Euclid’s Elements , c. 300 BCE , 1 is the earliest extant treatise of deductive mathematics in history, and is still regarded as a paradigm of an axiomatic science. 2 By deriving a large number of mathematical theorems from a relatively small number of undemonstrated
geometry. By contrast, Sextus expressly mentions the Epicureans as critics of geometry ( M III .94–107; M I .5, see section 3.3 below). Since variants of definitions that Sextus attacks in M III are found in Euclid’s Elements (= El. ), Heiberg (1888, LXXII ) takes Sextus to implicitly refer to
paper, by Benjamin Wilck, is on Euclid. It argues that Euclid’s Elements is committed to several metaphysical distinctions, namely distinctions first captured by Aristotle, and that there are different types of definitions which Euclid uses to implicitly make these distinctions. This is followed by a
attains greater exactness than other arts. Corroborating the historical development reading is Proclus, Commentary on Euclid’s Elements (Prologue 1, 9, 28.13–29.13), which paraphrases both (a) the progress argument as such and (b) DCMS 83.6–22’s remarks, which highlight the theoretical sciences’ rapid
Porphyry) that may lie behind these exchanges, see Lagouanère 2018, 231–44.
The Extramission Theory of Vision has a history going back to Empedocles and running through Plato, the Stoics, Galen, Euclid, Hero of Alexandria, and Ptolemy. This history is well surveyed in Lindberg 1976, 1
relation between these numbers. Propositions of this kind are discoverable by the mere operation of thought, without dependence on what is anywhere existent in the universe. Though there never were a circle or triangle in nature, the truths demonstrated by Euclid would for ever retain their certainty and