A recent post dealt with many of the English words based on the Latin verb vertere, meaning “turn,” focusing on those that precede the root vert with a prefix, and their various grammatical forms. This follow-up post defines some additional words in the vertere family: those beginning with vert. Those with the variant stem vers rather than vert will be outlined in a subsequent post.
Vertigo originally meant “a spinning or whirling movement” and later came to refer to a form of dizziness in which the sufferer has a sensation suggestive of spinning or whirling. The related adjective is vertiginous, which also applies neutrally to any spinning motion or judgmentally to frequent and unnecessary change.
A vertebra (plural: vertebrae) is a segment of the system of bones that constitute the spine, or backbone, of vertebrates; that last word refers to two classes of animals, the higher and lower vertebrates, possessing a spine of bone or cartilage or a similar process. It also serves as an adjective, as does vertebral—the spinal column is also called the vertebral column—and as an adjective, vertebrate also means “well formed or “well organized,” though this usage is rare. The connection to vertere is of the spine’s hinge-like quality, which allows animals to turn or bend their bodies. An invertebrate is an animal lacking a spine or a similar process.
In Latin, vertex and vortex both mean “whirl,” but in English the terms are distinct: Vertex applies to the top of the head, the highest point (such as a summit), or a point farthest from the base of an object or shape. (It also applies in geometry to the point at which two lines or curves meet.) A vortex, meanwhile, is a literal or figurative whirlpool. The adjective vertical is related and in one sense means “located at the highest point” but usually means “upright” or “lengthwise” and is an antonym of horizontal. In economic and sociological contexts, it can refer, respectively, to the scope of activity in the production of goods or to hierarchy.
So, the word “vertical” is related to “vertere”, and tangentially to “vortex” and “vertex”.
Note that there are lots of vertical vortices in the form or tornadoes, hurricanes, whirlwinds, cyclones, dust devils, and in water running down drains — but in aerodynamics and hydrodynamics, there are lots of horizontal vortices, too, and vortices at any angle following maneuvering aircraft and the tips of helicopter rotors.
In three-dimensional geometry, the word “vertex” is also related to “apex” because all triangles have three vertices, all tetrahedrons have four vertices, and all pyramids have five vertices, but all cones and pyramids also have an apex, which is one of the vertices.
Also, all triangles, cones, and pyramids have apices. The ones for cones and pyramids are unique, and for triangles, just choose one.
For a triangle, choose one side as the base B. Then the apex is the vertex opposite B, and distance between the apex and the base is called h. Then the area of the triangle is A = (1/2)Bh = Bh/2. This is easy to prove in Euclidean geometry.
There is a whole family of related geometrical words that end in “ex” or “ix”. In alphabetical order, we have {apex, centrex, directrix, helix, vertex}, and to these we could add the mathematical words index, matrix, and radix. In computer science, the words index, matrix, and radix are used a lot, too. “What is the index of that element in the matrix?”
The word “Unix” seems to be unrelated, but it was created by folks in the computer business, anyway.
The astronomical word “parallax” might be related, too, especially since it is a geometrical concept.
As for the endings “ex” vs. “ix”, I can just guess that this is a difference involving Greek and Latin roots. We have the same problem with the suffices (suffixes) {ar, er, or} , which come from Greek, Latin, or Anglo-Saxon roots.
It is enough to give you vertigo and make your head spin just like Regan’s in “The Exorcist”.
D.A.W.