5 Ratios Expressed as Triangle-measures.

Article 5
Ratios Expressed as Triangle-measures.

The triangle of a sector and its complementary triangle are measured by the two characteristic ratios. For, let the triangle $A_{1} O_{1} P_{1}$ and its complementary triangle $P_{1} O_{1} B_{1}$ be denoted by $T_{1}, T'_{1}$ ; then

\begin{aligned} \frac{T_{1}}{K_{1}} & = \frac{\frac{1}{2} a_{1} y_{1} sin ω_{1}}{\frac{1}{2} a_{1} b_{1} sin ω_{1}} = \frac{y_{1}}{b_{1}}, \\ \frac{T'_{1}}{K_{1}} & = \frac{\frac{1}{2} b_{1} x_{1} sin ω_{1}}{\frac{1}{2} a_{1} b_{1} sin ω_{1}} = \frac{x_{1}}{a_{1}} . \end{aligned}\}

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Article 5Ratios Expressed as Triangle-measures.

Article 5
Ratios Expressed as Triangle-measures.