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Античная арифмология в «Бракосочетании Филологии и Меркурия» Марциана Капеллы
С. 448–458.
Shakhov Y.
This paper deals with the representation of the ancient arithmological doctrine in Martianus Capella's encyclopaedic work “On the Marriage of Philology and Mercury”. The notions of arithmetic, which is the study of the number's mathematical properties, and arithmology, which is the pythagorean doctrine of the number's 'sacred' properties, as well as their mutual relation, are examined. I note that in Martianus Capella's work, as charactestic for the late antiquity, both arithmetic and arithmology are presented as components of Arithmetica, the study of numbers. An overview of the passages of “On the Marriage”, dedicated to the arithmological doctrine, follows. One of the passages considering the pentas is examined in more detail; I suggest an interpretation according to which the pentas is attributed to the god of Heaven. In conclusion I overview the main difficulties considering the study the sources of Martianus Capella's arithmology and note the importance of “On the Marriage” for the study of the ancient science and philosophy.
Istomina A., Arsalidou M., Developmental Cognitive Neuroscience 2024 Vol. 69 Article 101419
Mathematical operations are cognitive actions we take to calculate relations among numbers. Arithmetic operations, addition, subtraction, multiplication, and division are elemental in education. Addition is the first one taught in school and is most popular in functional magnetic resonance imaging (fMRI) studies. Division, typically taught last is least studied with fMRI. fMRI meta-analyses show that ...
Added: August 12, 2024
Посицельская М. А., Рудченко Т. А., Semenov A., Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2023 Т. 511 № 1 С. 21–54
В последние десятилетия в ряде российских школ реализуется уникальная на мировом уровне программа математического образования для начальной школы. В ней мир школьной арифметики радикально расширяется за счет базовых объектов современной математики и информатики. Эти объекты и операции над ними наглядны, что делает их намного более доступными, чем в традиционной арифметике. Расширяется и спектр видов деятельности ...
Added: March 14, 2024
Posicelskaya M. A., Rudchenko T. A., Semenov A., Doklady Mathematics 2023 Vol. 107 No. 1 P. S10–S41
In recent decades, several Russian schools have been implementing a world-unique education program of mathematics for elementary schools. In it, the landscape of school arithmetic is radically expanded due to the basic objects of modern mathematics and computer science. These objects and their operations are visual, making them much more comprehensible than traditional arithmetic. The ...
Added: March 14, 2024
Sergey Dudakov, Karlov B., Theory of Computing Systems 2021 Vol. 65 No. 3 P. 462–478
This paper is dedicated to studying decidability properties of theories of regular languages with classical operations: union, concatenation, and the Kleene star. The theory with union only is a theory of some Boolean algebra, so it is decidable. We prove that the theory of regular languages with the Kleene star only is decidable. If we ...
Added: November 12, 2023
Sergey Mikhailovich Dudakov, Mathematics 2022 Vol. 10 No. 3 Article 533
Let M be a commutative cancellative monoid with an element of infinite order. The binary operation can be extended to all finite subsets of M by the
pointwise definition. So, we can consider the theory of finite subsets of M. Earlier, we have proved the following result: in the theory of finite subsets of M elementary ...
Added: November 12, 2023
S. M. Dudakov, Journal of Physics: Conference Series 2021 Vol. 1902 Article 012060
Early we (with B. N. Karlov) have proved the following claim for the infinite cyclic monoid H. Let exp H be an algebra of finite subsets of H with the same operation, exp H must be a monoid again. So the theory of exp H is equivalent to elementary arithmetic. Thus, the theory of the monoid ...
Added: November 12, 2023
Zapryagaev A., / Series arXiv "math". 2022.
Added: December 7, 2022
Panchenko D., Schole. Философское антиковедение и классическая традиция 2019 Т. 13 № 1 С. 235–250
According to a standard idea of Greek science and philosophy, the shape of the sun is spherical. Such an idea appears already in Aristotle who offers, however, no good account for it, and only Stobaeus cites an authority, or rather collective authority, the Pythagoreans, for an early recognition of the idea in question. The ancient ...
Added: February 14, 2019
Капелла М., Центр гуманитарных инициатив, 2019.
