deletions | additions       diff --git a/4-Dimensions.tex b/4-Dimensions.tex  index 84fff4e..43a6991 100644  --- a/4-Dimensions.tex  +++ b/4-Dimensions.tex 
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Which results in a volume, the difference of volumes made by each set of 3 axes.  The Quaternanry Quaternary  will be \begin{equation} \begin{vmatrix}   t_1 & x_1 & y_1 & z_1 \\ 
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\end{vmatrix}  =t_1V^{234}_{xyz}-x_1V^{234}_{tyz}+y_1V^{234}_{txz}-z_1V^{234}_{txy}  \end{equation} Which can obviously take on other forms by going along the other rows to obtain the triple products according to $134$,$124$ or $123$ sets of vectors, with appropriate signs.