[ 289 ] 



XLVIII. On 7ievo Terms in Geometry. By Mr. M. Smith. 



To the Editor of the Philosophical Magazine and Journal. 

 Sir, 

 T HAVE long thought that one great impediment to the 

 ■*■ study of Solid Geometry consists in the defective state of 

 the present nomenclature adopted in that branch of the science. 

 This ma}' be exemplified in the fact that several of the most sim- 

 ple figures have no names whatever allotted to them, and can 

 therefore only be expressed by a circumlocution ; such for in- 

 stance is the figure of a brick, a box, or an apartment of a house, 

 "which, as the nomenclature now stands, can only be described as 

 a rectangtdar iiarallelopiped. Now as the six planes which 

 bound this figure are all rectangles, I would propose simply 

 to call it a rectagon. Again, as a rectagon all the sides of which 

 are squares is denominated a cube, I propose that where two 

 opposite sides (only) are squares, it should be called a cuboid ; 

 and this may be denominated oblong or oblate, according as 

 the inscribed spheroid is oblong or oblate. 



Anothei- figure much used in Spherics is that which bears the 

 same analogy (though not the same proportion) to the sphere 

 as the quadrant does to the circle, — perhaps the term spJie- 

 rant would well apply : it might be defined the eighth part of 

 a sphere, produced by the intersection of three planes at right 

 angles with each other passing through the centre of the sphere. 



For the convenience of expressing the area of spherical tri- 

 angles, or other portions of a spherical surface, I would pro- 

 pose to divide the curve surface of the spherant into 90, 5400, 

 and 324000 equal parts, to each of which divisions appropri- 

 ate names should be given. The advantage of this would be, 

 that in any spherical triangle the excess of the three angles 

 above 180 degrees would be the measure of the area, merely 

 changing the terms degrees, minutes, and seconds into the 

 new terms. By this arrangement the measure of solid angles 

 might also be expressed with much facility. 



Those geometrical figures which bear the same relation to 

 the sphere as the sector and segment do to the circle, ought 

 also to be furnished with names : the term sphcricon would 

 perhaps aptly designate the former, which is in fact formed by 

 a sphere and a coue; for the hitter, no name at present occurs 

 to me with which I am quite satisfied. 



In Astronomy also some new terms might be advantageously 

 applied, — such as zenilude for zenith distance ; and I would also 

 ])ropose tliat in stating the azimuth of any celestial body, it 

 might be denominated NE., NW,, SE., or 8\V., according to 

 the cardinal points between which it may be situated. Thus 



Vol. 65. No. 324. April 1 825. O o instead 



