bow: Kasheth, or the bow, was probably the title of the following threnody; so called, in the oriental style, because Saul's death was occasioned by that weapon, and because the bow of Jonathan, out of which "the arrow was shot beyond the lad," (1Sa 20:36), is celebrated in this song.
the book: Jos 10:13
Jasher: or, the upright, So LXX επι βιβλιου τον ευθους; Targum, siphra deooritha, "the book of the law;" the Arabic, "the book of Ashee. This is the book of Samuel." This book was probably a collection of divine odes, written to commemorate remarkable events.