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Euclid · Elements §2.def.1-2.def.2

Definitions of Right-Angled Parallelogram and Gnomon

Passage 25 of 316 · Greek

Summary

The definition of a right-angled parallelogram as being contained by its sides, and the definition of a gnomon in a parallelogram.

§2.def.1πᾶν παραλληλόγραμμον ὀρθογώνιον περιέχεσθαι λέγεται ὑπὸ δύο τῶν τὴν ὀρθὴν γωνίαν περιεχουσῶν εὐθειῶν.
Any right-angled parallelogram is said to be contained by the two straight lines containing the right angle.
§2.def.2παντὸς δὲ παραλληλογράμμου χωρίου τῶν περὶ τὴν διάμετρον αὐτοῦ παραλληλογράμμων ἓν ὁποιονοῦν σὺν τοῖς δυσὶ παραπληρώμασι γνώμων καλείσθω.
And in any parallelogramic area, let any one of the parallelograms about its diagonal together with the two complements be called a gnomon.

Notes

  1. §2.def.1περιέχεσθαι λέγεται — A 'nominative with infinitive' construction where the main verb λέγεται ('is said', third-person singular present passive) takes the nominative subject πᾶν παραλληλόγραμμον ὀρθογώνιον, which also functions as the subject of the passive infinitive περιέχεσθαι ('to be contained').
  2. §2.def.2παντὸς δὲ παραλληλογράμμου χωρίου — The genitive phrase παντὸς ... χωρίου at the beginning functions as a limiting or possessive genitive (genitive of reference) defining the whole domain. It acts as the antecedent for the pronoun αὐτοῦ ('its') in the subsequent partitive phrase τῶν περὶ τὴν διάμετρον αὐτοῦ παραλληλογράμμων, establishing the whole-to-part relationship.

Cite this passage

Euclid, Elements §2.def.1-2.def.2. Humanitext Reader, https://reader.humanitext.ai/en/text/urn:cts:greekLit:tlg1799.tlg001.humanitext-grc2:2.def.1-2.def.2

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