An elementary treatise on modern pure geometry (1893)
Lachlan, Robert · London, New York, Macmillan and Co. · leaf 30
considered as affected by sign. (ii) When several triangles have a common vertex A, we shall have {ABC)=iAB.AC.smBAC, where the lengths AB, AC axe to be considered as of invariable sign, but theangle BAC as affected by sign. From these two values for the area of the triangle ABC, we have thetheorem… … Thus let any line cut the lines OA, OB, OC,..., in the points A, B, C,...,and let OiV be drawn perpendicular to the line AB. Then we have, AB. ON=OA . 05.sin AOB, AC. 0N= OA. OC. sin AOC, where the segments AB, AC, &c , of the line AB, and the angles AOB, AOC,..., are aflFected by sign, but the…
Geometry
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