Euclid’s Elements

Considered one of the most influential and long-used textbooks of all time, Elements remains a key work in geometry’s logical development. Euclid’s ancient Greek text consists of thirteen books that demonstrate how to make logical proofs to ascertain certainty and investigate the unknown. The books also include some of the earliest known algorithms. The concepts Elements introduced would be critical in the development of algorithms by Islamic mathematicians and throughout the European Middle Ages. The text would again prove vital in early modern science, influencing Copernicus, Kepler and Galileo among countless others. Its legacy throughout the millennia is unquestioned. Like the seminal advancements in binary systems from I Ching, Elements played a critical role in moving the field of logic forward. Binary systems and logic would prove foundational to modern attempts to design computing machines, including by Gottfried Leibniz later in this chapter.