This paper is a contribution to our understanding of the constructive nature of Greek geometry. By studying the role of constructive processes in Theodoius’s Spherics, we uncover a difference in the function of constructions and problems in the deductive framework of Greek mathematics. In particular, we show that geometric problems originated in the practical issues involved in actually making diagrams, whereas constructions are abstractions of these processes that are used to introduce objects not given at the outset, so that their (...) properties can be used in the argument. We conclude by discussing, more generally, ancient Greek interests in the practical methods of producing diagrams. (shrink)

In the ancient civilizations, the sky has been observed in order to understand the motions of the celestial bodies above the horizon. The study of faiths and practices dealing with the sky in the past has been attributed to the sun, the moon, and the prominent stars. The alignment and orientation of constructions to significant celestial objects were a common practice. The orientation was an important component of the religious structure design. Religious buildings often have an intentional orientation to fix (...) the praying direction. In Islam, a sacred direction towards Kaaba located in the courtyard in the Sacred Mosque in Mecca has been used for praying and fulfilling varied ritual tasks. Therefore, the mosques had then to orientate towards the Qibla direction, being designated by a focal niche in the Qibla-wall, wherever they were built on Earth. In this study, the orientations of the historical Grand mosques in Turkey are surveyed with regard to the folk astronomy derived from pre-Islamic Arabian sources, early traditions of the Islamic period, and geometric-trigonometric computation in mathematical astronomy inherited and developed mostly from Greek sources according to the Islamic view of the World geography. (shrink)