Abarim Publications' online Biblical Greek Dictionary
The noun βατος (batos) means thorns or thornbush, which would make it an somewhat rarer equivalent of the more common noun ακανθα (akantha), thorn or prickle. In the Indo-European language basin, anything pointy or prickly would remind of laws and rules, and knowing how to safely navigate those prickly laws is of course what demarcates mankind from animal kind (see our article on Tigris).
In the Odyssey, Odysseus finds his father at work in the vineyard, wearing gloves against the βατος (batos) (Od.24.230). But a more famous βατος (batos) is of course the burning bush from which YHWH addressed Moses (Exodus 3:2-4). Four of the five occurrences of our noun in the New Testament indeed refer to this miraculous bush; see full concordance.
The Hebrew word for the burning bush is סנה (seneh), which corresponds to the name Sinai (סיני, sinay), the mountain where the Law was issued (Exodus 19-20; Acts 7:30). That means that the Hebrew mind employs the same link between law and prickly things as does the European one.
It's formally a mystery where our noun βατος (batos) may have come from, what it originally meant or even what it might have made Greek speakers of the first century think of. Speakers of Hebrew, however, would have remembered that the Lord commonly met Moses in the tabernacle, which would evolve into the temple, so that the burning bush was in fact the embryonic state of that (admittedly as displaced as Adam had been prior to his move to paradise, Israel prior to the move back to Canaan, and the Body of Christ prior to her move into the New Jerusalem).
The Hebrew word for temple is בית (bayit), which could surely pass as the source of our word βατος (batos). This noun בית (bayit), temple or house, is also strikingly similar to the noun בת (bat), daughter, from the noun בן (ben), son, which in turn resembles the verb בנה (bana), to build, and even the noun אבן ('eben), stone (hence the "living stones" as mentioned in 1 Peter 2:5).
Folks familiar with the gospel might additionally remember that Christ was made to wear a crown of thorns, which may have reminded some creative few of the circle of spear-carrying proto-senators called curia that marks the kind of republic in which no single tyrant has all power (see 1 Corinthians 15:24, and our article on κυριος, kurios).
The noun βατος (batos) is identical to the former but is a transliteration of the Hebrew noun בת (bat), a unit of liquid volume, equal to about 40 liters or 9 gallons (1 Kings 7:26, Isaiah 5:10, Ezekiel 45:10). Its similarity to the previous is accidental as it derives from a verb בתת (batat), to cut in two or sever (or in this specific case, to separate a limited volume of liquid from a much greater reservoir). In the New Testament, this word occurs in Luke 16:6 only.
The noun βατραχος (batrachos) means frog, and occurs in the New Testament only in Revelation 16:13. It's a mystery where this word comes from. Some claim it's onomatopoeic, and imitative of a frog's call (a play by Aristophanes features frogs singing βρεκεκεκεξ κοαξ κοαξ, brekekekex koax koax, which to some ears is perhaps somewhat similar to βατραχος, batrachos). Others suggest it might be Semitic and recall the Hebrew word for frog, which is צפרדע (separdea') and obviously doesn't actually resemble our word βατραχος (batrachos).
However, this Hebrew word for frog, צפרדע (separdea'), appears to relate to the verb צפר (sapar), which means to skewer or pierce through and which is also associated with piercing shrieks (of birds mostly, but perhaps also of frogs). Then there is an identical verb צפר (sapar) that means to leap (noun צפיר, sapir, describes a kind of bouncy goat), from which our Hebrew word for frog could be derived.
Since in Hebrew lore dry land represented reason (like language, a communal thing), and water one's formless emotions (always a private thing), frogs were natured with a dubious infidelity to either. Neither fish nor dedicated land dwellers, frogs were considered pests (Exodus 8:1-15), although frogs ate flies, which were even worse pests and carried disease and death (the Hebrew word for fly is זבוב, zebub, hence the name Beelzebub, or Lord of the Flies). This means that frogs were rather pest-control and only showed up when the land was already crawling with flies-slash-demons. Taking the frogs away would not clear up the initial pests but really only make it a great deal worse (Exodus 8:16-32; and see our article on αιμα, haima, blood).
