John Calvin Commentary Luke 1:3

"it seemed good to me also, having traced the course of all things accurately from the first, to write unto thee in order, most excellent Theophilus;" — Luke 1:3 (ASV)

Having carefully examined all things: the old translator renders it as having followed out all things;²⁰ and the Greek verb παρακολουθεῖν is taken metaphorically from those who tread in the footsteps of others, so that nothing escapes them.

So Luke intended to express his close and laborious investigation, just as Demosthenes employs the same word, when, in examining an embassy against which he brings an accusation, he boasts that his diligence was such that he perceived everything that had been done as well as if he had been a spectator.

²⁰ Omnia assequuto..