Why is a geometric progression called so? [duplicate]

Just curious about why geometric progression is called so. Is it related to geometry?

Solution 1:

Here's an extremely nice picture illustrating the geometric series and making it geometrically clear how it converges when $x<1$.

Dobbs 1918

$s-1=xs$ follows from $PN/ON=BA/OA$ which follows from the fact that $\triangle OAB$ is similar to $\triangle ONP$.

Solution 2:

Here is a geometric figure illustrating the geometric progression $1,r,r^2,r^3,r^4,r^5,\ldots$:

enter image description here

Solution 3:

Let $ABC$ is a right triangle with right angle $\angle ABC$, then if we draw the height $BH$, we have $$ |BH|^2=|AH||CH| $$ The geometric mean comes from here...

Solution 4:

The arithmetic and geometric adjectives come from the Pythagoreans before the Christian Era. Apparently, the expression “geometric progression” comes from the “geometric mean” (Euclidean notion) of segments of length $a$ and $b$: it is the length of the side $c$ of a square whose area is equal to the area of the rectangle of sides $a$ and $b$. The construction of the geometric mean with ruler and compass is well known for high school students; it involves "multiplication" and not "addition".