In the present state of mathematical science, cultivated as it has been, with assiduity, during the two preceding centuries, it can hardly be expected that any considerable improvement remains to be made in Plane Trigonometry, one of its most elementary theories. There is, however, one case in the resolution of oblique-angled triangles, which appears to me to admit of a solution somewhat more simple and convenient than those which are commonly known; it is that in which two sides and the included angle are given to find the third side.