A Comparison of Different Line Geometric Representations for Functions of a Comp

Gladys E C Gladys Elizabeth Corson Gibbens

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, . /i2 = 0, ^ ^Q* H3=Y'^Pw-fioWo+2ib2), X4=l, M4=l- By an argument similar to that used in section I, we see that it is not necessary to consider this general situation. Equations (16) should also have been obtained if, in the two perpendicular planes of reference, the x- and u- axes had been taken parallel to the line of intersection of the planes, while the variables from which the congru- ence was constructed were Z=az, This amounts to a transformation of both independent and dependent vari...ables, rotating them through angles corresponding to the angles between the individual real axes, and the line of intersection of their planes. Since our point of view is the study of the totality of all such functional relations, the more special case will sufl5ce. We may assume therefore, without loss of generality, a=ao=i8 = /3o=l 8 Line-Geometric Representations and (16) may be written (17) Xi = -(z+Zo), \2 = jXz-Zo-{-2ibi) X, = 0, X4=l, AH = 2("'+^o+2a2), /X2 = 0, M3=2''^m;~^°"^^^*'^' /ii=l.

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