چکیده:
This article is devoted to Kamāl al-Dīn al-Fārsī’s (d. 1319)
additions to some remarks contained in Book XIII of al-Ṭūsī’s
Taḥrīr uṣūl al-handasa, concerning the construction of a semiregular
polyhedron inscribed into a sphere using the movement
as a way for the construction. This treatise is one treatise among
ten found in a codex preserved at the Bibliothèque nationale de
Tunis.
خلاصه ماشینی:
For the second part, he offers a more precise construction: Imagine now the movement toward the center of the two cutting surfaces unchanged in their relation to the diameter, moving with similar movements, making the sides of the triangles greater and the sides of the rectangles smaller, until they all become equal.
Fārsī uses also motion in imagination and it was perhaps due to his familiarity with s works that he thought it suitable to follow his ideasبIbn al-Haytham and found an original way to construct a new class of polygonal prisms inscribed within a sphere unrelated to the classical techniques 4 used in the Archimedean tradition.
Vitrac [2007] gives a complete analysis of the use of Fārsī’s second proposition In this section of the treatise, Fārsī is more conventional: he enunciates the problem: To inscribe in a sphere a polygonal prism similar to a given polygonal prism.
Let SY be the edge of the constructed polygon inscribed in the circle produced by the plane passing through S on the given sphere.
s Elements presented by De Youngبan anonymous addition to Euclid This treatise contains nineteen propositions describing techniques for ب constructing polyhedra within other polyhedra or within spheres.
The following diagrams show the different steps in modern perspective: (به تصویر صفحه مراجعه شود) Figure 4 The anonymous author assumes implicitly two lemmas: the first is concerning similar ٤-s proposition VIبa direct consequence of Euclid regular polygons inscribed in different circles; it says that for all of them, the ratio of the edge of the polygon to its diameter is the same.