Os teoremas de pappus para os sólidos de revolução - Rautenberg, Robson Raulino (2013)
From the theorems found in the publication Geometriae Pars Universalisof 1668 are presented, for the ﬁrst time in portuguese, the proof of Pappus’s theorems for solids of revolution. This publication , originally written in latin, is due to the scottish mathematician James Gregory (1638-1675) and is prior to the development of Calculus. Furthermore some concepts of Calculus and center of gravity are also revised to present a proof of these theorems from these tools. Some direct cases for Pappus’s theorems are presented, where the axis of rotation or revolution is represented by one of the coordinate axes or by a straight line parallel to them. Also shown are cases where the axis of rotation is given by a straight tilted in the cartesian plane, showing the scope, efﬁciency and relative simplicity of applying these theorems.