When studying Euclid's elements we recommend to have a copy of Euler's books and, for the first six books, also a copy of the marvellous version by Oliver Byrne (1847). In this fantastic book, "coloured diagrams and symbols are used instead of letters for the greater ease of learners". If you are a teacher or a student in elementary or secondary school, don't miss this book. In this site we are going to draw a lot of diagrams, many in the style of Byrne, but following our own taste.
Byrne's book can be freely downloaded here:
Byrne's book (web link, pdf)Also, Nicholas Rougeux has developed an awesome web version of Byrne's work. You can find it here:
Rougeux's web version of Byrne's book (web link)The diagrams are generated with a geometry tool written by Predrag Janičić, called GCLC. The website is:
website of GCLC (web link)It is a very powerful tool and with a free license.
The extension of GCLC files is gcl and we usually render each image in PNG format.
If you want the images with arbitrary resolution, just change the .png by .svg in the url and you will find the SVG (vector graphics) version.
In the two mentioned sources you can find excellent proofs, so here we just try to come up with either a (hopefully) intuitive explanation of them or with an alternative proof.