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Geometrical Studies

Published online by Cambridge University Press:  23 June 2015

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The fragmentary nature of GS makes it difficult to read as it stands, and for this reason, I have rearranged the material slightly so that it falls into four primary, reasonably coherent, parts. Their titles are: ‘The nature of mathematical objects’, ‘Thirteen propositions of Euclid 1’, ‘The philosophy of parallel lines’ and ‘On the algebra of geometrical figures’. GS actually starts with ‘Thirteen propositions of Euclid 1’. The justification for the reversal of order in the translation is to have Hegel's philosophical basis for geometry available first, to provide a context for his detailed discussion of geometrical propositions. The reader can easily reconstruct the original order of GS as follows. Interchange the first and second parts and also the third and fourth parts. Next, move the passages marked a …. a', b …. b',c …. c' to the places in the text marked a-a', b-b' and c-c'. For the reader wishing to locate the original German passages in Dok., the page and paragraph for each of these passages are given at the start of that passage.

In addition, subtitles for sections in these parts have been added which do not appear in the original. They are included in the translation to help orient the reader. I have inserted in some places words not in the original in order to clarify the meaning of the text. These insertions as well as my comments on the text are also enclosed within square brackets. Further clarifications can be found in the appended endnotes.

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Copyright © The Hegel Society of Great Britain 2008

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References

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Euclid, (1781), Euklids Elemente, funf-zehn Büecher. Lorenz, J. F. tr., Halle: Oswald Seidensticker.Google Scholar
Euclid, (1956) The thirteen books of Euclid's Elements, Vol. 1, trans. Heath, T. L., Dover Publications, New York.Google Scholar
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