GRC

ὑπόβασις

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εως (ἡ) [ᾰ]
   I action de descendre, d’où :
      1 décroissance, baisse (des eaux, etc.) STR. 789 ; fig. diminution, dommage, PROCL. ;
      2 descente d’échelon en échelon, d’où continuation, succession, SEXT. P. 3, 187 ; M. 9, 306 ; CLÉM. 817 ;
   II action de se baisser, en parl. du cheval (v. ὑποϐιϐάζω) XÉN. Eq. 1, 14 ;
   III base, piédestal, pied, SEMUS (ATH. 38 b) ; JOS. A.J. 3, 8, 6.

Étym. ὑποϐαίνω.

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LSJ

εως, ἡ, (< ὑποβαίνω) going down, retiring, of the Nile floods, Str. 17.1.4; καθ’ ὑπόβασιν downwards, in bandaging, Sor. Fasc. 58; καθ’ ὑπόβασιν τῆς τῶν πρωτείων τάξεως downwards through the series, Ptol. Tetr. 46; οὕτω καθ’ ὑπόβασιν μέχρις ἀπείρου and so on ad infinitum, S.E. M. 9.306, cf. P. 3.87; successive diminution, of the terms in a series, opp. προκοπή, Iamb. in Nic. p. 19P. in Neoplatonism, declension, descent from eternity to the world, etc. (v. ὑποβαίνω IV), Procl. in Prm. p. 492 S., Inst. 21, 97, al., in Ti. 2.206 D., al., Aristid.Quint. 3.10; ὑ. ἑβδοματική Dam. Pr. 205; ἡ κατ’ οὐσίαν αὐτῶν ὑπεροχή τε καὶ ὑ. Hierocl. in CA 1 p. 419M., cf. Simp. in Ph. 774.21.
moral declension, Plot. 1.8.7; declension from perfect health, Aët. 4.1.
stooping or crouching down, esp. of a horse that lowers itself to take up the rider, X. Eq. 1.14; cf. ὑποβιβάζω II.
basement, pedestal, foot, Semus 15, Test.Epict. 8.23, IGRom. 4.685.16 (Sebaste), J. AJ 8.3.6.
Liddell-Scott-Jones, Greek-English Lexicon (9th ed., 1940)

Pape

ἡ,
1) das Herabgehen od. Rückwärtsgehen, dah. der Rückschritt, die Abnahme, S.Emp. adv.phys. 1.306.
2) das Niederlassen auf das Knie, die gebückte Stellung, bes. des Pferdes, welches den Leib streckt, um den Reiter aufsitzen zu lassen, Xen. de re Eq. 1.14.
3) die Grundlage, das Fußgestell, die Basis, Sp.; – Hesych. erkl. auch ὁ ἐνδότατος χιτὼν ἢ περίζωμα.
Pape, Griechisch-deutsches Handwörterbuch (3. Aufl., 1914)
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