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.