Search Results: geometria indivisibilibus continuorum nova quadam ratione by cavalieri bonaventura

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Bologna: Heirs of Evangelista Dozza, 1653. First edition. Hardcover. THE METHOD OF INDIVISIBLES. Second edition (first, 1635) of Cavalieri's text containing the discovery of the 'method of indivisibles', one of the most important forerunners of the integral calculus. Book II of the work includes the statement of 'Cavalieri's principle' for the determination of areas and volumes, which considers an area as made up of an indefinite number of equidistant parallel line segments ('omnes lineae'), and a solid as made up of an indefinite number of parallel plane areas. It states that, if two planar figures are contained between a pair of parallel lines, and if the lengths of the two segments cut by them from any line parallel to the including lines are always in a given ratio, then the areas of the two planar pieces are also in this ratio (there is an analogous principle for the determination of volumes). Cavalieri's principle provided a simple and effective alternative to the Archimedean method of… Read More