Proof the nine and the case of "Arithmetica Primary" in Cezar Pinheiro

Abstract

This article is inserted in the field of history of mathematics education and studies a mathematical content no longer prescribed in current textbooks, but that was taught in times past in schools: the proof by nine. It is intended to present the first evidence of this content, the different ways to interpret this and demonstrations for the four fundamental operations. It will be differentiate the terms “proof by nine” and "casting out nines" explaining the rule of the second. Finally, it will analyze the approach of proof by nine prescribed in the book of Cezar Pinheiro,named "Arithmetica Primary ", 1902. In this book the proof by nine is linked to the teachings of the four arithmetic operations and it is a written calculation verification test, which is not considered as a real test by the author.