Abstract

Art. 1. The tangential equation of a curve is, as is well known, a relation among the coefficients in the equation of a variable line, which being fulfilled, the line must be a tangent to the curve. Let O be the origin, OX, OY the axes; and let a variable line MN in any of its positions make an intercept ⋎ on OX and an angle ϕ with it; then the equation of the line is x + y cot ϕ - ⋎ = 0, and ⋎ and ϕ , the quantities which determine the position of the line, may be called its coordinates. From this it follows that any relation between ⋎ and ϕ , such as ⋎ = f ( ϕ , .............. (1) will be the tangential equation of a curve which is the envelope of the line.

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