awakening'', page 17, Courier Life Little is known about the life of Nicomachus except that he was a Pythagorean who came from Gerasa.} Historians consider him a Neopythagorean based on his tendency to view numbers as having mystical properties. The age in which he lived (c. 100 AD) is only known because he mentions Thrasyllus in his ''Manual of Harmonics'', and because his ''Introduction to Arithmetic'' was apparently translated into Latin in the mid 2nd century by Apuleius.Henrietta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paraphrase
A paraphrase () is a restatement of the meaning of a text or passage using other words. The term itself is derived via Latin ', . The act of paraphrasing is also called ''paraphrasis''. History Although paraphrases likely abounded in oral traditions, paraphrasing as a specific educational exercise dates back to at least Roman times, when the author Quintilian recommended it for students to develop dexterity in language. In the Middle Ages, this tradition continued, with authors such as Geoffrey of Vinsauf developing schoolroom exercises that included both rhetorical manipulations and paraphrasing as a way of generating poems and speeches. Paraphrasing seems to have dropped off as a specific exercise that students learn, a drop off that largely coincides with the removal of Classical texts from the core of Western education. There is, however, renewed interest in the study of paraphrases, given concerns around plagiarism and original authorship. Analysis A paraphrase typicall ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Internet Archive
The Internet Archive is an American digital library with the stated mission of "universal access to all knowledge". It provides free public access to collections of digitized materials, including websites, software applications/games, music, movies/videos, moving images, and millions of books. In addition to its archiving function, the Archive is an activist organization, advocating a free and open Internet. , the Internet Archive holds over 35 million books and texts, 8.5 million movies, videos and TV shows, 894 thousand software programs, 14 million audio files, 4.4 million images, 2.4 million TV clips, 241 thousand concerts, and over 734 billion web pages in the Wayback Machine. The Internet Archive allows the public to upload and download digital material to its data cluster, but the bulk of its data is collected automatically by its web crawlers, which work to preserve as much of the public web as possible. Its web archiving, web archive, the Wayback Machine, contains hu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erhard Ratdolt
Erhard Ratdolt (1442–1528) was an early German printer from Augsburg. He was active as a printer in Venice from 1476 to 1486, and afterwards in Augsburg. From 1475 to 1478 he was in partnership with two other German printers. The first book the partnership produced was the ''Calendarium'' (1476), written and previously published by Regiomontanus, which offered one of the earliest examples of a modern title page. Other noteworthy publications are the ''Historia Romana'' of Appianus (1477), and the first edition of ''Euclid's Elements'' (1482), where he solved the problem of printing geometric diagrams, the ''Poeticon astronomicon'', also from 1482, Haly Abenragel (1485), and Alchabitius (1503). Ratdolt is also famous for having produced the first known printer's type specimen book (in this instance a broadsheet displaying the fonts with which he might print). His innovations of layout and typography, mixing type and woodcuts, have subsequently been much admired. His graphic c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boethius
Anicius Manlius Severinus Boethius, commonly known as Boethius (; Latin: ''Boetius''; 480 – 524 AD), was a Roman senator, consul, ''magister officiorum'', historian, and philosopher of the Early Middle Ages. He was a central figure in the translation of the Greek classics into Latin, a precursor to the Scholastic movement, and, along with Cassiodorus, one of the two leading Christian scholars of the 6th century. The local cult of Boethius in the Diocese of Pavia was sanctioned by the Sacred Congregation of Rites in 1883, confirming the diocese's custom of honouring him on the 23 October. Boethius was born in Rome a few years after the collapse of the Western Roman Empire. A member of the Anicii family, he was orphaned following the family's sudden decline and was raised by Quintus Aurelius Memmius Symmachus, a later consul. After mastering both Latin and Greek in his youth, Boethius rose to prominence as a statesman during the Ostrogothic Kingdom: becoming a senator by a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Superparticular Ratio
