Zero
The Romans didn't have the Zero, which in turn means no calculus, which in turn means no steam engines (aside from Zeno and his demonstrator). As for the value of steam engines, consider mechanization of agriculture (though I do like the notion of improved horse collars, etc.) which would have left the Roman smallholders viable for far longer, which would have had the effect of prolonging the survival of the Republic. Steam engines also would make mining far easier (pumping water out of wells), and enabled transporation of grain across the Med far more easily than was the case in OTL. We might also remember that the Romans built superb roads and aqueducts, both of which would have benefitted from the use of steam technology (railroads and pumping stations).
My point is: get the zero, get calculus, and get steam engineering...
The Romans didn't have the Zero, which in turn means no calculus, which in turn means no steam engines (aside from Zeno and his demonstrator). As for the value of steam engines, consider mechanization of agriculture (though I do like the notion of improved horse collars, etc.) which would have left the Roman smallholders viable for far longer, which would have had the effect of prolonging the survival of the Republic. Steam engines also would make mining far easier (pumping water out of wells), and enabled transporation of grain across the Med far more easily than was the case in OTL. We might also remember that the Romans built superb roads and aqueducts, both of which would have benefitted from the use of steam technology (railroads and pumping stations).
My point is: get the zero, get calculus, and get steam engineering...