This digital reference of Euclid's Elements is assembled from several English translations from over 100 years ago that are now in the public domain. The purpose of this project is to facilitate research and study of the dense information of the 13 books through intelligent navigation, robust taxonomies and comprehensive search.
If a straight line be cut in extreme and mean ratio, the square on the whole and the square on the lesser segment together are triple of the square on the greater segment.
To cut a given finite straight line in extreme and mean ratio.
To cut a given straight line so that the rectangle contained by the whole and one of the segments is equal to the square on the remaining segment.
A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the less.
Euclid is the first major reference on what we commonly call the golden ratio today.
Howver, he referred to it as the "extreme and mean ratio"
Key references are in the featured panel on this page.
Recast Euclid's Elements into a state-of-the-art framework
This digital reference of Euclid's Elements is assembled from several English translations from over 100 years ago that are now in the public domain. The purpose of this project is to facilitate research and study of the dense information of the 13 books through intelligent navigation, robust taxonomies and comprehensive search.
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