In allegorical depictions of geometry, why show the earth as encircled by a snake?

Question

Various early modern allegorical paintings or engravings show a personification of geometry with a globe of the earth with a snake, and sometimes with a frog. Here are some examples:

(Only a detail of each work is shown, with a link to the full image.)

• Frans Floris the Elder (1519–1570), Geometry (1557); also shows a frog with the globe

Full image: https://commons.wikimedia.org/wiki/File:Geometry-by-Frans-Floris-1557.jpg

• Maerten de Vos (1532–1603), Allegory of the Seven Liberal Arts (1590); also shows a frog with the globe, easier to see in this lower-resolution version

Full image: https://commons.wikimedia.org/wiki/File:Marten_de_Vos_Seven_liberal_arts.jpg

• Maerten de Vos (and workshop), Allegory of the Seven Liberal Arts (before 1603)

Full image: https://commons.wikimedia.org/wiki/File:Maerten_de_Vos_(and_workshop)_Allegory_of_the_Seven_Liberal_Arts.jpg

• Engraving by A. Vallée after Maerten de Vos (date unknown); also shows a frog with the globe

Full image: https://wellcomecollection.org/works/gdxqxekg

• Cornelis Schut (1597–1655), engraving representing geometry and military science (date unknown)

Full image: https://wellcomecollection.org/works/rdun94gn

• Laurent de La Hyre (1606–1656), Allegory of Geometry (1649)

Full image: https://commons.wikimedia.org/wiki/File:La-hyre-geometry.jpg

Although half the examples are from Maerten de Vos, he seems not to have started the practice, and it did not end with him.

The reason for showing a globe of the earth is obvious: geometry. But what about the snake? Was it common to depict the earth with a snake to symbolize geometry? If so, does the snake have a specific symbolic meaning?

Secondarily, what about the frog that appears in the painting by Frans Floris and two of those by Maerten de Vos?

The idea of a snake encircling the world brings to mind Jörmungandr (which tended to swamp a lot of searches), but I see no connection between Jörmungandr and geometry. Likewise I can see no connection between other aspects of serpent symbolism and geometry. I imagine the snake is not meant to be Ouroboros, because none of the images show it eating its own tail.

In the Abrahamic religions, serpents can be associated with knowledge (forbidden or not), but there is no snake shown in connection with other forms of mathematical/scientific knowledge such as arithmetic or astronomy in the "seven liberal arts" paintings by de Vos listed above, nor in the separate paintings depicting arithmetic or astronomy by Floris (1, 2) or La Hyre (1, 2). So there appears to be no general connection of snakes with knowledge in these allegories. Also, the celestial globes shown with the personifications of astronomy in the paintings of de Vos and Floris are not shown encircled by snakes, so there appears to be no symbolic connections between the globe and the forbidden fruit.

Similarly, I have found no symbolic connection between frogs and geometry.