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Theophrastus · Fragments §71.1

The Definition of Axioms and Their Two Kinds

Passage 73 of 196 · Greek

Summary

Theophrastus' definition of an axiom, which presents two types: one applicable to things of the same kind and another applicable to all things universally.

§71.1Fr. 71 Ὁ Θ. οὕτως ὁρίζεται τὸ ἀξίωμα "ἀξίωμά ἐστι δόξα τις, ἡ μὲν ἐν τοῖς ὁμογενέσιν ἐὰν ἴσα ἀπὸ ἴσων, ἡ δὲ ἁπλῶς ἐν ἅπασιν. "
Fr. 71 Theophrastus defines the axiom as follows: "An axiom is a certain judgment, the one being in things of the same kind, as in 'if equals from equals', and the other simply in all things."

Notes

  1. §71.1ἐὰν ἴσα ἀπὸ ἴσων — An extremely elliptical expression referring to the well-known mathematical axiom "if equals are subtracted from equals, the remainders are equal" (ἐὰν ἀπὸ ἴσων ἴσα ἀφαιρεθῇ, τὰ καταλειπόμενά ἐστιν ἴσα). Here, the verb (such as ἀφαιρεθῇ "are subtracted") and the main clause ("the remainders are equal") are omitted, with only part of the conditional clause presented.
  2. §71.1ἡ μὲν... ἡ δὲ... — These feminine singular articles refer back to the preceding noun δόξα, dividing it into two classes. The articles function pronominally, with δόξα understood (i.e., "the one judgment..., the other...").

Cite this passage

Theophrastus, Fragments §71.1. Humanitext Reader, https://reader.humanitext.ai/en/text/urn:cts:greekLit:tlg0093.tlg010x09.humanitext-grc1:71.1

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