John,speaking Very generally,i think one may say that the Cross-cut saw is about as old as an axe,going back to stone tools.
Many ancient cultures would make tools by inserting microblades into the wood or bone matrix,and the saw was simply an engraver with few blades in a series,vs a single blade.
The saw,in principle, works in a similar manner as an axe,by each blade undercutting the grain at somewhat of an angle,just as you would when chopping across a log.
Saw teeth are smaller,and the cut more conservative of material due to that.
I think that the felling notch and the back-cut in felling are representative of the action of these two tools,with the notch being open much wider due to the size of the cutter used.
But they both accomplish the same thing-sever the fibers across their direction.
However,that all applies to cross-cuts only.
In Hewing,working down a timber Along it's grain,the saw is not so useful-saws work in a straight line(since cutters alternate,doing equal undercutting on each side),and the grain of wood is rarely,if ever,straight.
Also,cleaving the fibers that are only held together by lignin is not only much easier,but also prevents the damage to the many surface ones,preserving the structural integrity of the desired piece(which can then save on weigh,bulk,et c.).
In hewing work the axe would have so much more Natural tendency to follow close to the grain direction.
Thus the very sensible manner that Ernest follows-the initially cleft,riven,pieces are further refined by an axe,conforming them more to the more convenient to us shape(flat/straight to whatever degree),without sacrificing their essential linear fiber integrity.
I think one way of looking at the axe/saw equation is the degree to which people wanted to conform the reality to their Hypothetical,abstract,mental imaging.
The way we see,and think,is in part abstract and theoretical-like sighting down a straight line,imagining a straight,level plane,and so on-a planar geometry type deal.
It doesn't really exist in nature,or is met with very rarely,but it represents the Motion,the Movement,the direction if you will.
So as the greater technological capabilities developed,people tended to use them to bring to life their vision of these theoretical constructs.
Making the walls,the corners of the house,the many other surfaces and features perfectly flat,straight,square...And saw,traveling in a straight line as it tends to,helped with that,coming into greater and greater use.
(naturally it was quite a bit more complicated;people built Bigger,Taller structures as well,and the Vertical and the Straight were coming into their own as important physics of piling suff up unimaginably high,and so on).
But saws are indeed very old,and are also a fascinating and very complex tool.There's some stuff on the net about that,recently i've seen a wonderful video about traditional Japanese saw-making.It was an incredibly complex,intricate process-it isn't easy to forge a large and very thin plane,that is very smooth and even.
The saws are also "tensioned" in an intricate manner-speaking crudely,they're peened around their circumference expanding it-which stretches the middle,putting it in tension,like the middle of a trampoline-which gives the saw that ability to spring back to straight when flexed...
To make saws flat and even the metal scraping,planing,had to be perfected,a particular class of hand tools of their own...Chisels and neat jigs to cut the teeth evenly,files to sharpen them...Many such neat and complex details associated with saw-making,every bit as complex as axes...Just a bit different in aim
