Quantum redactiones paginae "Usor:Tchougreeff/QUOMODO sive HOW To/PRINCIPIA CALCULI DIFFERENTIALIS ET INTEGRALIS ITEMQUE CALCULI DIFFERENTIARUM FINITARUM AUCTORE ANDREA CARAFFA E SOCIETATE IESU ROMAE TYPIS IOANNIS BAPTISTAE MARINI ET SOCII MDCCCXLV" differant

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<math display="block">S = \int\int\chi(x , y)dxdy = \int\int\varphi(u, v)(f_u'\mathrm{f}_v'-f_v'\mathrm{f}_u')dudv.</math>
 
{{Ancora|180}}[[#180|180]]. Differentiantes aequationem <math>\varphi(u, v) = \chi(x, y)</math> assequimur (19) <math>\varphi'_u = \chi'_x\frac{xdx}{udu} + \chi'_y\frac{ydy}{udu} =
\chi'_x f'_u +,\chi'_y \mathrm{f}_u', \varphi'_v = \chi'_x\frac{xdx}{vdv} + \chi'_y\frac{ydy}{vdv} =
\chi'_x f'_v +,\chi'_y \mathrm{f}_v'</math>