360 Foreign Literature and Science. 
_“ The work under consideration contains a description of a 
variety of solids hitherto unnoted, and a number of new 
remarkable properties of those solids that have been long 
known. — In tracing the properties of the platonic bodies, the 
author shows that they naturally divide themselves into two 
series, each consisting of five solids ; and, what is remarka- 
ble, that each individual solid, in one. of the series, is to be | 
found in great abundance among crystals, whereas not a sin- 
gle individual in the other series has ever been found among 
such productions. The first he calls the natural, the other 
the artificial series. These two series bear a strong resem-- 
blance to each other ; inasmuch as the last in each series 
contains all the foregoing in the same series: the angular 
points of the contained solids may be traced out in the sur- 
face of the last solid : and what perhaps is equally remark- 
able is, that the whole of the solids composing the natural 
series are commensurable with each other when the first 
four are contained in the last, and that they are to each oth- 
er as the numbers 1, 3, 4,6 and 8. There is another solid 
whose extremities may be traced out in the surface of the 
ries in pairs, in every possible manner, and 
of their volumes in two tables; he has likewise given the 
ratios of a number of remarkable lines in or upon the solids, 
and has shown how each may be extracted from the others. 
The ratios between the members of the artificial series 
tween the numbers of the artificial series, and likewise be- 
tween their faces and their axes. The whole is illustrated 
SS EY SS OS a a I ee 
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