Fig. 5.39. Frequency graphs for duplicate cases.

- they all have already appeared in X(Q). It is clear that the best concurrence with the ideal graph in fig. 5.37 will be obtained when these two duplicates are placed next to each other, or simply identified.

Thus, if we discover two graphs resembling the shape of those in fig. 5.39 among the "chapters" of a chronicle numbered correctly in general, these "chapters" are, most likely, duplicates, - that is to say, they describe approximately the same historical events, and should be identified with each other. All of the above is applies to cases with several duplicates -three and more.

This method was also tested on experimental material. As a simple example, we considered an edition of The History of Florence by Machiavelli, 1973 (Leningrad), with detailed commentaries. It is clear that the commentary maybe considered a series of "chapters" duplicating the main text by Machiavelli. The main text was divided into "generation chapters", which made it possible to build a square frequency matrixK{T\, also covering the commentary to History. This matrix assumes the shape conditionally displayed in fig. 5.40, where thick inclined segments consist of squares filled with maxima. It means that our procedure successfully reveals known duplicates, in this case the commentary to the main text of Macchiavelli's History.

Fig. 5.40. An approximated frequency matrix for Machiavelli's History of Florence. One sees duplicates, or repetitions.

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