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The next fragment that we have dates from 75 - 125 AD and again appears to be notes by someone trying to understand the material of the Elements.
More than one thousand editions of The Elements have been published since it was first printed in 1482. Heath discusses many of the editions and describes the likely changes to the text over the years.
B L van der Waerden assesses the importance of the Elements in:-
Almost from the time of its writing and lasting almost to the present, the Elements has exerted a continuous and major influence on human affairs. It was the primary source of geometric reasoning, theorems, and methods at least until the advent of non-Euclidean geometry in the 19th century. It is sometimes said that, next to the Bible, the "Elements" may be the most translated, published, and studied of all the books produced in the Western world.
Euclid also wrote the following books which have survived: Data (with 94 propositions), which looks at what properties of figures can be deduced when other properties are given; On Divisions which looks at constructions to divide a figure into two parts with areas of given ratio; Optics which is the first Greek work on perspective; and Phaenomena which is an elementary introduction to mathematical astronomy and gives results on the times stars in certain positions will rise and set. Euclid's following books have all been lost: Surface Loci (two books), Porisms (a three book work with, according to Pappus, 171 theorems and 38 lemmas), Conics (four books), Book of Fallacies and Elements of Music. The Book of Fallacies is described by Proclus:-
Since many things seem to conform with the truth and to follow from scientific principles, but lead astray from the principles and deceive the more superficial, [Euclid] has handed down methods for the clear-sighted understanding of these matters also ... The treatise in which he gave this machinery to us is entitled Fallacies, enumerating in order the various kinds, exercising our intelligence in each case by theorems of all sorts, setting the true side by side with the false, and combining the refutation of the error with practical illustration.
Elements of Music is a work which is attributed to Euclid by Proclus. We have two treatises on music which have survived, and have by some authors attributed to Euclid, but it is now thought that they are not the work on music referred to by Proclus.
Euclid may not have been a first class mathematician but the long lasting nature of The Elements must make him the leading mathematics teacher of antiquity or perhaps of all time. As a final personal note let me add that my [EFR] own introduction to mathematics at school in the 1950s was from an edition of part of Euclid's Elements and the work provided a logical basis for mathematics and the concept of proof which seem to be lacking in school mathematics today.
J J O'Connor and E F Robertson
Список литературы
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