Commentary on Euclid's Elements

Prologue

Between the two types of magnitudes—those found in the world around us and those similarly divided in their composition—is there a distinction? We should not suppose that while there are sciences and modes of knowledge for divisible things, there is no unified science for the immaterial and intellectual contemplation original: theōrias. Indeed, we possess not merely one science, but many branches of inquiry and knowledge, and it is from that primary, unified science that the many specific branches receive their common principles original: logous. In the progression of knowledge, the path leads from the more particular toward the more universal, as all things are eventually gathered up into the common science of Being. This science seeks to examine those things that exist in themselves within our reality. It does not merely look at what is common to all quantities, but observes the truly permanent essence and existence of all their parts.

Geometry Proclus often treats Geometry as the paradigmatic science that bridges the gap between the material world and pure abstraction. extends through all these sciences, and they all receive their principles from it. This is because higher sciences utilize the primary hypotheses of demonstration original: apodeixeōn for the sciences situated beneath them. But the most perfect of sciences provides from itself itself the principles for all the others—offering fewer principles to some, and more particular principles to others. This is why Socrates in the Theaetetus A reference to Plato’s dialogue where Socrates discusses the nature of knowledge with the young mathematician Theaetetus., tempering the zeal of the young, called the "circular" sciences original: en kuklō epistēmas—this refers to the "encyclical" or general education that forms the foundation of all learning. "primary." He says that some of these concern first principles, while others remain separate from the rest. For those sciences that are more universal and rely on fewer principles contain many particular truths within themselves; however, those branches of knowledge that touch upon specific kinds of things stand apart from one another and lack a natural connection original: asympatheis (without sympathy) to each other, as they arise from different starting points...