15 4 Theory of Crjjlaififaiton. 



account of its extreme minutenefs, appears to be only a point, 

 but by the range of cubes M N S T (jig. 14, Plate VI.-) 

 which, fuppofing thefc cubes to be almoft infinitely fniall, 

 will prefent the appearance of a fimple ridge. By a necef- 

 fary confequence the pyramid will have for faces two trape- 

 ziums, fuch as D M N C, refill ting from the firft decrement; 

 and two ifofceles triangles, fuch as C N C, which will be- 

 produced by the fecond decrement*. 



Let us fuppofe, moreover, that, in regard to the laminae of 

 fuperpofition which arife on the face BCGH (Jig. 7, 

 Plate II), the decrements follow the fame laws, but by crofd 

 directions; fo that the more rapid of the two may take place 

 in proceeding from B C or G H towards the fummit of the 

 pyramid, and the flower in proceeding from C G or B H 

 towards the fame fummit. The pyramid refulting from 

 thefe decrements will be placed in a direction oppofite to 

 that refting on A B C D, and will have the pofition exhi- 

 bited fig. 17, where it is feen that the edge K L, which ter- 

 minates the pyramid, inftcad of being parallel to C D like 

 the edge M N (Jig. 14 and 15), is, on the contrary, parallel 

 to B C. We fhall then conceive what ought to be done in 

 order that the pyramid which will reft on D C G F (Jig. 7) 

 may be turned as reprefented jig. 16, and may have its ter- 

 minating edge P L\ parallel to C G (Jig. 7). I fhall fay no- 

 thing of the pyramids that will reft on the three other faces 

 of the cube, becaufe it is evident that each of thefe pyra- 

 mids ought to Hand like that which arifes on the oppofite 

 face. 



But as the decrements which produce the triangle C X P> 

 ( fig. 1 1) make a continuity with thole from which rclults the 

 trapezium C.BKL (Jig. 17), thefe two figures will be in 

 jhe fame plane, and will form a pentagon CNBKL (Jig. 18). 



* Here the face which correfponds to A li C D ( fig. 7.) has 25 (quarts 

 0:1 each fide, as may be fern fig. 14. and the ftructure of the pyramid in 

 queftion may be imitated artificially by obfervipg the order and number of 

 %Uc cubes reprefented, in the fajne figure, 



For 



