Final answer:
Euclid's Elements consists mainly of geometry and number theory, with its closest approximation among the options being geometry and algebra. It established foundational principles that have profoundly influenced mathematics and remained accurate over centuries.
Step-by-step explanation:
Euclid's Elements is comprised of geometry and a foundational form of number theory, making none of the provided options entirely accurate. However, the essence of the Elements closest aligns with option (a) among the given selections, as it is primarily concerned with geometric propositions and includes rudimentary aspects that later contributed to the development of algebra (there is no explicit algebra in the Elements).
It does not include trigonometry, calculus, probability, arithmetic, or statistics in the manner that we understand them today. Instead, Euclid laid the groundwork for Euclidean geometry, constructing a systematic framework starting from axioms and postulates to reach logically deduced theorems. The work consists of 13 books covering a range of topics from plane geometry, the theory of proportions, the properties of numbers, incommensurable lengths, and solid geometry. The profound influence of Euclid's Elements is evidenced by its continued use as a textbook into the twentieth century and the fact that none of its major claims have been proven inaccurate over time.
While the Elements does not explore trigonometry or calculus as we know them, it does establish principles that would be fundamental to their later development. For instance, the Pythagorean theorem presented by Euclid is a cornerstone of trigonometry. Similarly, while not delving into what we call algebra, Euclid dealt with general propositions about numbers—such as the prime number theorem and the fundamental theorem of arithmetic—which are considered part of number theory and are foundational to later algebraic concepts.