Сочинение Марциана Капеллы «Бракосочетание Филологии и Меркурия» (De nuptiis Philologiae et Mercurii), занимающее исключительно важное место в истории европейского образования и литературы, вместе с тем не слишком хорошо известно современному читателю и до относительно недавнего времени редко привлекало внимание серьезных исследователей, в том числе отечественных антиковедов и медиевистов. Предлагаемое вниманию читалей издание, призванное восполнить существующую лакуну в историко-филологической науке, ...
Added: September 30, 2018
Shakhov Y., В кн.: Индоевропейское языкознание и классическая филология - XXII. Материалы чтений, посвященных памяти профессора Иосифа Моисеевича Тронского, 18-20 июня 2018 г.: СПб.: Наука, 2018. С. 1369–1378.
The paper presents some arguments that may prove literary influnce of Martianus Capella's allegorical encyclopedia 'De nuptiis Philologiae et Mercurii' upon Severinus Boethius' 'De consolatione Philosophiae'. Two episodes of 'De consolatione' come under examination. The first of them, the apparition of Philosophia in the opening scene of Book I, is shown to have close parallels ...
Added: May 10, 2018
Reinhardt R., Научный диалог 2017 № 2 С. 207–215
The origins of the formation of the Italian model of self-organization of the scientific community and their perception by Italian scientists are covered. In the course of critical analysis the contentious issues of mapping the early stages of development of Italian science with the traditions of the Pythagoreans are revealed, which, in turn, has had ...
Added: March 2, 2018
Shakhov Y., В кн.: Возлюблю слово как ближнего: учебный текст в позднюю античность и раннее средневековье.: Индрик, 2017. С. 743–767.
Русский перевод седьмой книги энциклопедического сочинения Марциана Капеллы "Бракосочетание Филологии и Меркурия" ...
Added: November 29, 2017
Shakhov Y., В кн.: Возлюблю слово как ближнего: учебный текст в позднюю античность и раннее средневековье.: Индрик, 2017. С. 736–742.
Вступительная статья к русскому переводу седьмой книги энциклопедического сочинения Марциана Капеллы "Бракосочетание Филологии и Меркурия" ...
Added: November 29, 2017
Shakhov Y., В кн.: Возлюблю слово как ближнего: учебный текст в позднюю античность и раннее средневековье.: Индрик, 2017. С. 262–283.
Комментированный перевод первой книги энциклопедического сочинения Марциана Капеллы "Бракосочетание Филологии и Меркурия". ...
Added: November 29, 2017
Lečić N. D., В кн.: Аристотелевское наследие как конституирующий элемент европейской рациональности.: М.: Аквилон, 2017. С. 31–42.
In his reasoning concerning the relationship between surface or visible superficies (understood as the boundary or the limit of a body) and color (De sensu 439a19–b17), Aristotle asserts that the Pythagoreans called the surface (ἐπιφάνεια) color (χροιά), i.e. that they made no terminological difference between the former and the latter. In the scholarship on early ...
Added: November 16, 2017
Shakhov Y., Аристей. Aristeas: Вестник классической филологии и античной истории 2017 Т. XV С. 135–160
Комментированный перевод с латинского языка первой книги энциклопедического сочинения Марциана Капеллы "Бракосочетание Филологии и Меркурия". ...
Added: June 29, 2017
Lečić N. D., В кн.: Способы мысли, пути говорения.: СПб.: Алетейя, 2016. Гл. 4 С. 44–57.
In this paper we analyse the influence of various interpretations of direct and indirect doxographic testimonies concerning Early Pythagoreanism on our understanding of the most fundamental aspects of this movement. This is done through the example of texts giving hints of possible existence of advanced «pebble arithmetics» and number ontology among Early Pythagoreans. The author ...
Added: March 15, 2017
Lečić N. D., Schole. Философское антиковедение и классическая традиция 2017 Т. 11 № 1 С. 260–270
This article attempts to reconsider the customary assessment of the performances attributed to one of the last Early Pythagoreans, Eurytus of Tarentum. His practice of «defining» a thing with the number of pebbles needed to draw its silhouette is usually regarded as a naïve or unworthy version of the number philosophy of his teacher, Philolaus ...
Added: January 9, 2017
Lečić N. D., Платоновские исследования 2016 № 2 С. 258–278
In Theaetetus (145a–148a), Plato brings up Theaetetus’ retelling of a lesson by Theodorus of Cyrene, in which the latter demonstrated the incommensurability of the sides of squares containing three, five, and up to seventeen square feet with the side of one square foot. In this paper, we analyse modern scholarly attempts to reconstruct the exact ...
Added: November 26, 2016