Possible Calculation of Logarithms of Cosines in Vlacq's Trigonometria Artificialis

degree

15

minute

0

seconds	exact and rounded	with logarithms to 10 decimals	difference
0	9849437781	9849437781	0
10	9849381358	9849381358	0
20	9849324925	9849324925	0
30	9849268480	9849268480	0
40	9849212025	9849212025	0
50	9849155558	9849155558	0
60	9849099081	9849099080	1

This Demonstration shows that the logarithms of cosines can be calculated using tables of trigonometric functions calculated to 15 decimals (such as the tables of Pitiscus) and tables of logarithms calculated to 10 decimals (such as Vlacq's 1628 tables) with aid of linear interpolation. Eventual errors are only one unit in the last decimal. In the grid, only the fractional part of

10+

log

10

|cos(x)|

is given.