Vega's 1794 Table of Common Logarithms

This Demonstration shows a reconstruction of Vega's tables of common logarithms calculated to 10 decimals for the numbers from 10000 to 1001000. He observed that many logarithm mantissas of adjacent numbers have the same first three decimals, and that their differences have the same decimals at positions 7, 6, and sometimes 5 as well. Each page consists of 60 lines and each line has the logarithms of five consecutive numbers, but the first three decimals are only shown once, and the same is true for the common digits of differences. A page of de Decker–Vlacq's 1628 tables, which Vega used, consisted of 150 logarithms. So Vega halved the number of pages of these tables.

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DETAILS

Vega [1] used de Decker–Vlacq's tables and removed many, but not all, mistakes from them [2]. Babbage used Vega's tables for checking printer proofs of his 1827 tables [3, p. 29].
References
[1] J. B. Vega, Thesaurus Logarithmorum Completus (logaritmisch-trigonometrischer Tafeln), Leipzig, 1794, p. 633.
[2] D. Roegel. "A Reconstruction of de Decker-Vlacq’s Tables in the Arithmetica logarithmica (1628)." (Jan 16, 2014) locomat.loria.fr/vlacq1628/vlacq1628doc.pdf.
[3] D. Roegel. "A Reconstruction of Charles Babbage’s Table of Logarithms (1827)." (Jan 16, 2014) locomat.loria.fr/babbage1827/babbage1827doc.pdf.
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