For the purpose of this problem, the usual method begins, as we said, simply by representing as infinitely small certain parts of the object, in the form of derived functions determinable by differentiation from the originally given equation of the object in general (like the infinitely small absciss and ordinates in the rectification of a curve); from these parts it then takes those which can in some way be linked by elementary mathematics with the matter of the problem, likewise represented as infinitely small (in our example, the arc), and by virtue of this connection, once these parts are known, that part is also determined of which the problem was to find the magnitude.