közelítésével

Közelítésével is a Hungarian instrumental form derived from the noun közelítés, which has several related meanings. The core sense of közelítés is the act of approaching or drawing near, as well as an approximation or method used to represent or solve something. The suffix -ével attaches to the noun to indicate the means, method, or instrument by which an action is performed, equivalent to “by means of the approach” or “with the approach.”

In practice, közelítésével is used to describe the method or approach employed to achieve a result. In mathematics and the natural sciences, közelítés or közelítésével commonly refers to an approximation used to simplify a quantity or function. For example, a calculation may be carried out “a Taylor-sor közelítésével” (with the Taylor-series approximation). In broader discourse, the phrase can denote the general approach taken to address a problem or task, such as solving a problem “közelítésével” through a particular method.

Etymologically, the word combines közelítés (from közel, near) with the nominalizing suffix -ítés, and the instrumental suffix -ével marks the means. This construction is a standard part of Hungarian grammar for expressing how an action is performed or which method is used.

See also: közelítés, Taylor-sor közelítés, közelítéses megközelítés.