motivations of the more common proportions, contained chiefly in the 
firft fix Books of E#c/«// Elements, and without recourfe to E uclid, or any" 
other Geometrical Writer for proof of any thing averted in thofe*n.w E~ 
lements. 
Whereto is added the folution of an Arithmetical Problems, which the 
Author calls Addgiclf Squares, viz. 
A fquare of Cells being given, even or odd, filled With Numbers, either in 
an Arithmetical 'or Geometrical Vngrefjion fo to di/pofe all thofi Numbers 
into another like [quart of Cells, that all the Numbers of each band, whether to 
the right or to the left, upwards or downwards, or diagonally , the Numbers gi- 
ven being in an Arithmetical Vrogreffon, added together , do always make the 
fame Summe,<W thofe in ^Geometrical Vregreffion,nm\t\^X\Qd into one another 
do always make the fame Produd. 
II. SYNOPSIS OPTICA, Autk HONO RATO FA- 
18 R I, See. fefu, Lugduni Gall, in 4 . An. j 66 j. 
This Author pretends to have comprifedin this Treatife, containing 58 
P ropofitions, befides many Corollaries, all what hath been hitherto difeover'd 
in Optickfi and to have added thereto many curious and ufeful remarks not 
mentioned in other Authours. 
He begins with that part, which is themoft fimple, and confiders the 
S freight Ray, call’d by the general name of opticky : where he fhews,what 
is the caufe of thofe furprizing effeds of the P erfpettive, which fo pleafingly 
deceive the eye/examining there many curious Experiments, 
In the fecond part (the Catoptricks, that have for their Objed Rays Re- 
fielded) he gives an Account of all the Apparences in Rooking- glaffes, Con- 
yex,Concave,Cylindrical, &c. 
In the third ( the Dioptric kj, that confider Rays Re fr ailed) he treats large- 
ly of Telefcopes of all forts. Spherical, Elliptical, Hyperbolical as alfo of 
Adicrofcopes, and the effeds of all of them. Whereamongmanyotherpar- 
siculars^ne delivers and commends, -as an invention of E ufiachio Divini, the 
way of furnifhing a 7 alefcope with two Eye-Glafles, outwardly^?/, and in- 
wardly convex, fo as that they touch one another in the center of their con« 
vex fuperficies. 
In this part be explicates the Dodrine of Refradions and Parallaxes * 
annexi ng feveral Particulars concerning Comets , the Ring of $atnrn,&c. and 
concluding all with an Appendix, wherein having refuted the Spiral Hype- 
thefts, devilled, to fupport he Ptolemaic k^ fyfleme of the world, he advanceth 
a new one, judged by him very futable to render an account of the Motion 
Of the Celeftial Bodies vcv the fime fyfteme that fuppofeth the Earths im- 
mobility ,which he feems unwilling to defert. 
III. DEVI PERCUSSIONIS, JOH.ALPHONS. BORELLI. Bonon- 
fiiseiiH. i66y. 
Wboren^ 
