A volume entitled Opera posthuma (Leiden, 1703) contained his "Dioptrica," in which the ratio between the respective focal lengths of object-glass and eye-glass is given as the measure of magnifying power, together with the shorter essays De vitris figurandis, De corona et parheliis, &c. An early tract De ratiociniis tin ludo aleae, printed in 16J7 with Schooten's Exercitationes mathematicae, is notable as one of the first formal treatises on the theory of probabilities; nor should his investigations of the properties of the **cissoid**, logarithmic and catenary curves be left unnoticed.

The two treatises on the cycloid and on the **cissoid**, &c., and the Mechanica contain many results which were then new and valuable.

Thus Nicomedes invented the conchoid; Diodes the **cissoid**; Dinostratus studied the quadratrix invented by Hippias; all these curves furnished solutions, as is also the case with the trisectrix, a special form of Pascal's limacon.

The pedal equation with the focus as origin is p 2 =ar; the first positive pedal for the vertex is the **cissoid** and for the focus the directrix.

The Greek geometers invented other curves; in particular, the conchoid, which is the locus of a point such that its distance from a given line, measured along the line drawn through it to a fixed point, is constant; and the **cissoid**, which is the locus of a point such that its distance from a fixed point is always equal to the intercept (on the line through the fixed point) between a circle passing through the fixed point and the tangent to the circle at the point opposite to the fixed point.

**CISSOID** (from the Gr.

The term **cissoid** has been given in modern times to curves generated in similar manner from other figures than the circle, and the form described above is distinguished as the **cissoid** of Diodes.

A **cissoid** angle is the angle included between the concave sides of two intersecting curves; the convex sides include the sistroid angle.

Take a rod LMN bent at right angles at M, such that MN= AB; let the leg LM always pass through a fixed point 0 on AB produced such that OA = CA, where C is the middle point of AB, and cause N to travel along the line perpendicular to AB at C; then the midpoint of MN traces the **cissoid**.