Tabulka ekvací Měsíce z latinské encyklopedie Pavla Žídka a její srovnání s Almagestem, Toledskými a Alfonsinskými tabulkami

A table of lunar equations is included together with other astronomical tables in the encyclopedia Liber viginti arcium written around 1460 by the Czech scholar M. Pavel Zidek (Paulerinus). To clarify its relation with previous tables, numerical values of these tables were subjected to mathematical analysis and residual errors with respect to Ptolemy's underlying model were studied. To demonstrate wider contexts, Ptolemy's theory and the method of its use are reviewed through the translation of relevant passages from the Almagest and Cannons to Alfonsine tables by John of Saxony and by the corresponding formulae. It is shown that Ptolemy's approximate method of calculation differs from his precise model of lunar equations for about 1' at maximum (cf. Fig. 2). However, numerical errors in the table in Almagest can cause final errors that are several times higher. While errors in equatio argumenti 0 were decreased in the Toletan and Alfonsine tables, the truncation of data on minuta proportionalis increase the error again. It shows that, contrary to the suggestion by van Brummelen (1994), the errors in the tables prepared by Ptolemy or his followers are not a consequence of an ingenious analysis of the requirements for precision of individual quantities, but rather a result of rounding in the procedure of calculation. It is found that Zidek's tables are an extract from the Alfonsine tables with a significant number of the scribe's mistakes.