Sylvestre-François Lacroix - Collected Quotes

"Every quantity whose value depends on one or more other quantities is called a function of these latter, whether one knows or is ignorant of what operations it is necessary to use to arrive from the latter to the first." (Sylvestre-François Lacroix, "Traité de calcul differéntiel et du calcul intégral", 1797-1798)

"There exists a manner of viewing geometry that could be called géométrie analytique, and which would consist in deducing the properties of extension from the least possible number of principles, and by truly analytic methods." (Sylvestre-François Lacroix, "Traité de calcul differéntiel et du calcul intégral", 1797-1798) [first use of the "analyic geometry" expression)

"In order to indicate that a quantity depends on one or several others, either by operations of any kind, or by other relations, which it is impossible to assign algebraically, but whose existence is determined by certain conditions, we call the first quantity a function of the others." (Sylvestre-François Lacroix, "An elementary treatise on the differential and integral calculus", 1816)

"The subject of this branch of Analysis is the passage of one or more quantities through different states of magnitude, and the changes which consequently take place in other quantities, whose value depends on that of these first." (Sylvestre-François Lacroix, "An elementary treatise on the differential and integral calculus", 1816)

"The words positive and negative are general terms, that indicate the different states a quantity can be in, and that in special cases will have interpretations such as capital and debt, east and west, right and left, up and down, ascending and descending, winning and losing, etc. In each particular case it is up to us to choose which of the two states we wish to call positive, and thereby denote with the + sign, but once this is determined, we must consistently call the other state negative, and indicate it by the sign −." (Sylvestre-François Lacroix, "Beginselen der Stelkunst", 1821)

"[algebra and geometry] should be treated separately, as far apart as they can be, and that the results in each should serve for mutual clarification, corresponding, so to speak, to the text of a book and its translation." (Sylvestre-François Lacroix)