Abstract
In Chapter II. 1 we gave an indirect proof of the non-existence of a common measure for certain pairs of line segments (such as the side and diagonal of a square). In this chapter we shall develop a direct, constructive procedure for finding a common measure of two segments when a common measure exists. In the next chapter we shall complement the discussion of Chapter II. 1 by using this constructive procedure to give a second proof that the side and diagonal of a square do not have a common measure.
... the whole structure has just one cornerstone, namely the algorithm by which one calculates the highest common factor of two whole numbers.
P.G. Lejeune Dirichlet, Number Theory
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© 1982 Springer-Verlag New York Inc.
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Gardiner, A. (1982). Common Measures, Highest Common Factors and the Game of Euclid. In: Infinite Processes. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5654-0_5
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DOI: https://doi.org/10.1007/978-1-4612-5654-0_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-5656-4
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