•  5
    ArgumentThe Fourth Postulate of Euclid’s Elements states that all right angles are equal. This principle has always been considered problematic in the deductive economy of the treatise, and even the ancient interpreters were confused about its mathematical role and its epistemological status. The present essay reconsiders the ancient testimonies on the Fourth Postulate, showing that there is no certain evidence for its authenticity, nor for its spuriousness. The paper also considers modern mathe…Read more
  •  76
    Leibniz pursued the study of his new geometry, the analysis situs, throughout his lifetime. The following essays, the Ars Representatoria and the text Uniformis locus…, both go back to the early nineties of the seventeenth century. Although most of the analysis situs texts are still unpublished—which makes it very hard to see how this discipline might have evolved during the years—there seems to be no doubt that the beginning of 1690s marked a breakthrough in Leibniz’s studies.
  •  56
    Leibniz around 1700
    The Leibniz Review 16 55-69. 2006.
  •  7
  • Thinking and Calculating (edited book)
    Springer. 2022.
  •  18
    In this paper, I attempt a reconstruction of the theory of intersections in the geometry of Euclid. It has been well known, at least since the time of Pasch onward, that in the Elements there are no explicit principles governing the existence of the points of intersections between lines, so that in several propositions of Euclid the simple crossing of two lines (two circles, for instance) is regarded as the actual meeting of such lines, it being simply assumed that the point of their intersectio…Read more
  •  8
    The book offers a collection of essays on various aspects of Leibniz’s scientific thought, written by historians of science and world-leading experts on Leibniz. The essays deal with a vast array of topics on the exact sciences: Leibniz’s logic, mereology, the notion of infinity and cardinality, the foundations of geometry, the theory of curves and differential geometry, and finally dynamics and general epistemology. Several chapters attempt a reading of Leibniz’s scientific works through modern…Read more
  •  11
    Euclid’s Common Notions and the Theory of Equivalence
    Foundations of Science 26 (2): 301-324. 2020.
    The “common notions” prefacing the Elements of Euclid are a very peculiar set of axioms, and their authenticity, as well as their actual role in the demonstrations, have been object of debate. In the first part of this essay, I offer a survey of the evidence for the authenticity of the common notions, and conclude that only three of them are likely to have been in place at the times of Euclid, whereas others were added in Late Antiquity. In the second part of the essay, I consider the meaning an…Read more
  •  19
    The paper lists several editions of Euclid’s Elements in the Early Modern Age, giving for each of them the axioms and postulates employed to ground elementary mathematics.
  •  10
    The book offers a collection of essays on various aspects of Leibniz’s scientific thought, written by historians of science and world-leading experts on Leibniz. The essays deal with a vast array of topics on the exact sciences: Leibniz’s logic, mereology, the notion of infinity and cardinality, the foundations of geometry, the theory of curves and differential geometry, and finally dynamics and general epistemology. Several chapters attempt a reading of Leibniz’s scientific works through modern…Read more
  •  10
    The development of Euclidean axiomatics
    Archive for History of Exact Sciences 70 (6): 591-676. 2016.
    The paper lists several editions of Euclid’s Elements in the Early Modern Age, giving for each of them the axioms and postulates employed to ground elementary mathematics.
  •  6
    This book offers a general introduction to the geometrical studies of Gottfried Wilhelm Leibniz and his mathematical epistemology. In particular, it focuses on his theory of parallel lines and his attempts to prove the famous Parallel Postulate. Furthermore it explains the role that Leibniz’s work played in the development of non-Euclidean geometry. The first part is an overview of his epistemology of geometry and a few of his geometrical findings, which puts them in the context of the 17th-cent…Read more
  •  8
    La dimostrazione kantiana del Quinto Postulato di Euclide
    In Stefano Bacin, Alfredo Ferrarin, Claudio La Rocca & Margit Ruffing (eds.), Kant und die Philosophie in weltbürgerlicher Absicht. Akten des XI. Internationalen Kant-Kongresses, De Gruyter. pp. 31-42. 2013.
  •  12
    Leibniz on Geometry
    The Leibniz Review 15 127-132. 2005.
    Leibniz pursued the study of his new geometry, the analysis situs, throughout his lifetime. The following essays, the Ars Representatoria and the text Uniformis locus…, both go back to the early nineties of the seventeenth century. Although most of the analysis situs texts are still unpublished—which makes it very hard to see how this discipline might have evolved during the years—there seems to be no doubt that the beginning of 1690s marked a breakthrough in Leibniz’s studies.
  •  12
    This book brings together papers of the conference on 'Space, Geometry and the Imagination from Antiquity to the Modern Age' held in Berlin, Germany, 27-29 August 2012. Focusing on the interconnections between the history of geometry and the philosophy of space in the pre-Modern and Early Modern Age, the essays in this volume are particularly directed toward elucidating the complex epistemological revolution that transformed the classical geometry of figures into the modern geometry of space. Co…Read more
  •  7
    Leibniz around 1700: Three Texts on Metaphysics
    The Leibniz Review 16 55-69. 2006.