Based on fractal geometry, an objective and reproducible diagnosis of cervical cells was made, which differentiates normal cells from those with low-grade lesion (LEIBG) or cancer cells, quantitatively identifying ASCUS cells. Objective: to establish a diagnostic methodology of normal and preneoplastic cervical cells with simultaneous application of fractal and Euclidean geometry to define distinctive mathematical parameters of each of these states. Methods: digital photographs of twelve cytology cells of women between 20 and 55 years old (three superficial normal, three intermediate normal, three LEIBG and three ASCUS). Through a program, the fractal dimension of three mathematical objects was calculated: nucleus, cytoplasm and totality, from the box-counting method; simultaneously the number of pixels occupied by the surface of each one and the spaces occupied by the edge of these objects in each of the five grids were determined, to compare the obtained values. Results: when superimposing the two and four pixel grids, the values ​​of the occupation spaces of the nucleus make it possible to establish mathematical differences between the groups of cells, presenting as values ​​in the grid two: surface normals (53-56), intermediate normals (75 ), LEIBG (120-159) and ASCUS (104-121). Conclusions: a diagnostic mathematical methodology was established that differentiates preneoplastic states based on simultaneous fractal and Euclidean measurements of the edge of the cell nucleus. Abbreviations: LEIBG, low-grade squamous intraepithelial lesion; ASCUS atypical squamous cells of undetermined significance (atypical squamous cells of undetermined significance); GF, fractal geometry.