Reflections on the principle of continuity on the basis of Ibn al-haytham's commentary on proposition I.7 of euclid's elements

Arabic Sciences and Philosophy 13 (1):101-136 (2003)
After his refutation of the doubts concerning Proposition I.7 (in the Book of solving doubts), Ibn al-Haytham mentions three possible ways in which circles may intersect, submitting them to the following “intuitive” argument: one part of one of the two circles is situated inside of the other circle, and its other part is situated outside of it. One is therefore tempted to believe that the commentator accepts the principle of continuity in the case of circles, since his argument has the following meaning: if a circle is divisible into two parts (or, again, passes through two points), one of which (or one of the two points) is situated inside the other circle, and the other outside of it, then the two circles cut one another. The author of this article proposes to establish the limits of this belief, on the basis of the following reflections: 1). It will be noted first of all that what could be called the ‘principle of the intersection of circles’ does not constitute ipso facto a principle in the mind of Ibn al-Haytham: no allusion is made to it in the commentary on Proposition I.1, among others. 2) It will be established later on that if one accepts (according to the explanation of Ibn al-Haytham in his Commentary on the premisses) that a line is the result of the movement of a point, the principle of continuity should be considered by him as something which is obvious by itself, without being stated. This conclusion will be based on an analysis of the notion of continuity in its classical meaning, and on Ibn al-Haytham’s commentary on Proposition X.1. 3) On the other hand, we should note the presence of a ‘sketch’ of topological language, which Ibn al-Haytham develops for the notion of a circle (particularly in the Commentary): one could say in this context that his reflection constitutes an important, if not principal, stage in the process which was to lead to the explicit formulation of the principle of continuity. Footnotes1 Je voudrais remercier chaleureusement Monsieur R. Rashed d'avoir bien voulu lire la première version de cet article, m'envoyer certaines de ses publications et me communiquer ses suggestions dont j'ai essayé de tirer le plus grand profit dans la révision que voici. Toutes les insuffisances qui s'y trouvent ne peuvent que m'être imputées.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1017/S0957423903003059
 Save to my reading list
Follow the author(s)
Edit this record
My bibliography
Export citation
Find it on Scholar
Mark as duplicate
Request removal from index
Revision history
Download options
Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 29,827
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles
L'optique d'Ibn Al-Haytham Et la Tradition Ptoléméenne.Gérard Simon - 1992 - Arabic Sciences and Philosophy 2 (2):203.
The Scientific Method of Ibn Al-Haytham.Muhammad Saud - 1990 - Islamic Research Institute, International Islamic University.
The New Astronomy of Ibn Al-Haytham.Christian Houzel - 2009 - Arabic Sciences and Philosophy 19 (1):1-41.
Ibn Al-Haytham's Criticisms of Ptolemy's.A. I. Sabra - 1966 - Journal of the History of Philosophy 4 (2).
The Knowledge of Arabic Mathematics by Clavius.Eberhard Knobloch - 2002 - Arabic Sciences and Philosophy 12 (2):257-284.
Géométrie Et Philosophie: De Thabit Ibn Qurra À Ibn Al-Haytham.Alain Michel - 2003 - Arabic Sciences and Philosophy 13 (2):311-315.
The Celestial Kinematics of Ibn Al-Haytham.Roshdi Rashed - 2007 - Arabic Sciences and Philosophy 17 (1):7-55.
Added to PP index

Total downloads
28 ( #199,405 of 2,210,565 )

Recent downloads (6 months)
1 ( #380,793 of 2,210,565 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature