Gauss on Vega's Thesaurus Logarithmorum Completus
Gauss on Vega's Thesaurus Logarithmorum Completus
In [2] Gauss reviewed Vega's Thesaurus Logarithmorum Completus [5]. The trigonometric parts of these tables reproduce Vlacq's tables from 2 to 45 degrees, giving the logarithms of the trigonometric functions at 10-second intervals. From 0 to 2 degrees, the functions were interpolated for every second by Lieutenant Dorfmund under Vega's direction [4, p. 5; 1, p. 7]. Gauss observed that tabular results in the sine column were always equal to the sum of the corresponding tabular results in the cosine and tangent columns. But this relation is not always true for rounded values. He also compared samples of Vega's values with more accurate new computations and estimated that there were 47,746 inaccurate values in the trigonometric part of the Thesaurus. But he only found errors at the 10th decimal place.
In this Demonstration, Vlacq's part of Vega's trigonometric tables are reconstructed. The differences between rounded tan(x) and rounded sin(x) minus rounded cos(x) are also given. Note that instead of f(x)) Vega's (and Vlacq's) tables consist of . In tables, "Dif." means the absolute difference between two consecutive values in the preceding column.
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10+f(x)
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