Sentence examples for infinitesimal quantity from inspiring English sources

Indeed, the very idea of an infinitesimal quantity is paradoxical because the only number that is smaller than every positive number is 0 itself.

Traditionally, an infinitesimal quantity is one which, while not necessarily coinciding with zero, is in some sense smaller than any finite quantity.

The paradoxical idea of infinitesimal quantities preoccupied ancient Greek mathematicians, especially Archimedes, who used the concept to calculate volumes of circles, cylinders, and spheres.

The change could not help those who had lead in their bodies, but it sounded an alarm that even infinitesimal quantities of lead could be dangerous.

Through ingenious transformations he handled problems involving more general algebraic curves, and he applied his analysis of infinitesimal quantities to a variety of other problems, including the calculation of centres of gravity and finding the lengths of curves.

Infinitesimal quantities may be characterized as quotients b/m of a finite quantity b by an infinite quantity m.

The first employed infinitesimal quantities which, while not finite, are at the same time not exactly zero.

Connected with his new conception of the continuum is Peirce's increasingly frequent and sometimes pugnacious defenses of the doctrine of the reality of infinitesimal quantities.

As is well known, the inventors of the calculus relied on appeals to "infinitesimal" quantities, typically backed up by geometric or even mechanical considerations.

If this ratio is known, the infinitesimal quantities forming it may be replaced by any suitable finite magnitudes such as velocities or fluxions having the same ratio.

But traces of the traditional ideas did in fact remain in Cauchy's formulations, as evidenced by his use of such expressions as "variable quantities", "infinitesimal quantities", "approach indefinitely", "as little as one wishes" and the like[28].