On Divisions

work by Euclid

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July 1, 2026

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Euclid's work, On Divisions, deals with problems of dividing a given figure into specific ratios using straight lines. This treatise, restored from Arabic and Latin versions, focuses on geometric divisions and their applications. It is part of Euclid's broader contributions to mathematics, which include the foundational Elements, a comprehensive work on geometry and number theory. The Elements introduced rigorous deductive reasoning and is renowned for its axiomatic approach, establishing principles that influenced mathematics for over two millennia. The Euclidean algorithm, for instance, described in the Elements, is an efficient procedure for finding the greatest common divisor of two numbers.12345

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Euclid
Other writings
On Divisions (of figures)—restored and edited in 1915 from extant Arabic and Latin versions—deals with problems of dividing a given figure by one or more straight lines into various ratios to one another or to other given areas.
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On Divisions (of figures)—restored and edited in 1915 from extant Arabic and Latin versions—deals with problems of dividing a given figure by one or more straight lines into various ratios to one another or to other given areas.
Read More