εδοξεν verb - aorist active indicative - third person singular
dokeo  dok-eh'-o: to think; by implication, to seem (truthfully or uncertainly) -- be accounted, (of own) please(-ure), be of reputation, seem (good), suppose, think, trow.
καμοι personal pronoun - first person dative singular - contracted form
kago  kag-o': so also the dative case kamoi kam-oy', and accusative case kame kam-eh' and (or also, even, etc.) I, (to) me
παρηκολουθηκοτι verb - perfect active passive - dative singular masculine
parakoloutheo  par-ak-ol-oo-theh'-o: to follow near, i.e. (figuratively) attend (as a result), trace out, conform to -- attain, follow, fully know, have understanding.
ανωθεν adverb
anothen  an'-o-then: from above; by analogy, from the first; by implication, anew -- from above, again, from the beginning (very first), the top.
πασιν adjective - dative plural neuter
pas  pas: apparently a primary word; all, any, every, the whole
ακριβως adverb
akribos  ak-ree-boce': exactly -- circumspectly, diligently, perfect(-ly).
καθεξης adverb
kathexes  kath-ex-ace': thereafter, i.e. consecutively; as a noun (by ellipsis of noun) a subsequent person or time -- after(-ward), by (in) order.
σοι personal pronoun - second person dative singular
soi  soy: to thee -- thee, thine own, thou, thy.
γραψαι verb - aorist active middle or passive deponent
grapho  graf'-o: to grave, especially to write; figuratively, to describe -- describe, write(-ing, -ten).
κρατιστε adjective - vocative singular masculine
kratistos  krat'-is-tos: strongest, i.e. (in dignity) very honorable -- most excellent (noble).
θεοφιλε noun - vocative singular masculine
Theophilos  theh-of'-il-os: friend of God; Theophilus, a Christian -- Theophilus.