The Geometric Mindset is qualitatively different, in that it is inherently relational in nature and makes no assumptions for the initial presence of many "separate things".
In Newton's time, the disciplines of Geometry and Mathematics were deliberately kept separate from one another, as the two were viewed as completely different disciplines.
While algebra focuses on "bringing parts back together", Geometry involves a more active process of cutting and separating to develop the objects or items in the first place.
While modern approaches to mathematics often make the assumption that items are "just there" for the taking, the Geometric Approach makes no such assumptions.
Geometry, especially in its traditional form, makes use of construction, a process where an individual actively participates in the creation of figures and objects.
Geometry can be thought of beginning with a "field of potential" that a limitless quantity of objects and concepts can be sectioned out from.