( 280 ') 



14. In "Tabelle I" with the inscription "Coordinatenstellung des 

 /f" 00 " wc find, if under "C, Zweite Querlinie" the c, corresponds 

 to the chosen axis OF Q , thai the vertices 



— 6, 7, — 11, —12, 17, -18, 19, 20, 33, -34, 35, 36 



have 1 -J- e for value of z 1 and project themselves therefore in h 

 - compare plate IV 6 of the second memoir. From "Tabelle II" with 

 the inscription "Kanten des ^ 60U " we then deduce that (7,33) is 

 an edge of C 800 , that 14, 22, 25, 29, 51 are the live vertices adjacent 

 to this edge (7,33) and these points form a regular pentagon I\ l\l\l\ l\ 

 in the order of succession 14, 22, 51, 29, 25 and therefore a regular 

 starpentagon 1\I\I\PJ\ in the order 14, 51, 25, 22, 29. Turning 

 back to the column z, of "Tabelle I" we find at last that these 

 vertices 14, 51, 25, 22, 29 admit successively for z, the values 



1-0,4,3 + e, — 2,2(2 + ö), 



from which ensues that they project themselves - - compare again 

 plate \\ b of the second memoir — in k' , //,ƒ,/' , c. This result is 

 indicated in tig. 9. While the segments of the horizontal lines ap- 

 pearing there from right to left are indicated as to their relative 

 length by 



d, s, d, d, s, d, s, d, d, s, 



we lind, if we indicate by >S the point on any side of the star- 

 pentagon projecting itself in h, 



s 1 1\S d -f s I 



— - (7 — 3«), - - = — = — (5 — e) , 



'Sd t 2s 2 K ' r,J>, 4</ + 3* 10 v 



1 1\S 3d + a 1 



L\l\ ~ 2 J\ l\ ~ Qd -J- 3s " 6 ( ° " 



These results are in accordance with what has been found before ; 

 moreover they indicate quite definitely the place of each point of 

 division T ). 



15. If we apply the new method to the case of a trace as e t 

 parallel to one of the sides of the starpentagon, then the point ,S 

 projecting itself in e on plate IV' will have to divide the side 

 l\l\ externally into the ratio unity and this requires, as ,S does not 

 lie at infinity, that the edge l\l\ projects itself on OF c as ;i point. 



l ) As the second method gives something more in one respect than the first, 

 it might seem superfluous to communicate the first. We are not of' this opinion. 

 For the first method lias this advantage above the second that it leads imme- 

 diately to a construction of the polygon situated in the diagonal plane as the 

 section of a definite icosahedron by a definite plane. 



