WOLFRAM|DEMONSTRATIONS PROJECT

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.