In Egypt, frogs were considered fertility symbols (every year when the Nile flooded they showed up in huge numbers) and a frog-goddess was thought to hasten child birth. Greco-Roman culture too saw frogs as linked to fertility. The famous story by Aesop of Samos, The Frogs Who Desired A King obviously resembled the account of Israel asking YHWH for a king (1 Samuel 8:5-22).
Frogs were not among the kosher animals (Leviticus 11:9-12), so the Israelites wouldn't eat them. But recent excavations in Britain have revealed that humans have been eating frog legs for at least 10,000 years. That, plus the fly-slash-demon eating properties of frogs, brings us to the verb בתר (batar), to cut in two, which is not dissimilar to the verb בתת (batat) we mentioned above, and which is used in the Bible nearly solely to describe how a covenant was established by cutting animals in two. The verb בתר (batar), and the identical noun meaning part of half, occur a total of three times in Genesis 15:10, and twice in Jeremiah 34:18-19. In 2 Samuel 2:29 occurs the unexplained term בתרון (bitron), in association with Abner and company crossing the Jordan. And Song of Solomon 2:17, likewise, speaks of a mysterious בתר (beter).
The Talmud records that the prophet Isaiah was sawed in two by the evil king Manasseh, which appears to be alluded to in Hebrews 11:37. Most European words for frog (frosh, frosk, vors) are thought to stem from an assumed Proto-Indo-European root "preu-", meaning to hop (in Sanskrit provate and in Russian prygat mean to jump), but that's by no means certain. Here at Abarim Publications we've identified a long list of Greco-European words that may very well have stemmed from Semitic roots (the Greek and Latin alphabets are in fact adaptations from the Semitic one, and were probably imported along with some handy terms; see our articles on Aeneas and YHWH), and perhaps the European words for frog actually stem from the Hebrew verb פרס (paras), to divide or spread out (hence too the names Persia and Pharisee; in other words: "frogs" are "Farsis").
The familiar Grimm story of The Frog Prince may not simply be a fancy fantasy but rather based on a merger of the tropes of the Persian Prince and the Wandering Jew (or the "Mercurial", says Yuri Slezkine), and speak of the often obscure talents of immigrant Jews, who, although perpetually vilified, have given the world the alphabet, the weekend, the postal service and thus the internet, modern finance, the republic and science and even Christianity and Islam; all the things that "govern" the world today. It may not be clear to everyone, but indeed, the modern world is entirely Jewish (Zechariah 8:23), and familiar frog-metaphors (in slowly boiling water, in a narrow-visioned well) may be rooted in inexplicably violent pogroms and general anti-Semitism.
Traditionally, the Jews of Europe (and Asia) were Ashkenazi and those of Northern Africa were Sephardi. But the Muslim enclave in Spain had also drawn in Sephardic Jews, and when they began to be expelled in the late 15th century, some went north to Amsterdam and there established a unique Sephardic island in the middle of the Ashkenazi realm. By the 17th century, Holland had become a haven for Sephardic Jews, including Spinoza, and although everybody knew that the word Sephardic came from ספר (sapar), to write records, and not from צפר (sapar), to leap like a frog, the similarity between ספרדי (sephardi), Sephardic and צפרדע (separdea'), frog, would have escaped only the least humorous. Still, humorous or not, the vast influx of wealthy and learned Iberian Jews quickly earned Amsterdam its epithet Jerusalem of the West.
Also in the 17th century, the word kikker, meaning frog, was introduced into Dutch from an unclear source. This noun kikker is incomparable to any other language's word for frog, even the German word for toad, which is Kröte, from the High German Kreta, which clearly resembles the German for Crete, which is also Kreta. The English word "cretin", likewise, comes from Crete, rather similarly to how the word Gypsy derived from Egypt and Jew from Judah (and note that the Hebrew noun יד, yad, means hand, and the verb ידה, yada, to collectively praise or celebrate, whereas the Greek noun χειρ, cheir, also means hand, and the verb χαιρω, chairo, to collectively rejoice; hence our English word "choir"). The Dutch word for toad is pad, which is identical to the Dutch for "path", which may have signified proverbial drifters (or "Mercurials", says Yuri Slezkine). The Bible speaks of People Of The Way, and the Aramaic word for roadman, namely דורך (durek), from דרך (derek), road, became everybody's favorite Slavic word durak, or itinerant miscreant (even dwerg or dwarf; and note the similarity between the familiar word "gnome" and the noun γνωμη (gnome), from the verb γινωσκω (ginosko), to know; also note the link between the Dutch variant kikvors and vorst, meaning king).
