καταβεβλημένως

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προγράψαντες οὖν τά τε θεωρήματα καὶ τὰ ἐπιτάγματα τὰ χρεῖαν ἔχοντα εἰς τὰς ἀποδείξιας αὐτῶν μετὰ ταῦτα γραψοῦμές τοι τὰ προκείμενα → having therefore written at the beginning the theorems and the postulates that are necessary for their proofs, we will then write out for you the propositions

Source
Click links below for lookup in third sources:
Full diacritics: καταβεβλημένως Medium diacritics: καταβεβλημένως Low diacritics: καταβεβλημένως Capitals: ΚΑΤΑΒΕΒΛΗΜΕΝΩΣ
Transliteration A: katabeblēménōs Transliteration B: katabeblēmenōs Transliteration C: katavevlimenos Beta Code: katabeblhme/nws

English (LSJ)

Adv. pf. part. Pass. of καταβάλλω,

   A contemptibly, Isoc.15.305.

German (Pape)

[Seite 1339] weggeworfen, gemein, ζῆν, Isocr.

Greek (Liddell-Scott)

καταβεβλημένως: ἴδε καταβάλλω ἐν τέλει.

French (Bailly abrégé)

adv.
d’une façon commune, humblement.
Étymologie: part. pf. Pass. de καταβάλλω.