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

That Huygens rightly equated two minimum lateral oscillations of the same string to the time of the minimum circuit is abundantly clear from those things which are demonstrated in this little book.

Furthermore, the author of those demonstrations that are presented in the Journal adds the following to the demonstration of Prop. VI: "In this proposition of the Author (namely, Huygens), two conditions are missing: first, that the string must always be perpendicular to the surface of the conoid; second, that the gyration must always be made at a perpendicular height of half the latus rectum; without which nothing is determined." But that this proposition of Huygens is universal and should not be restricted by any conditions is clear from the demonstration which this little book presents, which is deduced generally not from conical motion—which is less simple due to centrifugal force—but from centrifugal force alone, and from the property of a parabolic surface. Furthermore, this very demonstration, which is found in the French Journal, will not conclude correctly unless the string, which is carried around in a conical motion, makes its circuits with the same forces as it would in free air without any parabolic surface; which, surely, could not happen unless the globe suspended from the string adhered perpendicularly to the parabolic surface. The second condition, as is manifest from the nature of the parabola, is contained in the first.

Finally, in the last place, one may see the description of the Planetary Automaton, which, as is clear from the automaton itself, he took care to have made in the year 1682, although we have not even now found its complete description, concerning which, therefore, a few small things must be noted.

The first is that the Author deleted those words on page 438, where he indicates how much the individual planets are to be advanced over twenty years so that they truly correspond to the state of the heavens, and in their place substituted these: "so that in twenty years no error can exist that is even visible." However, after many ages, where it may be necessary, it will be easily corrected by that method which...