Exegesis:

hina epignōs ‘in order that you may know exactly.’

hina with following subjunctive ‘in order that,’ here indication of purpose.

epiginōskō ‘to know,’ ‘to know exactly,’ ‘to learn,’ ‘to recognize.’ In the present context katēchēthēs, however interpreted (see below), implies that Theophilus had already some knowledge of the Gospel facts but not enough to be sure of their trustworthiness. Hence epiginōskō; carries here the nuance of ‘knowing exactly.’ The majority of translations do not bring out this nuance but the idea of ‘knowing exactly’ is also suggested by the object of epignōs, i.e. asphaleian ‘reliability,’ cf. Phillips, “that you may have reliable information”. That epiginōskō would mean ‘to have additional knowledge’ is improbable.

peri hōn katēchēthēs logōn tēn asphaleian ‘the reliability of the things that you have been taught.’ The connexion of the whole clause is as follows: hina epignōs tēn asphaleian tōn logōn peri hōn katēchēthēs; the relative clause peri hōn katēchēthēs logōn (with incorporation of the antecedent logōn) has been placed between the main verb epignōs and its object asphaleian in order to give greater emphasis to the latter, and because it is in accordance with literary usage.

katēcheō ‘to inform,’ or ‘to teach.’ When understood in the latter meaning the reference is to some form of instruction in the fundamentals of the Christian faith but not necessarily to what later became known as the instruction of the catechumens. In either meaning, therefore, katēchēthēs does not implicitly decide whether or not Theophilus was a Christian. If it is assumed that he is, then the more logical translation is ‘to teach,’ but this assumption then is based on other grounds than the meaning of katēcheō, cf. on v. 3, and the most that can be argued from the present phrase is that it does not exclude the possibility that Theophilus was already a Christian at the time Luke’s Gospel was written. Hence the mere fact that the meaning ‘to teach’ is favoured is in itself no indication of the translator’s choice in this question. Both interpretations are well represented among commentators and translators, but the majority favour ‘to teach.’

logos ‘word’; here it must either be understood in the very general meaning ‘matter,’ ‘thing,’ or in the rather special meaning ‘story,’ preferably the former.

asphaleia ‘truth,’ ‘trustworthiness,’ ‘reliability,’ preferably the last.

Translation:

Know, or, ‘understand,’ ‘discern clearly’ (Chinese RC), se rendre compte (Bible de Jérusalem); the aspect is ingressive. In some languages ‘to know/perceive’ and ‘to see’ are rendered by the same term (Sranan Tongo); elsewhere exact knowledge is referred to by a figurative expression, ‘to be clear to the self’ (Toraja-Sa’dan).

The truth concerning the things of which you have been informed. This complex phrase usually has to be recast as a clause, e.g. ‘that the things … are true,’ or, trying to reproduce the emphasis of the Greek, ‘that the things … have actually occurred (Telugu), or, are perfectly certain (Tamil), or, are entirely reliable.’ A further shift is found in Apache, ‘that you may truly know the things…, how they happened.’ Cf. also the Kituba and Shipibo-Conibo quotations in the note on vv. 1-4. The things of which you have been informed, again, will often have to be restructured, e.g. ‘what people have taught you’ (Sranan Tongo), ‘the words they told you’ (Shipibo-Conibo), ‘the way you have learned’ (Chinese Union Version), ‘the things you have heard’ (Tboli).

Quoted with permission from Reiling, J. and Swellengrebel, J.L. A Handbook on the Gospel of Luke. (UBS Handbook Series). New York: UBS, 1971. For this and other handbooks for translators see here . Make sure to also consult the Handbook on the Gospel of Mark for parallel or similar verses.