Page:Philosophical Transactions - Volume 002.djvu/225

 into another like square of Cells, that all the Numbers of each band, whether to the right or left, upwards or downwards, or diagonally, the Number given being in an Arithmetical Progression, added together, do always make the same Sum, and those in a Geometrical Progression, multiplied into one another, do always make the same Product.

II. , Auth., ''Soc. Jesu.'' Lugduni Gall. in 4°. Ann. 1667.

This Author pretends to have comprised in this Treatise, containing 58 Propositions, besides many Corollaries, all what hath been hitherto discover'd in Opticks, and to have added thereto many curious and useful remarks, not mentioned in other Authors.

He begins with that part which is the most simple, and considers the streight Ray, called by the general name of Opticks; where he shews, what is the cause of those surprizing effects of the Perspective, which so pleadingly deceive the eye; examining there many curious Experiments.

In the second part (the Catoptricks, that have for their Object Rays, reflected) he gives an account of all the Apparences in Looking-Glasses, Convex, Concave, Cylindrical, &c.

In the third (the Dioptricks, that consider Rays refracted) he treats largely of Telescopes of all sorts, Spherical, Elliptical, Hyperbolical' as also of Microscopes, and the effects of all of them: Where, among many other particulars, he delivers and commends, as an invention of Eustachio Divini, the way of furnishing a Telescope, with two Eye-Glasses, outwardly flat, and inwardly convex, so as that they touch one another in the center of their convex Superficies.

In this part he explicates the Doctrine of Refractions and Parallaxes; annexing several particulars concerning Comets, the Ring of Saturn, &c. and concluding all with an Appendix, wherein having refuted the Spiral Hypothesis, devised to support the Ptolemaick System of the World, he advanceth a new one, judged by him very suitable to render an account of the Motion of the Celestial Bodies in the same System that supposeth the Earths immobility, which he seems unwilling to desert.

III. DE VI PERCUSSIONIS, JOH. ALPHONS. BORELLI. Bononiæ in 4°. 1667.

Whereas in the doctrine of Percussion several things are to be accurately distinguish'd, as the Force percussive, the Motion, or the Velocity of the Percussion, and the Resistance of the Body percussed; and then an Estimate to be made of the Proportion of those three to one another. This Author pretends to have both assigned that Difference, and demonstrated the Proportion; adding, that though Galileo saw and acknowledged (vid. at the end of his fourth Dialogue De motu projectorum) That the Force of Percussion was Infinite, or (rather) unlimited, yet he there referr'd discoursing upon that Argument to another opportunity; which not having been performed by him (for ought could be found by any of his Writings, either Printed