4 AB, BC, CA, A, B, C the 2 AC x CB: ACq+CBq the three sides. three angles. - A Bq:: R: CʊS, C. If ACq+CBq be greater Let AB+BC+AC=2P.| Let AD be perpendicular to BC. 1. If ABq be less thanACq+CBq. FIG. 16. BC: BA+AC:: BA - AC: BD - DC, and BC the sum of BD, DC is given; therefore each of them is given. (7.) 2. If ABq be greater than ACq+CBq. FIG. 17. BC: BA+AC:: BA-AC: BD+DC; and BC the difference of BD, DC, is given, therefore each of them is given. (7.) And CA CD :: R : CoS, C. (1.) and C being found, A and B are found by case 2 or 3. CONSTRUCTIONS OF THE TRIGONOMETRICAL CANON. A Trigonometrical Canon is a Table, which, beginning Constructions of the Trigonometrical Canon. PROP. I. THEOR. The two sides of any right angled triangle being given, Fig. 28: the other side is also given. For (by 47. 1.) ACq=ABq+BCq, and ACq-BCq =ABq, and interchangeably AСq—ABq = BCq. Whence, by the extraction of the square root, there is given AC=✔ ABq+BCq; and AB=√ ACq—BCq; and BC ACq—ABq. |