%0 Journal Article
%T Rogerius Joseph Boscovich / Ru£¿er Josip Bo£¿kovi£¿, De calculo probabilitatum qu£¿ respondent diversis valoribus summ£¿ errorum post plures observationes, quarum singul£¿ possint esse errone£¿ certa quadam quantitate, The editio princeps of Bo£¿kovi£¿¡¯s autograph in the Bancroft Library within the University of California at Berkeley
%A Martinovi£¿
%A Ivica
%J -
%D 2018
%X Sa£¿etak Here published is the editio princeps of Bo£¿kovi£¿¡¯s autograph De calculo probabilitatum qu£¿ respondent diversis valoribus summ£¿ errorum post plures observationes, quarum singul£¿ possint esse errone£¿ certa quadam quantitate, housed in 1962 at the Bancroft Library within the University of California at Berkeley, in the collection Boscovich Papers, call number: Carton 1, Part 1: no. 62, Folder 1:79. The transcription is accompanied by notes and introduction. The latter contains the following: (1) description of the manuscript; (2) outline of the contents of Bo£¿kovi£¿¡¯s writing related to the theory of probability, notably the mathematical problem as formulated by Bo£¿kovi£¿; (3) description of the status of investigation, with regard to the fact that until today Oscar Sheynin, Russian science historian, has been the only scholar to study this manuscript, about which he published three articles in the 1970s. Following in these initial research steps is the investigation primarily aimed at: (4) exact dating of this undated manuscript; (5) establishment of whether the manuscript was completed or not; and, lastly, (6) assessment of its significance within Bo£¿kovi£¿¡¯s work and within the history of science in the eighteenth century. The mathematical problem, introduced in the title of Bo£¿kovi£¿¡¯s manuscript as the ¡°calculus of probabilities which correspond to various values of the sum of errors after several observations,¡± under the condition that single observations can differ from the exact measurement ¡°for a given quantity,¡± Bo£¿kovi£¿ formulated as follows: ¡°If in a certain series of observations equally probable errors 1, 0, £¿1 are presupposed for single observations, we ask the ratio of probability for single sums, which sums can thence be obtained after a given number n of observations. Error sums can take on all the values from n up to £¿n for different combinations. The probabilities for any value will relate as the numbers of combinations, from which the same value is obtained. In order to determine this number for single sums, may the series of these errors be arranged in three lines: I 1, 1, 1, 1, 1, 1, 1, 1 etc. II 0, 0, 0, 0, 0, 0, 0, 0 etc. III £¿1, £¿1, £¿1, £¿1, £¿1, £¿1, £¿1, £¿1 etc. Then we ask the numbers of combinations for single values of the sum of errors from 0, 1, 2 etc. up to n. The numbers [of the combinations] for [the sums of errors] £¿1, £¿2, £¿3 etc. can be easily found; these numbers will be the same as the numbers for [the sum of errors] 1, 2, 3 etc., because once those [with the positive sum of errors] are found, these [with the
%K Ru£¿er Bo£¿kovi£¿
%K theory of errors
%K theory of probability
%K combinatorics
%K discordant observations
%K 18th century mathematics
%K geodesy
%K astronomy
%K geophysics
%U https://hrcak.srce.hr/index.php?show=clanak&id_clanak_jezik=325006