Background: The concomitant use of fractal and Euclidian measurements has led to the development of new methodologies of cell evaluation, including a diagnosis of cervical cells that set up differences between normality and various degrees of lesion, to carcinoma. Aim: To confirm the diagnostic capacity of the methodology based on fractal and Euclidian geometry for the mathematical diagnosis through a blind study of normal cells and with different types of lesion, as atypia of undetermined significance (ASCUS), low grade squamous intra-epithelial lesion (LGSIL) and high grade squamous intra-epithelial lesion (HGSIL). Methods: 100 cells of Papanicolaou tests were analyzed and divided into 4 groups according to conventional parameters: 25 normal, 25 ASCUS, 25 LGSIL and 25 HGSIL. By means of the Box-counting Fractal Space, we calculated the fractal dimension and occupying spaces of the border and surface in pixels of the cell nucleus and cytoplasm. The diagnostic parameters of the previously developed methodology were applied and compared with the conventional diagnosis, setting up sensibility, specificity, negative likelihood ratio and Kappa coefficient. Results: The values of the occupation of the border and surface of the cell nucleus and cytoplasm were consistent with the values found by the diagnostic methodology previously found. The subtraction of the nucleus and cytoplasm frontiers presented values between: 189 and 482 for normality; 159 and 432 for ASCUS; 126 to 401 for LGSIL and 39 to 122 for HGSIL. A sensitivity and specificity of 100%, and a Kappa coefficient of 1 were obtained. Conclusions: The capacity of the methodology to diagnose quantitatively the different stages in the evolution of the cervical cells observed in Papanicolaou tests was confirmed, from normality to HGSIL.