Which Greek philosopher invented the Scientific Method?

The modern scientific method is based on observation, and experiment, and the formulation of (economic!) hypotheses, that may later be expanded into theories. Early proponents of the scientific method were $\text{Newton}$, and $\text{Galileo}$, and (much earlier), the Arabic natural philosopher $\text{Ibn al-Haytham}$, who was called $\text{Ptolemaeus Secundus}$ for his works on optics......and who apparently (and rightly) placed much emphasis upon experiment.
$\text{Archimedes}$ of Syracuse was active in the 3rd century BC, however, his reputation as a scientist, as a prodigious mathematician, was apparently not fully developed in antiquity, while his reputation as an inventor was widely recognized in his day (so much so that the Roman general who sacked Syracuse was under orders to ensure his safety - not a good enough precaution in a brutal siege).