Abstract
Proposition I. In every acute angled plane triangle, the sum of the three tangents of the three angles multiplied by the square of the radius, is equal to the continued product of the tangents. Demonstration .—Let AH, HI, and IB be the arches to represent the given angles; and AG, HK, and BT be their & tangents, put r the radius, AG = a , and BT = b , Then r 2 / a and r 2 / b will be the tangents of HD and DI.
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