TOS episode- Crew meets immortal from Earth's past

Question

In this episode, Kirk and an away team go to another planet they find uninhabited except for a millennia-old man who claims to have been various figures in Earth's history, including Alexander the Great (and possibly Julius Caesar, I'm not sure).

Answer 1

This is Requiem for Methuselah.

Here's Memory Alpha's brief synopsis of the episode:

While the Enterprise searches for the rare cure to a deadly disease, the landing party is confronted by a reclusive man who is willing to kill to preserve his privacy.

And here's the actual dialogue from the relevant scene:

MCCOY: Physically human but not human. These are earlier versions of Rayna, Jim. She's an android.

FLINT: Created here by my hand. Here, the centuries of loneliness were to end.

SPOCK: Your collection of Leonardo da Vinci masterpieces, Mister Flint, they appear to have been recently painted on contemporary canvas with contemporary materials. And on your piano, a waltz by Johannes Brahms, an unknown work in manuscript, written in modern ink. Yet absolutely authentic, as are your paintings.

FLINT: I am Brahms.

SPOCK: And da Vinci?

FLINT: Yes.

SPOCK: How many other names shall we call you?

FLINT: Solomon, Alexander, Lazarus, Methuselah, Merlin, Abramson. A hundred other names you do not know.

SPOCK: You were born?

FLINT: In that region of earth later called Mesopotamia, in the year 3834 BC, as the millennia are reckoned. I was Akharin, a soldier, a bully and a fool. I fell in battle, pierced to the heart and did not die.

MCCOY: Instant tissue regeneration coupled with some perfect form of biological renewal. You learned that you were immortal and

FLINT: And to conceal it. To live some portion of a life, to pretend to age and then move on before my nature was suspected.

SPOCK: Your wealth and your intellect are the product of centuries of acquisition. You knew the greatest minds in history.

FLINT: Galileo, Socrates, Moses. I have married a hundred times, Captain. Selected, loved, cherished. Caressed a smoothness, inhaled a brief fragrance. Then age, death, the taste of dust. Do you understand?

SPOCK: You wanted a perfect, ultimate woman, as brilliant, as immortal as yourself. Your mate for all time.

FLINT: Designed by my heart. I could not love her more.

_{Star Trek: The Original Series S03E21 "Requiem for Methuselah"}