Workshop Història de les Matemàtiques

The impact of Greek mathematics procedures in the Renaissance and in the 17th century mathematics

Organizers: Maria Rosa Massa-Esteve (UPC); Mónica Blanco Abellán (UPC) and David Rabouin (Sphere, Université Paris Cité)

Group of History of Science and Technique (SOC-STEM, UPC) and Sphere (Université Paris Cité)

Faculty of Mathematics and Statistics. Auditorium, 3 September 2024

The mathematical advances from the Renaissance to the 17th century can be attributed to the interplay of three fundamental forces. The first was the classical mathematical heritage of the 16th century, exemplified by the direct revival in Greek and Latin translations of works by Euclid, Archimedes, Aristarchus and others. The second was the so-called ‘revolution of infinity’, i. e. the extension of mathematics through the use of infinite procedures and the study of geometrical objects of infinite dimension. The third was the appearance of algebra (especially symbolic language and the analytical method) and its use in problem solving.

While we have recently investigated the last two ideas, the ‘revolution of infinity’ and the emergence of algebra, this time we want to focus on the impact of Greek or classical mathematics on the mathematical developments of the 17th century, including the early 18th century.

The questions might be: What implicit or explicit influences of Greek ideas can be found in the emergence and development of infinitesimal calculus? Or in the creation of analytic geometry as a new discipline? In fact, the idea is to consider the past in order to understand new mathematical developments. Topics such as the theory of proportions in Book V of Euclid's Elements, the solution of geometrical problems in Pappus’ Collection or quadrature in Archimedes’ works can be some good examples.

Therefore, the aim of this workshop is to reflect on these influences by analysing Renaissance and 17th century sources through the underlying ideas of the past, which in the 16th century came, in many cases, through very good translations of Greek works.

PROGRAM

10:00- 10:15 Presentation with the welcome of the Dean of the Faculty of Mathematics and Stadistics Prof. Jordi Guàrdia.

First session: Chair Maria Rosa Massa-Esteve

10:15- 10:45 Fàtima ROMERO VALLHONESTA: Euclid’s Elements in the algebraization of mathematics.

10:45-11:15 Juan NAVARRO LOIDI: Printed versions of Euclid’s Elements in Spanish.

11:15-11:30 Coffee break

Second session: Chair Mònica Blanco Abellan

11:30-12:00 Antonio LINERO BAS-Antonio MELLADO ROMERO: Euclid’s Elements and the resolution of equations into Hérigone's Mathematical Course.

12:00-12:30 David VIRGILI CORREAS: “Restoring” the method of the Ancients: Antonio Hugo de Omerique’s allegedly purely geometrical analysis (1698).

12:30-12:45 Discussion

13:00-15:00 Lunch

Third session: Chair David Rabouin

15:15-15:45 Arilès REMAKI: Comparison of the notion of limit between Mengoli and Gregory: between possible and impossible.

15:45-16:15 Maria Rosa MASSA-ESTEVE: From ratios of ratios to logarithms in Mengoli’s Geometriae Speciosae Elementa (1659).

16:15-16:30 Coffee Break

Fourth session: Chair Davide Crippa

16:30-17:00 David RABOUIN: Ratios and numbers in Leibniz.

17:00-17:30 Mònica BLANCO ABELLAN: The study of classical curves in the early works on differential calculus.

17:30-18:00 Final Discussion