Exegesis:

kai epedothē autō biblion tou prophētou Ēsaiou ‘and to him was given the book of the prophet Isaiah,’ i.e. at his own request. This clause is in the Greek the beginning of a new sentence.

epididōmi ‘to give,’ ‘to hand over.’

biblion (also v. 20) ‘book,’ ‘scroll,’ here in the latter meaning as shown by anaptuxas, see below.

kai anaptuxas to biblion ‘and having unrolled the scroll.’

heuren ton topon hou ēn gegrammenon ‘he found the place where it was written.’ heuren means here that he found what he was looking for. topos ‘place’ means here ‘passage.’

hou ēn gegrammenon ‘where it was written.’ The pluperfect tense of the Greek represents an adjustment to the historic (aorist) tense of the main verb heuren. The purpose of the clause is to connect topon with the following quotation.

Translation:

There was given to him, or, ‘the attendant (see v. 20) handed him,’ ‘he received.’

The book of the prophet Isaiah, or, ‘the writing(s) of the prophet I.,’ ‘what (or, the book that) the prophet I. wrote,’ ‘the book containing what the prophet I. had spoken’; cf. also on 3.4. — Book, or, ‘writing,’ or the closer historical equivalent ‘scroll,’ ‘sacred roll’ (Marathi). The specific term in the receptor language may refer to a different object, e.g. a long strip of bark folded plait-wise (Batak Toba 1885) or a bundle of loose palm leaves held together by strings between two wooden covers (Balinese).

He opened, or a more specific term that fits the distinctive features of the term rendering “book”, e.g. ‘unrolled,’ ‘unfolded,’ ‘loosened (the strings of).’

He found, or indicating the implied search (cf. on 2.16), ‘he selected’ (Marathi), ‘he sought and found,’ ‘he found what he sought’ (cf. below). The context clearly implies that Jesus read aloud the passage he had found. Usually this is sufficiently clear from the reference to reading aloud in v. 16; if not, one may have to say here, ‘he found and read the place…,’ ‘he found the passage he sought/wanted and read what was written there’; or one may have to add a reference to reading at the beginning of v. 20 (which see).

The place where it was written, or using one specific term, “this text” (The Four Gospels – a New Translation), ‘these verse’ (Bahasa Indonesia RC, using a term that specifically refers to Koranic verses, and by extension to verses in the holy books of other religions). For the rendering of the relative clause see on 2.23. Balinese employs here one of its other formulas to introduce a quotation, i.e. ‘which its-wording (lit. its-being-pronounced) thus,’ thereby trying to suggest that the words quoted were read aloud.

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.