Why are some shapes named after the amount of sides while others are named after the amount of angles?


I know -angle means… angles (triangle = three angles), and -agon means side (pentagon = 5 sides). But why was it decided that the naming conventions would be different by having some shapes named after the amount of angles and others be named after the amount of sides?


Additional superfluous thoughts:

Since rectangles are not named after the amount of angles (rect- means 90°, which is why all squares are rectangles), are all 4-sided shapes like trapezoids without 90° angles quadragons or quadangles?

EDIT: changed the structure of a sentence

In: 6

The “-agon” also means angles; a pentagon is a 5-angled shape. But the “-gon” term comes from Ancient *Greek*, while the “-angle” thing comes from Ancient *Latin*.

So for some reason when geometry was being done in Latin they used their own word for a triangle (a “tres angulus” thing) but kept the Greek words for more complicated shapes (Latin “pentagonum” from Greek “πέντε γωνος” / “pente gonos”). A Latin 5-angled shape would be a “quinque angulus” or probably something like a quingulus? But it isn’t a word we use.

This is also why we generally use Greek numbers when talking about polygons (poly- being Greek for many, whereas the Latin would be multi-, so a polygon would be a multiangle or multangle?); so heptagon (not septagon, or septangle), although they end up being similar for most numbers. Except not always; a 9-angled shape is a nonagon (using the Latin “non-” for nine, not the Greek “en-“).

The term for a general 4-sided shape is “quadrilateral”, just to make things even more confusing. This is Latin, but this time uses a term to do with sides (“lateralis”), although the term “quadrangle” does exist, it just isn’t generally used in geometry. The Greek for 4 is tessara/τέσσᾰρᾰ or tetra-/τετρα-, and the term “tetragon” can be used for a 4-angled shape (but again, not very often in English geometry). It is also where we get tetrahedron (τετράεδρον); a 4-surface shape (the -εδρον or edron part being related to a seat or place for sitting, coming to mean a face in the geometry sense), and tesseract for a 4-dimensioanl 4-“sided” shape (the -ἀκτίς or -act part being to do with rays or beams, because a tesseract is a cube projected with rays into 4-dimensions).

So a triangle is a 3-angled shape in Latin. A heptagon is a 7-angled shape in Greek. And a quadrilateral is a 4-sided shape in Latin.

There are probably historical reasons for why these terms developed differently, probably to do with who was studying them, when, and how common the terms were. I have no clue what they are, though.