Geometric(al) is here opposed to arithmetic(al). These adjectives refer to how solutions were found in the past before algebraic methods were developed. Geometry was believed to be a more powerful instrument for solving complex problems.
Basically problems linked to sums were solved using arithmetic, and problems linked to products/ratios/exponents were solved by geometry. E.g. it is easy to "see" the product of two numbers by looking at the rectangle area, and the square root extraction was therefore a geometry problem.
Using this opposition, a proportion, a sequence (progression) or a series could be qualified as arithmetical or geometrical.
Other answers already dated the use of the wording, I'm just adding extracts of a book using this conventional split, Arithmetical Institutions. Containing a Compleat System of Arithmetic Natural, Logarithmical, and Algebraical in all Their Branches, by John Kirby in 1735:
Arithmetical vs. geometrical ratios
(Note how ratio was used both for the common difference and the common ratio. This is now different in En. but it persisted in my native language (Fr.): Latin ratus gave ratio but also raison (reason). Raison is the word used to refer to the common difference and common ratio.)
Arithmetical proportion and progression
Geometrical ratio and progression
(Note geometrical ratios are a family including simple, multiplicate, harmonical and contraharmonical. Details are found in the same book.)