Annotations:

Verse. 1. Exhort] Or, desire.
Supplications, prayers] Either these words are synonymous, all signifying the public devotion of the Church in her service and Liturgy; or they may be thus distinguished: by demseis: and meant prayers as we make in our necessities and distresses, to prevent and avoid evils that may befall, or are come upon us, by proseuchas, such prayers wherein we sue for good things at God’s hand, namely spiritual and temporal blessings; by enteuxeis, such prayers wherein we entreat for the good of others.

For all men] That is, all kinds of men, Jew and Gentiles, bond, free, faithful, infidels, friends, enemies, great men and mean ones, public and private; or, as the word is often taken in Scriptures, as Matthew 4:23, pasan noson, all diseases, that is, all sorts of diseases, Luke 11:42, pan lachanon, all manner of herbs.

V. 2. For Kings] He mentions Kings particularly, either because the Kings and Magistrates were then enemies to the Church, and persecutors of the Saints of God, and some might peradventure make scruple whether they ought to pray for such; the Apostle therefore resolves they ought; and yields a double reason for it, the former in this verse, that through God’s blessing upon their Government we may enjoy peace (Jer. 29:7). The latter in the fourth verse, because God excludes no sorts or conditions of men from the means of salvation. Or he names Kings in the first place, because they are highest in dignity, and upon the good use of their power very much depends the safety of the Church and Common-wealth.

authority] Or, eminent place.
honesty] Or, comeliness.

V.4. all men to be saved] By as much as appeared unto us by the will revealed in the Gospel, he excluding none by name, neither nation or condition whatsoever, Matthew 28:19. Mark 16:15. Or all, may be taken, not pro singulus generium, but pro geniribus singulorum. Verse. 1.

V. 5. Between] Gr. of. the man Christ Jesus] The Apostle does not add man to exclude the divine nature from his Mediatorship: for he is God revealed in the flesh, 1 Tim. 3:16. And God has purchased his Church by his blood, which through the eternal Spirit he offered without spot unto God, Heb. 9:14, but to express that nature in which he paid the ransom for us, mentioned in the verse following; and to show that our Mediator being a man, all sorts of men have by faith free access unto him and his offering, Heb. 2:10.

V. 6. a ransom for all] All that do believe in him, Matthew 20:28. John 3:16 and 10:15, Rom. 1:16 and 3:22.
to be testified in due time] Or a testimony. Gr. Tec. For all in due time. The word marturion, is left out in the Greek copy by Tecla, and the sense is full without it, “Who gave himself a ransom for all in due time;” but if retain the word because most copies have it, the meaning is, “That the ransom he paid was a real testimony of his Mediatorship betwixt God and man, whereby he reconciled both.” Or the meaning is, “That though their ransom were paid at one time, yet it is testified to several nations, kairois idois, at several seasons appointed by God for their conversion.

Annotations Upon all the Books of the Old and New Testament: This Second Edition so enlarged, As they make an entire Commentary on the Sacred Scripture: The like never before published in English. Wherein The Text is Explained, Doubts Resolved, Scriptures Paralleled (London: Printed by John Legat, 1651). [Some reformatting; some spelling modernized; italics original; and underlining mine.]

[Notes:  1) My focus here is the comments on verse 4. The surrounding comments are offered for context’s sake. 2) For the most part, I find these various Annotations (e.g., Dutch, Westminster, Poole, Leigh, and Diodati, et al), to be fairly useless. For more often than not, one only sees quaint assertions driven by systematic assumptions, not exegetical. 3) They often list alternative interpretations which effectively render the work unhelpful. 4) They are often self-contradictory. The so-called committee authored Poole’s Annotations is a case in point. 4) They are often barely coherent, as the case above demonstrates. On the one hand, God wants all men to be saved by revealed will, but on the other hand, Christ is the mediator between God and some men, even, as we are to pray for all sorts of men.  Many of these authors were fooled into thinking that the the expression “all sorts of men” somehow properly captures the import of the Pauline expression “all men” and that, somehow, appeals to “all kinds of herbs” somehow legitimizes this step.  6) Lastly, these annotations are offered to show that the unlimited reading of 1 Timothy 2:4 has been a viable reading within Reformed theology.]