Some commentators assume kikker to be onomatopoeic, but frogs, even Dutch ones, don't sound like "kikker", and certainly didn't start doing that suddenly in the 17th century, so as to warrant a whole new Dutch word to describe them. Instead, the Dutch word kik describes a short glottal sound (as in: geen kik geven; a kikker is someone who utters kiks), rather reminiscent of how Ladino or Hebrew would have sounded to Dutch ears. Moreover, the industrious Dutch tended to distinguish between doers and lookers (doeners en kijkers), whereas the mercantile Dutch distinguished between buyers and lookers (hence kijken, kijken, niet kopen). Jews were traditionally academics (kijkers) rather than laborers (doeners). The phrasal verb een kik geven may thus have originated in een kijkje geven/nemen; to have a look.
Despite its many doers and few lookers, the United States of the Netherlands became the modern world's first Republic. It was established in 1579 upon revolt against totalitarian Spain, where all those Sephardic Jews came from and had a bone to pick with. Less than three decades into the new Republic, some British brethren moved to Leiden (a city 30 km south of Amsterdam), saw how it was done, crossed the Atlantic and did it there too (Plakkaat van Verlatinghe became Declaration of Independence). Particularly since Erasmus of Rotterdam (1466- 1536), the common European words for circle, which signifies the Republic, all derive from the Greek word κυκλος (kuklos), circle. The first depiction of the Dutch as frogs is from 1599 (the war against Spain raged from 1568 to 1648).
From the 19th century on, and for continued obscure reasons, Holland became known as Frog Land (in Dutch: kikkerland). Soon after in the New World, Jews began to be called Kikes, which was likewise never properly explained.
Kermit the Frog, in case you were wondering, was named after a sound engineer and colleague of Jim Henson named Kermit Kalman Cohen. The name Kermit may be Gaelic (Kermode, or son of Dermot), but it also rather reminds of כרמית (kermit), little vineyard (after כרם, kerem, vineyard; also see αμπελων, ampelon, vineyard; Isaiah 3:1). The word Muppet relates to "map" via the Latin mappa, cloth, and ultimately from the Hebrew term מפה (mapah), flag or banner, from the verb נפה (napah), to flutter or move to and fro. The Muppet Show is the dysfunctional Republic that is the world ("All the world's a stage...") and Kermit the Frog ("Sweet are the uses of adversity...") is its reluctant director (Isaiah 9:6). Rather poetically, and as an unintentional reflection upon Aesop's wise fable, a modern Dio sang: all you need is love and understanding (rather than some king; long live the republic!). It was a big hit in the Netherlands. The appearance of the sin-eater in Wales and environs has never been properly explained, but perhaps it too was based on the fly-eating frog.
Rabbinical literature tends to interpret the frog as symbol of anti-Semitism (one frog starts to croak and soon many more follow; hence perhaps Pepe the Frog), but the opposite might rather be truer, namely that the frog is a long forgotten symbol for the Jew, or at least the sort of person with the nous to detect a loose fly and eat it too. People who don't appreciate frogs also don't understand how the destruction of the frogs brings about uncontrollable and devasting clouds of flies the next season. Europeans tend to speak of the Holocaust (meaning wholly burnt), but apply it only to the direct victims of the genocide. The Jews, quite contrarily, speak of the Destruction of Europe (the whole of it), understanding that the eradication of the Jewish presence in Europe certainly heralded a complete collapse of sanity in the generations to follow. If Europe is presently collapsing, it is doing so because there aren't enough fly-eaters to stave off mass madness (for more on this particular topic, see our article on Apollyon).
That said, the formation of the noun βατραχος (batrachos) may very well have been helped along by the term בתרך (batrach), meaning your part (of the covenant), from the verb בתר (batar), to cut in two.