Academic journal article Journal of the History of Ideas

The Drawing Board of Imagination: Federico Commandino and John Philoponus

Academic journal article Journal of the History of Ideas

The Drawing Board of Imagination: Federico Commandino and John Philoponus

Article excerpt

INTRODUCTION

Federico Commandino (1509-75), court mathematician to Francesco Maria della Rovere and founder of the school of Urbino, can be considered the ultimate personification of the humanist-scientific project that Paul Lawrence Rose famously identified as the "renaissance of mathematics" in sixteenth-century Italy.1 The idea of a revival of ancient mathematics is explicitly found in the opening lines of Commandino's dedication letter to the Duke of Urbino from his 1572 edition of Euclid's Elements:

Most illustrious prince, when I come to think how great the fame and dignity of mathematical skill once had been among those ancient men of a happier age and genius, I cannot but greatly deplore the condition of our times, in which the elegance and splendor of a noble discipline is completely consumed by immense squalor and darkness. . . . Nonetheless, my pain lessens day by day, because I know that these arts, after having been lovingly awakened by men of high learning from foreign regions, are very carefully promoted.2

Commandino's humanist-editorial endeavors earned him the title of "restaurator mathematicarum" from his students Guidobaldo del Monte and Bernardino Baldi,3 and just like Commandino's other translations in the domain of Greek mathematics,4 his translation of Euclid's Elements (Pesaro, 1572)5 became an instant success and served as a basis for many subsequent translations of the Elements, well into the eighteenth century.

However, in this article I will focus not on the Latin translation of the Elements but on the preface to this translation,6 where Commandino formulates his views on the ontology and epistemology of mathematics. Although the prolegomena have already been studied, scholars too easily reduce Commandino's ideas to a rather superficial synthesis of Neoplatonic and Aristotelian elements, lacking originality.7 For example, until now, no attention whatsoever has been paid to Commandino's very subtle use of the sixth-century commentary on Aristotle's De Anima by the Christian commentator John Philoponus. In this article I will demonstrate how Commandino receives and transforms the ancient commentary tradition to develop a theory of mathematics capable of incorporating a geometrical imagination into the traditional, Aristotelian inspired abstractionist account of mathematics. Moreover, I will argue that, in depicting imagination as a mental drawing board for geometrical figures, Commandino directly relies on Philoponus's concept of mathematical imagination. From a broader perspective, this case-study will further elucidate the important role played by the ancient commentary tradition in the domain of Renaissance philosophy of mathematics, and, more specifically, in the formation of a key concept as mathematical imagination.

COMMANDINO'S IN ELEMENTA EUCLIDIS PROLEGOMENA

In the eight-page prolegomena Commandino explicitly positions himself in a tradition started by the fifth-century Neoplatonist Proclus8 and continued by-among others-the Jesuit mathematician Christopher Clavius (1538- 1612) and the famous mathematician and astronomer John Dee (1527- 1608). Each adds a preliminary meta-mathematical discourse that situates the reading of Euclid's magnum opus within a broader philosophical and educational framework:9 Proclus places the Elements in the framework of Neoplatonism, Clavius in the reform of the Jesuit ratio studiorum,10 and Dee, with his famous Mathematicall Praeface, in a Platonic-spiritual conception of geometry.11

In the opening lines of the prolegomena Commandino provides us with the following structure of his account.12 The first part-which will be the focus of our argument and which is given as an appendix to this article- will discuss (1) the subject matter of mathematics; (2) the place and dignity of mathematics with respect to other disciplines; (3) the definition of mathematics; and (4) the origin of mathematics. The second part will deal with (5) the usefulness of mathematics. …

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