Page:The Construction of the Wonderful Canon of Logarithms.djvu/95

TRIGONOMETRICAL PRoposiITIONS. 71 Now add the logarithm of the half sum, namely 1819061, Halve the latter and you have the logarithm 568611, to which corresponds the arc 34° 30’, and double this arc is the base required, namely 69°.

''Conversely, given the three sides, to find any angle. The solution of this problem ts given in my work on. Logarithms, Book II. chap. vi. sect. 8, but partly by logarithms and partly by prosthapharesis of arcs.''

It ts to be observed that in the preceding and following problems there ts no need to discriminate between the different cases, since the form and magnitude of the several parts appear in the course of the calculation.

Another direct converse of the preceding problem follows.—

Alve the given base, namely 69°, and you have 34° 30’, the logarithm of which is 568611. Double the latter and you have 1137222; corresponding to this is the arc 18° 42’, which note as the second found.

As before, take for the first found the arc 0° 44’, corresponding to the logarithm 4357140.

The complements of the two arcs are 89° 16’ and 71° 18’; their half sum is 80° 17’, and its logarithm 14449;