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ע"י גזירת <math>f(u,v)=0</math> ביחס ל <math>x,y</math> , אנחנו מסיקים ש:
<math>(1) \qquad {\operatorname{d\partial}\!f\over\operatorname{d\partial}\!v}{\operatorname{d\partial}\!v\over\operatorname{d\partial}\!x}+{\operatorname{d\partial}\!f\over\operatorname{d\partial}\!u}{\operatorname{d\partial}\!u\over\operatorname{d\partial}\!x}=0, \qquad {\operatorname{d\partial}\!f\over\operatorname{d\partial}\!v}{\operatorname{d\partial}\!v\over\operatorname{d\partial}\!y}+{\operatorname{d\partial}\!f\over\operatorname{d\partial}\!u}{\operatorname{d\partial}\!u\over\operatorname{d\partial}\!y}=0</math> .
אם נסמן <math>\qquad {\operatorname{d\partial}\!f\over\operatorname{d\partial}\!v}=f_v,{\operatorname{d\partial}\!f\over\operatorname{d\partial}\!u}=f_u</math>, ואת <math>{\operatorname{d\partial}\!v\over\operatorname{d\partial}\!x}, {\operatorname{d\partial}\!u\over\operatorname{d\partial}\!x}, {\operatorname{d\partial}\!v\over\operatorname{d\partial}\!y}, {\operatorname{d\partial}\!u\over\operatorname{d\partial}\!y}</math> בתור <math>v_x, u_x, v_y, u_y</math>, מערכת המשוואת <math>(1)</math> תראינה כך:
<math>(2) \qquad f_v\cdot v_x+f_u\cdot u_x=0, \qquad f_v\cdot v_y+f_u\cdot u_y=0</math> .
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