For about half a century I have been trying to find the explanation for some words, one of them being congruence as defined in Synthetic Geometry, all over the English language literature. The closest answer I ever came to was a footnote in the book by Veblen and Young on Projective Geometry. However, the explanation was in terms of algebra, and not in terms of Synthetic Geometry.

Math World Wolfram has several web pages about congruence, but no explanation in terms of Synthetic Geometry. So, after some 50 years of searching no success. I very much doubt that I will ever find it.

Some years ago I read that Newton-Leibniz controversy caused that mathematics in Britain was behind mathematics in Continental Europe for about one hundred years. Could Newton-Leibniz controversy be blamed that some words from Synthetic Geometry are non-existent in English language literature? Not likely. In my opinion Newton-Leibniz controversy which has long since been resolved, has nothing to do with some mathematical words not being in English language literature. The reason is probably the fashion which somehow crept into the world of mathematics. It became fashionable to concentrate at different times on different branches of mathematics. Geometry was largely neglected, and branches of geometry such as Descriptive Geometry and Synthetic Geometry were completely ignored.

If there are mathematicians in English speaking countries who would like to find out about the words such as congruence, they would have to go a century back in time to find appropriate literature in Continental Europe. One of the best books is Die Geometrie Der Lage, written in German by Prof Dr Theodor Reye. There were several editions of that book in the 19th century and the beginning of the 20th century. The problem is that it is very difficult to find a copy of this book. Very few are still around. A rare book, definitely an antique book and a collector's item.

On Internet one can see the copy of that book published by Ruempler in Hannover in 1866. The URL is:
http://dz-srv1.sub.uni-goettingen.de/sub/digbib/loader?did=D159088
However, the best edition of that book was published in three volumes in Leipzig in 1909. I do not remember the publisher since I have seen that edition only once, as a student, and that was about half a century ago. All three volumes were in private collection. The University of Zagreb had an old edition from the 19th century, and so did the University of Toronto. 1909 edition is probably not available at German universities since they have put an old edition from the 19th century online. The advantage of the 1909 edition is in the fact that it has greatly expanded content.

In my book on Synthetic Geometry there is no mention of congruence or some other words missing in English language literature. I did not get that far. The original idea was to write some 400 pages. However, when I reached about 200 pages, I realized that no publishing house was interested in publishing my manuscript. So, I stopped writing, xeroxed the manuscript and published it myself in the early 1980s.

By the way, the publishers were right. There were no buyers. The copies are still collecting dust somewhere down in the basement.

Friday,   12 d  03 me  2004 a,   22 h  12 min  44 s   GMT