Henry Briggs

Exercises

1. Use the prosthaphaeretic rule cos a cos b = [cos(a + b) + cos(a-b)]/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.
2. 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.
3. 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.
4. Use logarithms to perform the following exponentiations: (a) 2²⁰; (b) 1.06¹⁰.  Use eight place accuracy in recording the values of the logarithms (from your calculator) and determine the accuracy of the power calculated.
5. 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.
6. 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.
7. 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.