Henry Briggs
Exercises

Use the prosthaphaeretic rule cos
a
cos b = [cos(a + b) + cos(ab)]/2
to multiply these pairs
of numbers: (a) 641 x
520; (b) 80765 x
97803. Use three
decimal place accuracy to record the angles, and six place accuracy in
the cosine values (taken from your calculator). In each case, determine
the accuracy (number of correct significant digits) of the product.

Use logarithms to perform the same
multiplications as in #1 above. Use five place accuracy in recording
the values of the logarithms (from your calculator) and determine the accuracy
of the product calculated.

Use logarithms to perform the following
divisions: (a) 3 ÷ 7; (b) 569 ÷ 144. As in #2,
use five place accuracy in recording the values of the logarithms (from
your calculator) and determine the accuracy of the quotient calculated.

Use logarithms to perform the following
exponentiations: (a) 2^{20}; (b) 1.06^{10}. Use eight
place accuracy in recording the values of the logarithms (from your calculator)
and determine the accuracy of the power calculated.

Use logarithms to perform the following
extractions of roots: (a) the square root of 73; (b) the fifth root of
60. Use eight place accuracy in recording the values of the logarithms
(from your calculator) and determine the accuracy of the power calculated.

Briggs determines the future value
V of the investment of a principal amount P at an interest
rate of r % over a period of t years by the proportion
V/P = [(100 + r)/100]^{t}. In
another example in the Arithmetica Logarithmica, he uses logarithms
to determine the annual rate of interest needed so that a principal P
of 1234£ (in Elizabethan English currency) appreciates to a value
of 2000£ over a full decade. Solve this same problem.

In another interest problem, Briggs
considers (a) what principal must be invested at 6% annually in order to
earn 57 gold pieces of interest each year; and (b) if this same principal
is left to earn interest for 10 years, what will its future value be?
Solve these problems.
Return to the calendar
last modified 11/5/02
Copyright (c) 2000. Daniel E. Otero