Euclid's Elements Euclid's Elements The Elements ( "Stoicheia") is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC. It is a collection of definitions, postulates, propositions (theorems and constructions), and mathematical proofs of the propositions. The books cover plane and solid Euclidean geometry, elementary number theory, and incommensurable lines. "Elements" is the oldest extant large-scale deductive treatment of mathematics. It has proven instrumental in the development of logic and modern science, and its logical rigor was not surpassed until the 19th century. Euclid's "Elements" has been referred to as the
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