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Linea 13 124:
\chi'_x =\frac{\varphi'_u \mathrm{f}_v'- \varphi'_v \mathrm{f}_u'}{f_u'\mathrm{f}_v'-f_v'\mathrm{f}_u'}, \chi'_y =\frac{\varphi'_v \mathrm{f}_u'- \varphi'_u \mathrm{f}_v'}{f_u'\mathrm{f}_v'-f_v'\mathrm{f}_u'}
</math>
quibus formulis integrale duplum <math>\int\int dxdy \sqrt{(1+\chi'_x_{x}^{2}+\chi'_y_{y}^{2})}</math> exhibens (173) quadraturam superficiei curvae <math>z = \chi(x,y)</math>, transformatur in
<math>\int\int dudv \sqrt{ [(f_u'\mathrm{f}_v'-f_v'\mathrm{f}_u')^2+(\varphi'_u \mathrm{f}_v'- \varphi'_v \mathrm{f}_u')^2+(\varphi'_v \mathrm{f}_u'- \varphi'_u \mathrm{f}_v')^2]}.</math>
Fac v. gr. ut <math>x , y , z</math> dentur per coordinatas polares , nimirum (elem. 352) <math>x = \Delta\sin\theta\cos\omega, y=\Delta\sin\theta\sin\omega,
Receptum de "https://la.wikipedia.org/wiki/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"