The "reasons" behind the history of the calculus are many.
But a possible source of the "project" of
founding mathematics on number concepts rather than geometrical ones
may be searched in the development of algebraic symbolism and tools in the 16th and 17th Centuries.
As an example, consider Leibniz's own words in his Historia et origo calculi differentialis (ca.1714), translated into:
it certainly never entered the mind of anyone else before Leibniz [the memoir is written by Leibniz in third person] to institute the notation peculiar to the new calculus by which the imagination is freed from a perpetual reference to diagrams [emphasis added], as was made by Vieta and Descartes in their ordinary or Apollonian geometry [i.e. conic sections]; moreover, the more advanced parts pertaining to Archimedean geometry, and to lines which were called "mechanical" [i.e. transcendent curves] by Descartes, were excluded by the latter in his calculus.
But now by the calculus of Leibniz the whole of geometry is subjected to analytical computation [emphasis added], and those transcendent lines that Descartes called mechanical are also reduced to equations chosen to suit them, by considering the differences $dx, ddx$, etc., and the sums that are the inverses of these differences, as functions of the $x$'s; and this, by merely introducing the calculus, whereas before this no other functions were admissible but [...] powers and roots.
Consider Euclid's Elements (c.300 BC): Book V deals with magnitudes:
Prop.V.1: If any number of magnitudes are each the same multiple of the same number of other magnitudes, then the sum is that multiple of the sum.
The proposition is illustrated with segments.
In 1638 Galileo Galilei, in the Discorsi e Dimostrazioni Matematiche Intorno a Due Nuove Scienze, still illustrates his theorems on motion with ratio between segments.
Then we have the invention of the calculus and the language began to change.
The first calculus textbook from Guillaume de l'Hôpital:
Definition I. Those quantities [quantités] are called variable which increase or decrease continually, as opposed to constant quantities that remain the same while others change.
With Leonhard Euler:
Caput I: De Functionibus in Genere. Quantitas constans est quantitas determinata, perpetuo eumdem valorem servans.
Ejusmodi quantitates sunt numeri cujusvis generis [emphasis added], quippe qui eumdem, quem semel obtinuerunt, valorem constanter conservant [...].
Finally we may consider Augustin-Louis Cauchy's Cours d'Analyse (1821), Preliminaries:
First of all, we will indicate what idea will be appropriate to attach to the two words number and quantity. We always take the meaning of numbers in the sense that is used in arithmetic, where numbers arise from the absolute measure of magnitudes, and we will only apply the term quantities to real positive or negative quantities, that is to say to numbers preceded by the signs $+$ or $−$. Furthermore, we regard these quantities as intended to express increase and decrease, so that a given magnitude will simply be represented by a number if we only mean to compare it to another magnitude of the same type taken as a unit, and by the same number preceded by the sign $+$ or the sign $−$, if we consider it as being capable of increasing or decreasing a given magnitude of the same kind.
Conclusion: whith the development of the main new branch of mathematics: analysis, the concepts of number and function, rather than geometrical concepts, became the fundamental ones.