In mathematics, a superparticular ratio, also called a superparticular number or epimoric ratio, is the ratio of two consecutive integer numbers. More particularly, the ratio takes the form: :\frac = 1 + \frac where is a positive integer. Thus: Superparticular ratios were written about by Nicomachus in his treatise ''Introduction to Arithmetic''. Although these numbers have applications in modern pure mathematics, the areas of study that most frequently refer to the superparticular ratios by this name are music theory and the history of mathematics. Mathematical properties As Leonhard Euler observed, the superparticular numbers (including also the multiply superparticular ratios, numbers formed by adding an integer other than one to a unit fraction) are exactly the rational numbers whose continued fraction terminates after two terms. The numbers whose continued fraction terminates in one term are the integers, while the remaining numbers, with three or more terms in their c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harvard University Press
Harvard University Press (HUP) is a publishing house established on January 13, 1913, as a division of Harvard University, and focused on academic publishing. It is a member of the Association of American University Presses. After the retirement of William P. Sisler in 2017, the university appointed as Director George Andreou. The press maintains offices in Cambridge, Massachusetts near Harvard Square, and in London, England. The press co-founded the distributor TriLiteral LLC with MIT Press and Yale University Press. TriLiteral was sold to LSC Communications in 2018. Notable authors published by HUP include Eudora Welty, Walter Benjamin, E. O. Wilson, John Rawls, Emily Dickinson, Stephen Jay Gould, Helen Vendler, Carol Gilligan, Amartya Sen, David Blight, Martha Nussbaum, and Thomas Piketty. The Display Room in Harvard Square, dedicated to selling HUP publications, closed on June 17, 2009. Related publishers, imprints, and series HUP owns the Belknap Press imprint, whi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ivor Bulmer-Thomas
Ivor Bulmer-Thomas CBE FSA (30 November 1905 – 7 October 1993), born Ivor Thomas, was a British journalist and scientific writer who served eight years as a Member of Parliament (MP). His career was much influenced by his conversion to the Church of England in his youth, and he became a pious believer on the Anglo-Catholic wing of the Church. A brilliant scholar and champion athlete while at university, Bulmer-Thomas wrote biographies and worked as a sub-editor on ''The Times'' during his early life. His experience in wartime Italian propaganda led him to doubt its value. Serving in the Attlee Labour Party government in junior roles made him resent the influence of the Labour left; he fell out with party policy on nationalisation and moved to the Conservative Party. He was a workaholic and after leaving politics he became a leading layman in the Church of England; an interest in historic buildings led him to set up the Friends of Friendless Churches group, which campaigns to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Middle Age
In the history of Europe, the Middle Ages or medieval period lasted approximately from the late 5th to the late 15th centuries, similar to the post-classical period of global history. It began with the fall of the Western Roman Empire and transitioned into the Renaissance and the Age of Discovery. The Middle Ages is the middle period of the three traditional divisions of Western history: classical antiquity, the medieval period, and the modern period. The medieval period is itself subdivided into the Early, High, and Late Middle Ages. Population decline, counterurbanisation, the collapse of centralized authority, invasions, and mass migrations of tribes, which had begun in late antiquity, continued into the Early Middle Ages. The large-scale movements of the Migration Period, including various Germanic peoples, formed new kingdoms in what remained of the Western Roman Empire. In the 7th century, North Africa and the Middle East—most recently part of the Eastern Ro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadrivium
From the time of Plato through the Middle Ages, the ''quadrivium'' (plural: quadrivia) was a grouping of four subjects or arts—arithmetic, geometry, music, and astronomy—that formed a second curricular stage following preparatory work in the ''trivium'', consisting of grammar, logic, and rhetoric. Together, the '' trivium'' and the ''quadrivium'' comprised the seven liberal arts, and formed the basis of a liberal arts education in Western society until gradually displaced as a curricular structure by the ''studia humanitas'' and its later offshoots, beginning with Petrarch in the 14th century. The seven classical arts were considered "thinking skills" and were distinguished from practical arts, such as medicine and architecture. The ''quadrivium'', Latin for 'four ways', and its use for the four subjects have been attributed to Boethius—who likely coined the term. It was considered the foundation for the study of philosophy (sometimes called the "liberal art ''par excellen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edward Grant
Edward Grant (April 6, 1926 – June 21, 2020) was an American historian of medieval science. He was named a Distinguished Professor in 1983. Other honors include the 1992 George Sarton Medal, for "a lifetime scholarly achievement" as an historian of science.Academic page in Indiana University (archived 4 November 2013) Biography Edward Grant was born in 1926. He attended City College in where he graduated in 1951. He continued to the |
