This chapter deals with stereographic projection, which is superior to other projections of the sphere because of its angle-preserving and circle-preserving properties; the first property gave instrument makers a huge advantage and the second provides clear astronomical advantages. The earliest text on stereographic projection is Ptolemy's Planisphere, in which he explains how to use stereographic projection to solve problems involving rising times, suggesting that the astrolabe may have existed already. After providing an overview of the astrolabe, an instrument for solving astronomical problems, the chapter considers how stereographic projection is used in solving triangles. It then describes the Cesàro method, named after Giuseppe Cesàro, that uses stereographic projection to project an arbitrary triangle ABC onto a plane. It also examines B. M. Brown's complaint against Cesàro's approach to spherical trigonometry.
$$H^1$$-conforming finite element cochain complexes and commuting quasi-interpolation operators on Cartesian meshes
