• Journal for History of Mathematics
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• v.24 no.2
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• pp.17-30
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• 2011

This study inquires into the change between two method of indivisibles, which Cavalier suggested. To cope with the objection of use of indivisibles, he modified his first method of indivisibles. Through the analysis of this transition, this study reveals the feature that Cavalier changed into reflecting the density of the figures so as to avoid the paradox related to the indivisibles and this change has the aspect of incomplete lemma-incorporation method according to Lakatos' theory.

• Journal for History of Mathematics
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• v.23 no.4
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• pp.47-58
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• 2010

This study suggests new interpretation about ancient mathematician Archimedes' 'method'. For this, we examined the core issue related to the interpretation of the 'method' and identified the unclear relation between the principle of the lever and the indivisibles, both of which have consisted of the main point of arguments. And by having conducted the exploratory historical guesswork about Archimedes' careful use of indivisibles, we make a hypothesis that the role of the principle of the lever in Archimedes' 'method' should be the control of ratio of change.

• Journal for History of Mathematics
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• v.18 no.3
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• pp.67-78
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• 2005

In this paper we deals with Leibniz's definition of infinite and infinitely small quantities, infinite quantities and theory of quantified indivisibles in comparison with Galileo's concept of indivisibles. Leibniz developed 'method of indivisible' in order to introduce the integrability of continuous functions. also we deals with this demonstration, with Leibniz's rules of arithmetic of infinitely small and infinite quantities.

• Journal of the Korean School Mathematics Society
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• v.11 no.1
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• pp.19-30
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• 2008

Cavalieri is chiefly remembered for his work on the problem "indivisibles." Building on the work of Archimedes, he investigated the method of construction by which areas and volumes of curved figures could be found. Cavalieri regarded an area as made up of an indefinite number of parallel line segments and a volume of an indefinite number of parallel plane areas. He called these elements the indivisibles of area and volume. Cavalieri developed a method of the indivisibles which he used to determine areas and volumes. We call this Cavalieri's principle which states that there exists a plane such that any plane parallel to it intersects equal areas In both objects, then the volumes of the two objects are equal. Cavalieri's principle and method of the indivisibles are very important to understand of volume of a pyramid for gifted students.