Together with other entries on first-person forms of the same verb and its compounds (tau 430, tau 1147, epsilon 3344; alpha 3621, epsilon 2674, epsilon 2738, kappa 954, sigma 1648; cf. the related verbs at alpha 4347, delta 642, delta 645, delta 849, epsilon 3784), this entry is a marginal interpolation in the Suda, found also by Adler in one or both of what she calls the Lexica Syntactica, (or Glossae syntacticae, p.xvi §3), Gudianum (edited only with specimens by Sturz in his 1818 edition of the Etymologicum Gudianum, i.e. without any of these entries) and Laurentianum (codicis Laur. 59.16f. 239ff.). See the similar collections of verbs with the cases they govern in Anecdota Oxoniensia, ed. J.A. Cramer (1.275-307, all of which are taken up in the Suda) and in Anecdota graeca, ed. I. Bekker, vol. I (= Lexica Segueriana) 117-180.
This verb represents in Greek the Indo-European root *dheugh- ('hit, meet'; cf. German treffen, uniting the same two meanings; cf. Herter's zielt und trifft), with dissimilation of the initial aspirate. It does not, however, have this meaning in this present tense, but rather 'prepare, try to produce or achieve, craft', originally of the hammering of leather and heated metal and chiseling or sculpting of stone and ivory (see tau 375 for fuller discussion of these meanings; cf. LSJ, web address 1). It is also used of the gods as the craftsmen of human suffering and similar notions.
In the Epimerismoi [Parsings] of Homer (Anecdota Oxoniensia, vol. 1) we find the following: teu/xw, teu/cw, e)/tuxon, te/teuxa, te/teugmai (410.3-30), e)tu/xqhn (138.10-18). Bruno Snell (at p. 178 of the article cited below) assigned the verb to the same class as feu/gw 'I am running away, trying to escape', feu/comai 'I intend to escape', e)/fugon 'I successfully escaped', pe/feuga 'I am in the state of freedom'; cf. lei/pw, e)/lipon.
Modern dictionaries such as LSJ (followed reluctantly by Villard Leglay in her important dissertation cited below) blur this original pattern by dividing the forms from this root between two verbs, teu/xw (web address 1) and tugxa/nw (web address 2). Boisacq went so far as to deny any relation between the two.
There are the following forms recognized in the Suda:
Present and imperfect actives: (a) teu/xw; (b) tugxa/nw + genitive (tau 1147, epsilon 3341) 'I happen to be in the process of meeting, succeeding', (c) + dative 'fall to the lot of' (cf. aorist active below and note on tau 1147), 'fall in with' (sigma 1648 and other compounds); (d) titu/skw (tau 697, 'aim to hit or join'). See also the imperative at tau 1146. Forms in -tuxe/w (epsilon 3781, epsilon 3784, from eu)tuxh/s) and -teu/ktw (alpha 4347, cf. tau 375, tau 428) are secondary formations.
Future active: teu/cw 'I shall prepare' (e.g. Homer, Iliad 15.249, Odyssey 1.277, 2.196, 10.290, 12.347, 13.397, 22.14, 24.197, 476).
Future middles: teu/comai (Homer, Iliad 5.653, 19.208, tau 432, epsilon 1469, epsilon 2674, pi 1321, sigma 1639) 'I intend to hit, meet, succeed' + genitive, even where the present tense governs the dative (epsilon 2674). Chantraine classes this future middle as desiderative (Grammaire homérique 440-41), and it is glossed with an aorist subjunctive at pi 1321, sigma 1639. One cannot predict the outcome of the attempt to succeed in a goal, meet a person or a military enemy or hit the mark.
Aorist actives and passives: (a) e)/teuca 'produced, crafted, created'(stressing the ergativity of the subject; in Homer used primarily of the craftsman god Hephaestus) + accusative, with its passives e)tu/xqhn, e)teu/xqhn (cf. Orion [Author, Myth], p.7 Sturz on the participles a)tuxqei/s, a)tuxei/s), (b) te/tuxon ‘prepared’ (exclusively of food and meals; cf. tau 419), (c) e)/tuxon + genitive 'hit, met, achieved' (see at length epsilon 3344), (d) + dative 'was acquired, fell to the lot of, fell in with', (e) e)tu/xhsa 'hit (with missile in war), fell to the lot of', apparently no more than a metrical alternative for e)/tuxon in epic hexameter (Chantraine, Grammaire homérique 415-16).
Aorist middle: (a) e)teuca/mhn, apparently only in compounds, cf. alpha 3591, of trying and failing to hit, (b) tetu/xonto + accusative, chiefly in the Homeric phrase tetu/konto/ te dai=ta (Iliad 1.467, 2.430, 7.319, etc., tau 419) 'they had (a meal) prepared for them'.
Perfect active: te/teuxa + genitive 'have found, have secured' and at Homer, Odyssey 12.423 'is made of'.
Perfect passives: See the discussion at tau 375. The original meaning of these forms has its full force at Hesiod, Theogony 581, of many intricate designs hammered by Hephaestus on the crown of the Ancestress of Woman. But usually elsewhere, it is little more than the verb 'to be': ‘have been made, are’ (cf. Hesychius epsilon6593). Its common pluperfect passive may be glossed by the imperfect (sch. Homer, Iliad 13.346) and its future perfect passive by the future (Apollonius the Sophist, Homeric Lexicon 151; Homer, Iliad 12.345, 358, 21.322, 585; Anecdota Oxoniensia 1.411.19-21, in error).
Note the existence of teteuxh=sqai from a related but different stem, 'to have been equipped with armour' (Apollonius, Homeric Lexicon 151.36; Hesychius tau595; etc.).
[1] This form of the verb takes the genitive only of the material of which a thing is prepared or crafted, e.g. leather at Homer, Odyssey 12.423: r(inoi=o teteuxw/s ‘made of hide’; but perhaps originally of stone or heated metal hit by a craftsman with hammer or chisel (see above and tau 428). It is used more frequently with those forms assigned by modern dictionaries to tugxa/nw for the object aimed at, met, achieved or hit (Smyth, Greek Grammar §§1349, 1350, 1353): see tau 1147, tau 430, epsilon 3344.
[2] This applies to this particular form, and to those assigned in modern dictionaries to teu/xw. Some compounds govern the dative as the indirect object governed by the prefix.
[3] For this form after a neuter plural subject subject see tau 375. It probably refers here to the stone work done with a tu/xos (tau 1148) to hew stone, but may also refer to relief sculpture in stone and chasing of the metallic surfaces of the palace.
[4] Homer, Iliad 13.21-22 (web address 3). Two lines, referring to Poseidon's home in the sea at Aegae, are here abridged and reordered. Poseidon was known as *ai)/gaios and worshipped in a town of this name on Euboea (Eustathius Commentary on the Iliad 2.565ff.). The lines surrounding these are often regarded as corrupt (e.g. Leaf ad loc.). Note that outside Homer li/mnh refers to stagnant lake or marsh water (lambda 551, cf. alpha 3416, alpha 4160, alpha 4296, etc.).