Plato (428–347 BC) was a Classical Greek philosopher, mathematician, student of Socrates, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the Western world.
He wrote a dialogue named Timaeus (Greek: Τίμαιος, Timaios) one of Plato’s dialogues, mostly in the form of a long monologue given by the title character, written circa 360 BC. The work puts forward speculation on the nature of the physical world and human beings. [source]
“For whenever in any three numbers, whether cube or square, there is a mean, which is to the last term what the first term is to it; and again, when the mean is to the first term as the last term is to the mean—then the mean becoming first and last, and the first and last both becoming means, they will all of them of necessity come to be the same, and having become the same with one another will be all one”; thereby he implies the aesthetically perfect proportion known as Golden ratio or Golden mean. (31c – 32a).” [source]
Euclid (323–283 BC) is often referred to as the “father of geometry”, where he wrote the collection of 13 books named “The Elements” and was written in Greek around 300 BC. In “The Elements”, he gave the first recorded definition of the golden ratio, which he called, as translated into English, “extreme and mean ratio”.
Many historians do not believe that Euclid’s Elements represents his original work so there is the question of who studied the golden ratio before Euclid. Proclus, a Greek mathematician who lived several centuries after Euclid, wrote in his commentary of the Elements:
“Euclid, who put together the Elements, collecting many of Eudoxus’ theorems, perfecting many of Theaetetus’, and also bringing to irrefragable demonstration the things which were only somewhat loosely proved by his predecessors”