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

This was evident, partly from the inscription affixed to the tables, partly from the fact that the numbers in these tables corresponded exactly to those numbers which he mentions in this treatise as if they were drawn from the tables, and finally, partly from the fact that the remaining numbers corresponded to our own calculation. However, in the demonstration of the table that concerns the posterior sun dogs, we did not wish to use the curve that is created by the collection of refracted rays, although we saw that it could be constructed much more easily through that means; both because the discovery of these curves was published long after this little book was written by the Author, and because we conjectured, not vainly as we think, that the Author had not used it.

In this dissertation on sun dogs, he sets the diameter of the halo, which appears most frequently, at almost 45 degrees everywhere; however, in that French treatise on the halo of the year 1667, which seems to have been written after this dissertation—although published long before it—he mentions the diameter of 44 degrees everywhere, as this magnitude, it is likely, was more approved by him from more accurate observations. Therefore, the calculation in those tables, which we said we found on the slip of paper, also concerned the 44-degree halo diameter, not the 45-degree one. Yet, so that it might not appear that something was lacking in the tables for anyone because of this, we have added a fourth table, which applies to the 45-degree halo. The table could indeed have been extended to any thickness of the snowy nucleus, so that if multiple halos or lateral sun dogs of different distances were to appear, the proportion of the nucleus to the water globe or cylinder could be immediately determined from the table. We had already constructed such a table extended to all varieties of nuclei, but since the Author had primarily looked only to certain nuclei, we neglected to add it to these.