# Page:Scientific Memoirs, Vol. 3 (1843).djvu/691

 Columns on which are in­scribed the primitive data. Number of the operations. Cards of the operations. Variable cards. Statement of results. Number of the Operation cards. Nature of each operation. Columns acted on by each operation. Columns that receive the result of each operation. Indication of change of value on any column. $\scriptstyle{^1\mathbf{V}_{0~}=m}$ 1 1 $\scriptstyle{\times}$ $\scriptstyle{^1\mathbf{V}_{0~}\times~^1\mathbf{V}_{4~}=}$ $\scriptstyle{^1\mathbf{V}_{6~}\ldots\ldots}$ \scriptstyle{\left\{\begin{align}&\scriptstyle{^1\mathbf{V}_{0~}=~^1\mathbf{V}_{0~}}\\&\scriptstyle{^1\mathbf{V}_{4~}=~^1\mathbf{V}_{4~}}\end{align}\right\}} $\scriptstyle{^1\mathbf{V}_{6~}=mn'}$ $\scriptstyle{^1\mathbf{V}_{1~}=n}$ 2 " $\scriptstyle{\times}$ $\scriptstyle{^1\mathbf{V}_{3~}\times~^1\mathbf{V}_{1~}=}$ $\scriptstyle{^1\mathbf{V}_{7~}\ldots\ldots}$ \scriptstyle{\left\{\begin{align}&\scriptstyle{^1\mathbf{V}_{3~}=~^1\mathbf{V}_{3~}}\\&\scriptstyle{^1\mathbf{V}_{1~}=~^1\mathbf{V}_{1~}}\end{align}\right\}} $\scriptstyle{^1\mathbf{V}_{7~}=m'n}$ $\scriptstyle{^1\mathbf{V}_{2~}=d}$ 3 " $\scriptstyle{\times}$ $\scriptstyle{^1\mathbf{V}_{2~}\times~^1\mathbf{V}_{4~}=}$ $\scriptstyle{^1\mathbf{V}_{8~}\ldots\ldots}$ \scriptstyle{\left\{\begin{align}&\scriptstyle{^1\mathbf{V}_{2~}=~^1\mathbf{V}_{2~}}\\&\scriptstyle{^1\mathbf{V}_{4~}=~^0\mathbf{V}_{4~}}\end{align}\right\}} $\scriptstyle{^1\mathbf{V}_{8~}=dn'}$ $\scriptstyle{^1\mathbf{V}_{3~}=m'}$ 4 " $\scriptstyle{\times}$ $\scriptstyle{^1\mathbf{V}_{5~}\times~^1\mathbf{V}_{1~}=}$ $\scriptstyle{^1\mathbf{V}_{9~}\ldots\ldots}$ \scriptstyle{\left\{\begin{align}&\scriptstyle{^1\mathbf{V}_{5~}=~^1V_{5~}}\\&\scriptstyle{^1\mathbf{V}_{1~}=~^1\mathbf{V}_{1~}}\end{align}\right\}} $\scriptstyle{^1\mathbf{V}_{9~}=d'n}$ $\scriptstyle{^1\mathbf{V}_{4~}=n'}$ 5 " $\scriptstyle{\times}$ $\scriptstyle{^1\mathbf{V}_{0~}\times~^1\mathbf{V}_{5~}=}$ $\scriptstyle{^1\mathbf{V}_{10}\ldots\ldots}$ \scriptstyle{\left\{\begin{align}&\scriptstyle{^1\mathbf{V}_{0~}=~^0\mathbf{V}_{0~}}\\&\scriptstyle{^1\mathbf{V}_{5~}=~^0\mathbf{V}_{5~}}\end{align}\right\}} $\scriptstyle{^1\mathbf{V}_{10}=d'm}$ $\scriptstyle{^1\mathbf{V}_{5~}=d'}$ 6 " $\scriptstyle{\times}$ $\scriptstyle{^1\mathbf{V}_{2~}\times~^1\mathbf{V}_{3~}=}$ $\scriptstyle{^1\mathbf{V}_{11}\ldots\ldots}$ \scriptstyle{\left\{\begin{align}&\scriptstyle{^1\mathbf{V}_{2~}=~^0\mathbf{V}_{2~}}\\&\scriptstyle{^1\mathbf{V}_{3~}=~^0\mathbf{V}_{3~}}\end{align}\right\}} $\scriptstyle{^1\mathbf{V}_{11}=dm'}$ 7 2 $\scriptstyle{-}$ $\scriptstyle{^1\mathbf{V}_{6~}-~^1\mathbf{V}_{7~}=}$ $\scriptstyle{^1\mathbf{V}_{12}\ldots\ldots}$ \scriptstyle{\left\{\begin{align}&\scriptstyle{^1\mathbf{V}_{6~}=~^0\mathbf{V}_{6~}}\\&\scriptstyle{^1\mathbf{V}_{7~}=~^0\mathbf{V}_{7~}}\end{align}\right\}} $\scriptstyle{^1\mathbf{V}_{12}=mn'-m'n}$ 8 " $\scriptstyle{-}$ $\scriptstyle{^1\mathbf{V}_{8~}-~^1\mathbf{V}_{9~}=}$ $\scriptstyle{^1\mathbf{V}_{13}\ldots\ldots}$ \scriptstyle{\left\{\begin{align}&\scriptstyle{^1\mathbf{V}_{8~}=~^0\mathbf{V}_{8~}}\\&\scriptstyle{^1\mathbf{V}_{9~}=~^0\mathbf{V}_{9~}}\end{align}\right\}} $\scriptstyle{^1\mathbf{V}_{13}=dn'-d'n}$ 9 " $\scriptstyle{-}$ $\scriptstyle{^1\mathbf{V}_{10}-^1\mathbf{V}_{11}=}$ $\scriptstyle{^1\mathbf{V}_{14}\ldots\ldots}$ \scriptstyle{\left\{\begin{align}&\scriptstyle{^1\mathbf{V}_{10}=~^0\mathbf{V}_{10}}\\&\scriptstyle{^1\mathbf{V}_{11}=~^0\mathbf{V}_{11}}\end{align}\right\}} $\scriptstyle{^1\mathbf{V}_{14}=d'm - dm'}$ 10 3 $\scriptstyle{\div}$ $\scriptstyle{^1\mathbf{V}_{13}\div~^1\mathbf{V}_{12}=}$ $\scriptstyle{^1\mathbf{V}_{15}\ldots\ldots}$ \scriptstyle{\left\{\begin{align}&\scriptstyle{^1\mathbf{V}_{13}=~^0\mathbf{V}_{13}}\\&\scriptstyle{^1\mathbf{V}_{12}=~^1\mathbf{V}_{12}}\end{align}\right\}} $\scriptstyle{^1\mathbf{V}_{15}=\frac{dn'-d'n}{mn'-m'n}=x}$ 11 " $\scriptstyle{\div}$ $\scriptstyle{^1\mathbf{V}_{14}-~^1\mathbf{V}_{12}=}$ $\scriptstyle{^1\mathbf{V}_{16}\ldots\ldots}$ \scriptstyle{\left\{\begin{align}&\scriptstyle{^1\mathbf{V}_{14}=~^0\mathbf{V}_{14}}\\&\scriptstyle{^1\mathbf{V}_{12}=~^0\mathbf{V}_{12}}\end{align}\right\}} $\scriptstyle{^1\mathbf{V}_{16}=\frac{d'm-dm'}{mn'-m'n}=y}$ 1 2 3 4 5 6 7 8