The Triparty — Third Part

It is in the third part of the Triparty that Chuquet presents his algebra, which he calls “la rigte des premiers.” Strictly, this translates as “the rule of firsts”, the word “first” designating an unknown quantity to the power 1, written conventionally today as x. However, in order to distinguish clearly between “first numbers” (encountered earlier in the manuscript) and “firsts” in the context of the algebra, “premiers” is here translated as “first terms”. Chuquet does not explicitly claim originality for his algebra, and it might appear that his singling out of the rule of intermediate numbers alone as his own invention suggests that the algebraic material is derived from earlier works of other writers. Certainly, Chuquet makes an explicit claim for his expression “rule of first terms”, commenting that the unknown had earlier simply been designated as “thing”; but, as this third part unfolds, its originality becomes more and more obvious and justifies the title for its author “father of French algebra”, at one time accorded to de la Roche on the strength of almost the same algebraic material — but not strictly the same, since de la Roche did not include some of the more sophisticated aspects of Chuquet’s writings.