( 718 ) 



Tlie plane OCC' is tlie plane of position of y and a, inlersected 

 bj V in ( U', I>v ft in ()(\ Vv^. 3 is sn|)jK)s('(l to lie in that |)lane 

 of position. We iiave made fartheron iji li,^-. I the angles A'(JB', 

 COD', Col) e(pial to /^AüB = <f, and the direetions of rotation 

 indicated in those planes belong to a donble rotation to the right. 

 Fig. 4 is siijiposed to lie iji th(^ jdane (>l)l)'. ajid the lines OG* and 

 OG' are drawn in it in such a way, that ODC D' G' ^OCFC' F' . 



- D 



Fig. 3. Fig. 4. 



We shall consider the jilane B()(t more closely. Let ns project 

 OB and (Hr both on «, then it is not difiicnlt to see that the 

 exeention of those two operations, each of which is threcdimensional, 

 gives as a resnlt two lines O// and GK, nintnally })erpendicnlar 

 (see tig. 5, su[)[K>sed to lie in «). 



The [>rojecting planes are successively : (JIIF' (lig. 6) and OGA' 



A' 



Fig. 5. Fig. 6, Fig. 7 



We shall directly see that OB and ( ^F' are situated on diffe- 

 rent sides of OH, and OG and OA' on different sides of OK, 

 and that /JtiOB == / KOG, if we suppose ourselves to be successively 

 in the threedimensional spaces, in which the i)rojecting takes place. 



So we «ee that the plane BOG has t\vo mutually perpendicular 

 vectors, making equal angles with a and projecting itself on a 

 according to two ]»er])endicular vectors namely OB and OG, ju-qjecting 

 themselves according to OH and OA: the chai'acleristic of equiangular 

 intersection. 



Let us still examine of which kind that equiangular intersection 

 is ; we shall then perceive that on account of OB being transferred 

 into OG by the equiaiigular double rotation 



