Gerbert of Aurillac’s Letter on the Area of an Equilateral Triangle: Philosophical and Theological Perspective. Epistola a Gerberto abbate Bobiensi et fortasse jam archiepiscopo Ravennae ad Adelbol­dum de causa diversitatis arearum trigoni aequilateri geometrice arithmeticeve expensi, Trans. by Aleksandr A. Artamonov

Abstract

The publication contains a translation of Gerbert of Aurillac’s letter «On the cause of the difference between areas of an equilateral triangle» addressed to Adelbold of Utrecht and written in 999. This letter is well known in the history of mathe­matics as «the first mathematical text of the Middle Ages deserving this name» (this definition was provided by Hermann Hankel in 1874), while its author, be­ing the intellectual sun of Ottonian Renascence, is well known today as the most prominent Western philosopher and mathematician of the age. At the same time, the intellectual heritage of Gerbert of Aurillac still needs in-depth research. The letter provided in the publication serves as an illustration of Gerbert’s mathe­matical thinking; accompanied by the translator’s commentary, the text exceeds the limits of mathematical field and demonstrates the specifics of Gerbert’s philosophical worldview as the result of creative elaboration of Boethius’ intel­lectual heritage – in particular, of the latter’s metaphysical approach to mathe­matics, which was neglected by the western intellectuals after Boethius’ death. In the letter, the author analyses geometrical and arithmetical approaches to the cal­culation of equilateral triangle’s area, shows that these approaches provide dif­ferent results and, thus, proposes his own solution of this contradiction. In his proposed solution, Gerbert demonstrates a specific approach to the correlation between the wholeness of the figure and the wholeness of square units used for area’s calculation. The use of the formulation “wholeness of faith” (integritas fidei) in combination with Gerbert’s metaphysical understanding of mathematics allows us to explain his philosophical and theological worldview through his
geometrical ideas.