Article 4
Charactersitic Ratios of Sectorial Measures.

Let $A_1{O}_1{P}_1=S_1$, be any sector of a central conic; draw $P_1{M}_1$ ordinate to $O_1{A}_1$, i.e. parallel to the tangent at $A_1$; let $O_1{M}_1=x_1,M_1{P}_1=y_1,O_1{A}_1=a_1$, and the conjugate radius $O_1{B}_1=b_1$; then the ratios $\frac{x_1}{a_1},\frac{y_1}{b_1}$ are called the characteristic ratios of the given sectorial measure $\frac{S_1}{K_1}$. These ratios are constant both in magnitude and sign for all sectors of the same measure and species wherever these may be situated (Art. 3). Hence there exists a functional relation between the sectorial measure and each of its characteristic ratios.