I did a one-minute research and found that 1st Killing babies or abandoning them was common back then, but was organised by Sparta's government then 2nd they did left them in Mount Taygetus but I couldn't find proof they thew them off, nor that they didn't 3rd Fun Fact: when abandoning them, the parents bound the newborn's legs so that other spartans would know it's disabled and won't adopt him