Jamieson, Fausset and Brown on Jeremiah 36:23

23. three or four leaves--not distinct leaves as in a book, but the consecutive spaces on the long roll in the shape of doors (whence the Hebrew name is derived), into which the writing is divided: as the books of Moses in the synagogue in the present day are written in a long parchment rolled round a stick, the writing divided into columns, like pages.

pen-knife--the writer's knife with which the reed, used as a pen, was mended. "He" refers to the king (Jr 36:22). As often as Jehudi read three or four columns, the king cut asunder the part of the roll read; and so he treated the whole, until all the parts read consecutively were cut and burnt; Jr 36:24, "all these words," implies that the whole volume was read through, not merely the first three or four columns (1Ki 22:8).