The aim of this study is to identify in the arithmetic of Hippolyte Rivail (1804-1869), first volume, the Anschauungunterricht or intuitive method, as formulated by Pestalozzi. Hippolyte Rivail was a direct disciple of Pestalozzi in Yverdon (Switzerland) and became a popularizer of the ideas of the Swiss pedagogue through the textbooks he published and the teaching given in schools in Paris. The investigative question was answered in the light of cultural transfers, according to Fontaine; for the treatment of the data, the documentary analysis method was used, initially constructing a documentary corpus that covered the arithmetic published from 1805 to 1824, in several countries and, which mention in their titles the name of Pestalozzi. 4 categories were chosen for the critical analysis: 1) preliminary discourse; 2) use of the arithmometer; 3) mental calculation; 4) the tables of units and fractions. It was concluded that: Rivail's arithmetic is an example of a manual that carries a pedagogical proposal from another cultural space, disseminated in another national space, Breaking Borders and with appropriations of a cultural agent who disseminated it. Pestalozzi's intuitive method is that followed by Rivail, although he modified it. There are strong indications that he emphasized the use of the arithmometer much more than that of Pestalozzi's paintings and stimulated mental calculation, in parallel with the use of the arithmometer and, used various concrete objects as means of visualizing arithmetic concepts.