Maclaurin's object was to found the doctrine of fluxions on geometrical demonstration, and thus to answer all objections to its method as being founded on false reasoning and full of mystery.
By geometrical consideration it can be shown that the angle subtended by p, as seen from F, must be inversely as the square of its distance r.
This, and the inclination of the orbit being given, we have all the geometrical data necessary to compute the coordinates of the planet itself.
The most beautiful portion of the mosque, however, still exists in the prayer chamber of Hakim, where are to be found the earliest examples of the cusped arch and the origin of many of the geometrical patterns in stucco at the Alhambra.
The "axioms" of geometry are the fixed conditions which occur in the hypotheses of the geometrical propositions.