# 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. ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{0~}=m}}$ 1 1 ${\displaystyle \scriptstyle {\times }}$ ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{0~}\times ~^{1}\mathbf {V} _{4~}=}}$ ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{6~}\ldots \ldots }}$ {\displaystyle \scriptstyle {\left\{{\begin{aligned}&\scriptstyle {^{1}\mathbf {V} _{0~}=~^{1}\mathbf {V} _{0~}}\\&\scriptstyle {^{1}\mathbf {V} _{4~}=~^{1}\mathbf {V} _{4~}}\end{aligned}}\right\}}} ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{6~}=mn'}}$ ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{1~}=n}}$ 2 " ${\displaystyle \scriptstyle {\times }}$ ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{3~}\times ~^{1}\mathbf {V} _{1~}=}}$ ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{7~}\ldots \ldots }}$ {\displaystyle \scriptstyle {\left\{{\begin{aligned}&\scriptstyle {^{1}\mathbf {V} _{3~}=~^{1}\mathbf {V} _{3~}}\\&\scriptstyle {^{1}\mathbf {V} _{1~}=~^{1}\mathbf {V} _{1~}}\end{aligned}}\right\}}} ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{7~}=m'n}}$ ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{2~}=d}}$ 3 " ${\displaystyle \scriptstyle {\times }}$ ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{2~}\times ~^{1}\mathbf {V} _{4~}=}}$ ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{8~}\ldots \ldots }}$ {\displaystyle \scriptstyle {\left\{{\begin{aligned}&\scriptstyle {^{1}\mathbf {V} _{2~}=~^{1}\mathbf {V} _{2~}}\\&\scriptstyle {^{1}\mathbf {V} _{4~}=~^{0}\mathbf {V} _{4~}}\end{aligned}}\right\}}} ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{8~}=dn'}}$ ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{3~}=m'}}$ 4 " ${\displaystyle \scriptstyle {\times }}$ ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{5~}\times ~^{1}\mathbf {V} _{1~}=}}$ ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{9~}\ldots \ldots }}$ {\displaystyle \scriptstyle {\left\{{\begin{aligned}&\scriptstyle {^{1}\mathbf {V} _{5~}=~^{1}V_{5~}}\\&\scriptstyle {^{1}\mathbf {V} _{1~}=~^{1}\mathbf {V} _{1~}}\end{aligned}}\right\}}} ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{9~}=d'n}}$ ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{4~}=n'}}$ 5 " ${\displaystyle \scriptstyle {\times }}$ ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{0~}\times ~^{1}\mathbf {V} _{5~}=}}$ ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{10}\ldots \ldots }}$ {\displaystyle \scriptstyle {\left\{{\begin{aligned}&\scriptstyle {^{1}\mathbf {V} _{0~}=~^{0}\mathbf {V} _{0~}}\\&\scriptstyle {^{1}\mathbf {V} _{5~}=~^{0}\mathbf {V} _{5~}}\end{aligned}}\right\}}} ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{10}=d'm}}$ ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{5~}=d'}}$ 6 " ${\displaystyle \scriptstyle {\times }}$ ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{2~}\times ~^{1}\mathbf {V} _{3~}=}}$ ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{11}\ldots \ldots }}$ {\displaystyle \scriptstyle {\left\{{\begin{aligned}&\scriptstyle {^{1}\mathbf {V} _{2~}=~^{0}\mathbf {V} _{2~}}\\&\scriptstyle {^{1}\mathbf {V} _{3~}=~^{0}\mathbf {V} _{3~}}\end{aligned}}\right\}}} ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{11}=dm'}}$ 7 2 ${\displaystyle \scriptstyle {-}}$ ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{6~}-~^{1}\mathbf {V} _{7~}=}}$ ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{12}\ldots \ldots }}$ {\displaystyle \scriptstyle {\left\{{\begin{aligned}&\scriptstyle {^{1}\mathbf {V} _{6~}=~^{0}\mathbf {V} _{6~}}\\&\scriptstyle {^{1}\mathbf {V} _{7~}=~^{0}\mathbf {V} _{7~}}\end{aligned}}\right\}}} ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{12}=mn'-m'n}}$ 8 " ${\displaystyle \scriptstyle {-}}$ ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{8~}-~^{1}\mathbf {V} _{9~}=}}$ ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{13}\ldots \ldots }}$ {\displaystyle \scriptstyle {\left\{{\begin{aligned}&\scriptstyle {^{1}\mathbf {V} _{8~}=~^{0}\mathbf {V} _{8~}}\\&\scriptstyle {^{1}\mathbf {V} _{9~}=~^{0}\mathbf {V} _{9~}}\end{aligned}}\right\}}} ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{13}=dn'-d'n}}$ 9 " ${\displaystyle \scriptstyle {-}}$ ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{10}-^{1}\mathbf {V} _{11}=}}$ ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{14}\ldots \ldots }}$ {\displaystyle \scriptstyle {\left\{{\begin{aligned}&\scriptstyle {^{1}\mathbf {V} _{10}=~^{0}\mathbf {V} _{10}}\\&\scriptstyle {^{1}\mathbf {V} _{11}=~^{0}\mathbf {V} _{11}}\end{aligned}}\right\}}} ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{14}=d'm-dm'}}$ 10 3 ${\displaystyle \scriptstyle {\div }}$ ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{13}\div ~^{1}\mathbf {V} _{12}=}}$ ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{15}\ldots \ldots }}$ {\displaystyle \scriptstyle {\left\{{\begin{aligned}&\scriptstyle {^{1}\mathbf {V} _{13}=~^{0}\mathbf {V} _{13}}\\&\scriptstyle {^{1}\mathbf {V} _{12}=~^{1}\mathbf {V} _{12}}\end{aligned}}\right\}}} ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{15}={\frac {dn'-d'n}{mn'-m'n}}=x}}$ 11 " ${\displaystyle \scriptstyle {\div }}$ ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{14}-~^{1}\mathbf {V} _{12}=}}$ ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{16}\ldots \ldots }}$ {\displaystyle \scriptstyle {\left\{{\begin{aligned}&\scriptstyle {^{1}\mathbf {V} _{14}=~^{0}\mathbf {V} _{14}}\\&\scriptstyle {^{1}\mathbf {V} _{12}=~^{0}\mathbf {V} _{12}}\end{aligned}}\right\}}} ${\displaystyle \scriptstyle {^{1}\mathbf {V} _{16}={\frac {d'm-dm'}{mn'-m'n}}=y}}$ 1 2 3 4 5 6 7 8