The following problem appears in Robert Simson's “Opera Quaedam Reliqua,” pp. 472–504 :

“ Si a duobus punctis datis A, B ad circulum positione datum CDE inflectantur utcumque duae rectae AC, BC circumferentiae rursus in D, E occurrentes; juncta DE vel continebit datum angulum cum recta ad datum punctum vergente ; vel parallela erit rectae positionae datae; vel verget ad datum punctum:” i.e. if from two given points A and B any two straight lines AC, BC are drawn to a circle CDE given in position, and they meet the circumference again in D and E, then the straight line DE (I.) will inake a constant angle with a straight line passing through a fixed point, or (II.) will be parallel to a straight line given in position, or (III.) will pass through a given point. This final form of the result was only arrived at by Simson after he obtained the aid of Matthew Stewart.