Foundations of geometry association of meanings makes the axioms of the system true statements, then the interpretation is called a model of the system. In a model, all the theorems of the system are automatically true statements. In discussing axiomatic systems several properties are often focused on: "Euclidean geometry" is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described (although non-rigorously by modern standards) in his textbook on geometry: the "Elements". Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated
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