Otdfbt

За двумя зайцами погонишься, ни одного не поймаешь.

We have the same proverb, 二兎を追う者は一兎も得ず, which is considered borrowed from somewhere, so I am curious whether we borrowed it from the Russians or whether we and the Russians borrowed it from some other nation.

It also seems odd to suggest that someone could literally chase hares, because hares run much faster than humans do. I cannot imagine a hunter chasing a hare and am curious how this proverb could come into existence.

Searching in Google Books, I found that the earliest instance of using this proverb in Russian books indexed by Google is apparently this one:

И такъ съ Филиппомъ воспослѣдовало тогда по пословицѣ: "Кто погонится вдругъ за двумя зайцами, тотъ ни одного не поймаeтъ" (From a book of 1767 entitled "Самуила Пуфендорфа введенiе въ исторiю знатнѣйшихъ европейскихъ государствъ"; the book is a Russian translation from German.)

The second earliest instance found by me is this one:

Сей простосердечный старикъ, разсуждая такимъ образомъ, погнался въ одно время, какъ говорятъ, за двумя зайцами ... (From a Russian book of 1785 entitled "Родственникъ Магомета, или цѣлительное дурачество"; the book is a Russian translation from French.)

As these books are translations from German and French, it appears that the trace leads to Europe.

Following the trace, I found an old French-German dictionary of 1807 that gives this proverb in French and German:

Il ne faut pas chasser, courir deux lièvres à la sois; qui court deux lièvres n'en prend point; man muß nicht zwei Hasen auf einmal jagen; wer zwei Hasen auf einmal jagt, bekommt gar keinen

Then I decided to check the English literature and found the following sentence in an English book of 1614:

It appeares that he was very much distracted; hunting (as we say) two Hares at once with one Hound.

Another English book of exactly the same year (1614) contains this:

The Hound that followes two Hares, will catch neither.

It now starts making sense: the hound, not the hunter, chases the hares! Apparently, "погонишься за двумя зайцами"
is a figurative comparison to a hound chasing two hares!

I am curious as to where the trace ultimately leads to.

My question is this: What is the ultimate origin (or, in other words, the deepest root) of the Russian proverb about two hares, or what evidence is there about this?

Came into European languages from Greek via Erasmus' Latin translation:

Ὁ δύο πτῶκας διώκων οὐδέτερον καταλαμβάνει

Duos insequens lepores, neutrum capit

(English: By chasing two rabbits, he catches neither; from Adagia 3.3.36).

from Wikipedia:

Adagia (singular adagium) is the title of an annotated collection of Greek and Latin proverbs, compiled during the Renaissance by Dutch humanist Desiderius Erasmus Roterodamus. Erasmus' collection of proverbs is "one of the most monumental ... ever assembled" (Speroni, 1964, p. 1).

The first edition, titled Collectanea Adagiorum, was published in Paris in 1500, in a slim quarto of around eight hundred entries. By 1508, after his stay in Italy, Erasmus had expanded the collection (now called Adagiorum chiliades or "Thousands of proverbs") to over 3,000 items, many accompanied by richly annotated commentaries, some of which were brief essays on political and moral topics. The work continued to expand right up to the author's death in 1536 (to a final total of 4,151 entries), confirming the fruit of Erasmus' vast reading in ancient literature.

Commonplace examples from Adagia

Many of the adages have become commonplace in many European languages, and we owe our use of them to Erasmus.

The Oxford Dictionary of Proverbs, 2014, page 413, has that proverb as If you run after two hares you will catch neither and gives reference to Erasmus' Adages III. ccxxxvii, where the proverb is in Latin, duos insequens lepores, neutrum capit. The proverb is often wrongly attributed to Publilius Syrus, (fl. 85 – 43 BC), like on this page, although the page is otherwise good since it gives the translations of the proverb into many languages, and many of those translations don't mention hares at all.