The beginning and end and middle of times: Scholars are uncertain about the meaning of this line. Good News Translation takes it to be a reference to knowledge necessary for establishing the calendar. This is one of the plausible guesses, and we recommend it. Contemporary English Version is similar with “about the way a calendar is determined.” Translators may also say something like “about the way they determine a calendar [or, the order of days, months, and years].”
The alternations of the solstices and the changes of the seasons: There is no unanimous agreement about the sense of this line either, but it is certainly a reference to astronomy. Vílchez takes the view that one noun refers to the solstices (the two solstices are the first days of summer and winter) and the other (seasons) to the equinoxes (the two equinoxes are the first days of spring and autumn).
Since we have a reasonable idea of the general meaning in this verse, but we are uncertain of the exact meaning of several terms, the translator is well advised to express the general meaning rather than trying to see that every word is somehow represented. We believe that Good News Translation expresses the meaning, as understood by some scholars, fairly clearly: “by the movements of the sun, the changing seasons.”
It is important to understand the structure of Good News Translation for verses 17-19. Verse 17a mentions that God has given Solomon “true understanding of the forces of nature.” Then some of these forces of nature are named in verses 17b-18a: (1) “what the world is made of,” (2) “how the elements behave,” and (3) “how the calendar is determined.” Verses 18b-19 then give four ways the calendar is determined: (1) “the movements of the sun,” (2) “the changing seasons,” (3) “the constellations,” and (4) “the cycles of years.” We are recommending that translators accept this interpretation, but will recommend a rather different model at the end of verse 20.
Quoted with permission from Bullard, Roger A. and Hatton, Howard A. A Handbook on The Wisdom of Solomon. (UBS Helps for Translators). New York: UBS, 2004. For this and other handbooks for translators see here.

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