236 Mathematics. — Portrait of Buchanan* 



MATHEMATICS. s 



It is well known to mathematicians, that the doctrine of 

 solid angles was left in a very imperfect state by Euclid, and 

 has scarcely at all been advanced by subsequent geometers 5 

 one of the latest commentators on Euclid, Professor PI ay fair, 

 having remarked that " we have no way of expounding, 

 " even in the simplest cases, the ratio which one of them 

 "bears to another. " Dr. Gregory, of the Royal Military 

 Academy, has recently invented a theory of solid angles, 

 which is at once simple', satisfactory, and universal in its 

 application. By means of this theory, the relative mag- 

 niludes of solid angles may be ascertained, not only when 

 they are of the same class, — as those formed by the meeting 

 of three planes, those by the meeting of four planes, the 

 angles at the vertices of cones, &c. : but angles of one 

 class may be compared with those of another, with respect 

 to magnitude; and their mutual relations determined, by 

 processes as obvious and elementary as the usual operations 

 in Plane Trigonometry. He finds, for example, that the 

 solid angles of the regular tetraedron, octaedron, hexae- 

 dron, and of the right-angled cone, are denoted by the 

 numbers 87*7361 1," 216*35185, 250, and 292*89322, re» 

 jpectively ; the maximum limit of solid angles being ex- 

 pressed by 1000, 



Having been favoured with a most exquisite original por- 

 trait of Buchanan, by Titian, we have procured it to be 

 engraved by Woolnoth in his best manner, as one of the 

 embellishments of the present Number. Such of our readers 

 as wish to possess proofs (of which a few have been worked 

 oiT) of this admirable likeness may obtain them from the 

 Publishers of the Magazine, at five shillings each. 



Xotice respecting the Preface to the 4th Edition of the 

 Encyclopaedia Britannica . 

 In writing the preface to the Encyclopaedia Britannica, 

 some mistakes having occurred, relative to the writers en- 

 gaged in the publication, the conductors of that work beg 

 leave to assure their subscribers and the public, that they 

 are v* holly unintentional ; as it never could be their design 

 to detract, in any way, from the merits of the authors 

 whom they employed. They understand, in particular, 

 from Dr. Kirby, that the article Physiology , attributed by 

 mistake to another gentleman, was written by him ; and 

 that the following articles, viz. Farriery, Geography, 



Geology) 



