To draw the longbow. To exaggerate. The force of an arrow in the longbow depends on the strength of the arm that draws it, so the force of a statement depends on the force of the speaker's imagination. The longbow was the favourite weapon of the English from the reign of Edward II. till it was superseded by fire-arms. The “long-bow” was the hand-bow, as distinguished from the crossbow or bow fitted on a stock.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894