I was thinking about the Socrates quote "No man has the right to be an amateur in the matter of physical training. It is a shame for a man to grow old without seeing the beauty and strength of which his body is capable"
It made me wonder what specific physical training would somebody like him be doing. As strength is mentioned would something we could recognise as resistance training have been performed and if so what equipment/apparatus would have been involved?
That line gets quoted out of context a lot. It's not really about anything we would recognise as a "workout routine". Xenophon, the author of this piece, is talking about the individual responsibility of Athenian citizens to train for war, since the Athenian state neglected to organise such training. As such, it reflects Xenophon's obsession with the shoddy state of military training outside Sparta, and his belief that any means (including appeals to the vanity of young men) were justified to bring citizens to exercise more. I wrote about the quote in more detail here.
As for the specific exercises Sokrates would recommend, Xenophon makes him speak at length about the benefits of dancing:
"I remarked something else, too,—that no part of his body was idle during the dance, but neck, legs, and hands were all active together. And that is the way a person must dance who intends to increase the suppleness of his body. And for myself," he continued, addressing the Syracusan, "I should be delighted to learn the figures from you."
"What use will you make of them?" the other asked.
"I will dance, by Zeus."
This raised a general laugh; but Sokrates, with a perfectly grave expression on his face, said: "You are laughing at me, are you? Is it because I want to exercise to better my health? Or because I want to take more pleasure in my food and my sleep? Or is it because I am eager for such exercises as these, not like the long-distance runners, who develop their legs at the expense of their shoulders, nor like the prize-fighters, who develop their shoulders but become thin-legged, but rather with a view to giving my body a symmetrical development by exercising it in every part?"
-- Symposion 2.16-17
(Sokrates doesn't want you to skip leg day.)
Plato also recommends dancing as preparation for war, although his advice is more mixed. Like Aristotle, Plato was aware that simply exercising the body was not actually enough; warriors had to familiarise themselves with their weapons. He therefore declares that in his ideal state all combat sports (and their exercise regimes) will be banned. Instead, men and women were to train specifically at horse riding, archery, javelin throwing, and spear fighting in heavy armour. Like Xenophon, Plato (himself a former wrestler) believed that simply bulking up wasn't enough to be useful to the city in times of war. The most easily applied form of training was a balanced form of exercise like dancing, but the best training was the actual practice of carrying and using weapons.