acient logic just didnt work that way
in the 1700eds someone sees he cant pay enough workers to do enough useful labour to produce enough goods to stay competitive on the market and so he desings a machine to multiply the useful labor
in the 100ds someone sees a mine doesnt produce enough ore so they showe another 300 prisoners of war inside after cleaning out the dead bodies of the previous work shift
but its not olnly the slave labour thing
the concept that machines can preform useful tasks other than killing other people didnt realy cach on untill the midle ages
the whole concept of machine was wery far from the idea of an motor of any kind
maibe if it prowed to have some aplication in war, possibly a seige weapon, or a machine to be used by the besiged to fight of the attackers
then after that, maybe, the concepts used in said machines could of been aplied to ships, or possibly used to help in lager architectural projects
but as to how it would afect the empire, it wouldnt, at least not before it would start to colapse, then betveen the 300 and 500 tehnologies might dewelop from it to replace the lack of laborers as the urban areas became seriously underpopulated, cities turned into towns clustering around fortifications, and the imperial rural sistem colapsed, and the need for self suficiency arose, and would remain a problem during the rest of the midle ages
it is in the midle ages period especially from 1300 onwards that such tehnology would find realy widespread aplication
thys howewer doesnt necesarily mean the industrial revolution would start earlier, or that it would happen at all
chances are this would butterfly away many crucial social and political factors necesary for the development of capitalist economy and modern industry as we know it