Foundations of geometry different sets of axioms for Euclidean geometry, any of these can replace the Euclidean parallel postulate. The following partial list indicates some of these theorems that are of historical interest. Absolute geometry is a geometry based on an axiom system consisting of all the axioms giving Euclidean geometry except for the parallel postulate or any of its alternatives. The term was introduced by János Bolyai in 1832. It is sometimes referred to as neutral geometry, as it is neutral with respect to the parallel postulate. In Euclid's "Elements", the first 28 propositions and Proposition I.31 avoid using the parallel postulate,
Ptolemy I of Tusculum (temporarily) resumed. Ptolemy and his nephew the prefect were holding the Castel Sant'Angelo. Peter Colonna and Rainald Senebaldi turned to the pope's side and, soon after Christmas, Ptolemy and the rest of the imperialists in the Eternal City were forced to flee by the pope, who soon died. Ptolemy I of Tusculum Ptolemy I ( or ; died 1126) was the count of Tusculum in the first quarter of the twelfth century. He was a son of Gregory III. Peter Pisanus, in his "Vita Paschalis II" refers to Ptolemy and the abbot of Farfa as the allies of the emperor