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

A geometric diagram showing a lens (arc AC) with light rays converging from point B through the lens to points P, Q, E, and L. Points N, H, C, K are marked along the axis.

...E B or EC as 69 to 44. Of such parts, therefore, NC is 24, CD will be 44, and of the parts that NC is 25, CE will also be 44. Therefore, the line CD will be to CE as 25 to 24, and thus DE will be 1/50 of CD, and FG of AB. But if we consider that the greatest concentration of rays is by far at PRQ, and not at FDG, it will simultaneously become clear that the focus of the lens is at PRQ, such that RE is 1/50 of RC or RH, and PR is 1/50 of BH, just as the angle RBP is 1/50 of the angle BRH. This is the very thing the Author intends.

Nor can we refrain from noting on this occasion that the illustrious Newton communicated to us that he had learned more accurately through recent experiments that PQ is 1/50 of AB, and RE is approximately 1/25 of EH. By this, the angle of aberration becomes slightly smaller, which in a microscope will not be greater than 15' 36" (whereas by Prop. 63 of the Dioptrics it is found to be 17' 12"), nor in a telescope greater than 28' 24" (whereas in the same Prop. it is found to be 31' 20"). Hence it is evident that if the former, larger value does not cause harm in telescopes or microscopes, this smaller one will not cause harm either. It is also easily clear that if we wish to follow this more accurate ratio of aberration, in the rule which he provides in the final Proposition of the Dioptrics, 55 should be put in place of 50.

We have added the figures pertaining to the Dioptrics, engraved on wood, to the Text itself; for some of them were already completed by the Author...