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By Pickert G.

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Cavalieri was the first to use such quantities systematically, or to lay down rules for the guidance of the mind in dealing with them. he employed them divisibles," which, is it known is well The manner in which " The Method of Inknown, opened a new as and successful career to geometry. * The study of his method is, indeed, a necessary prerequisite to a knowledge of the rise, the aiature, the difficulties, and the fundamental principles of that analysis. In the method of indivisibles lines are considered composed of points, surfaces as composed of lines, and volumes as composed of surfaces.

And to the cuba- CHAPTER THE METHOD OF III. INDIVISIBLES. KEPLER introduced the consideration of infinitely great and infinitely small quantities into the science of mathematics. Cutting loose from the cautious and humble method of the ancients, which seemed to feel shores of truth, this enterprising and sublime genius boldly launched into the boundless ocean of the infinite. His example was contagious. its way along the Others entered on the same dark and perilous voyage of discovery, and that, too, without chart or compass.

6. follow. Is the definition of a limit, all-imthen, of the one a mere matportant idea of the infinitesimal calculus, ter of convenience, or should it be conformed to the nature of things ? The variables in the calculus are always subjected to certain conditions or laws of change, or changing according to those conditions If either reach their limits or they do not. and in they do reach them, then let this fact be stated laws they in the defi- or rigidly adhered to without wavering in the as be done this vacillation.

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Analytische Geometrie by Pickert G.


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