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This article discusses the traditional opposition between arithmetic on abacus and arithmetic on paper. The authors show that in the 15th century there was a desire for synthesis, reflecting more a desire to integrate legacies than a strict separation. The algorism model, developed in the beginning of the 13th century, triumphs but does not impose itself in all cultures of calculation.The work of Jean Adam which is analysed here is particularly interesting for these cultures of calculation. Punctuated with practical advice for accountants, his treatise deals with fractions and a few rules of proportionality, notably the rule of three, which gently leads him to calculations on paper.In 1475, Jean Adam dedicated his work to Nicole Thilhart, a close associate of the royal power. The political context is marked by Louis XI’s authoritarian political practice and a desire to structure the state apparatus over the long term. Like Nicolas Chuquet, Jean Adam belongs to a group of men marked by the mathematical influence of Barthélemy de Romans. Like the algorist from Lyon, Jean Adam decided to live from his mathematical knowledge and it seems that his mathematical culture was not foreign to his social ascension.