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This lecture covers the historical development of projective geometry, focusing on the orientation of the polar axis in celestial geometry. It explores the concept of obliquity of the ecliptic, the precession of the equinoxes, and the impact of these astronomical phenomena on climate variations. The lecture delves into the construction of the celestial vault, the role of gnomonic projections, and the significance of the eccentricity of Earth's orbit. It also discusses the historical context of astronomical observations, including the use of gnomons and the measurement of solstices. The presentation concludes with a detailed examination of the celestial geometry principles applied in ancient and modern contexts.