Christiani Hugenii Zelemii, dum viveret, toparchae opuscula postuma, quae continent dioptricam. Commentarios de vitris figurandis. Dissertationem de corona & parheliis. Tractatum de motu. De vi centrifuga. Descriptionem automati planetarii

...they collect rays, he thought it necessary to inquire further into how great the aberration would be in each case. Hence, he considers the structure of the eye, and explains how the defects of eyes in the elderly and the nearsighted may be corrected with spectacles. Afterwards, he examines the effects of lenses, namely with what apparent size relative to the true size, and in what orientation objects are represented, whether vision occurs through one lens or several. He then proceeds to Telescopes, consisting of two, three, or four lenses—whether convex or partly convex and partly concave—and he determines the ratio of magnification, the orientation of the objects, and the amplitude of the angle of vision for each. On this occasion, he had simultaneously explained how the defect of aberration due to the figure, which is uncorrectable in telescopes that contain only convex lenses, can nevertheless be removed in those which are composed of a convex and a concave lens; this is achieved by the following artifice.

Given the focal distance of the outer lens, and the ratio according to which we wish the objects to be magnified in diameter (which is as b to c), and given from these also the ratio of the aberration of the extreme ray to the thickness of the lens (which is as f to g), he places the concave lens between the outer lens and its focus, in such a way that the focus of both lenses is the same point, so that the aberration of a ray parallel to the axis coming from the side of the common focus equals the thickness of the lens multiplied by the number bf/cg. If this thickness is called q, the aberration will be bfq/cg. If this is set equal to the value given according to the Rule in Prop. 27 of the Dioptrics, namely 27a²q+24adq+7d²q/622 (in which a designates the semi-diameter of the convex surface, and d the distance of the dispersion point), it will be easy to find the semi-diameter of the convex surface, and once that is known, also the semi-diameter of the concave one, since it is equal to ad/2atd from that same Proposition. Although this discovery at first seemed to have...