From OE 'forþ' (forward), from PIE *per- — the positive degree of the series forth / further / first.
Out from a starting point and forward or into view; onward in time or space.
From Old English 'forþ' (forward, onward, out, ahead, into view), from Proto-Germanic *furþa- (forward, further ahead), from PIE *pr̥-to- or *pro-to-, a suffixed form of the directional root *per- (forward, through, before, in front of, first). The PIE root *per- is one of the fundamental spatial and temporal roots in the reconstructed proto-language, encoding the concept of forward motion, passage through, priority, and being in front. It underlies an extraordinary range of English vocabulary: 'for,' 'fore,' 'from,' 'far,' 'first,' the prefix 'fore-' (forearm, foresee, forehead), the prefix 'pre-' (from Latin 'prae-' via the same root), the prefix 'pro-' (from Greek and Latin), 'forward,' 'forth,' and 'further' are all traceable to this ancestral directional concept. Old English 'forþ' was used as an adverb of motion
The phrase 'and so forth' (meaning 'and so on, continuing forward') and 'back and forth' (meaning forward and backward) both preserve 'forth' in its pure Old English sense of 'forward.' The word 'forthright' (direct, straightforward) literally means 'going forth rightly' — moving forward in a straight line.