The paper discusses Michel Chasles’ “principle of correspondence” of 1864, which reads as follows: When, on a straight line \(L\), two series of points \(x\) and \(u\) are such that \(a\) points \(u\) correspond to a single point \(x\), and that \(b\) points \(x\) correspond to a single point \(u\), then the numbers of points \(x\) which coincide with corresponding points \(u\) is \((\alpha+\beta)\). When, around a point \(I\), two pencils of straight lines \(IX\) and \(IU\) are such that \(a\) lines \(IU\) correspond to a single point \(IX\), and that \(b\) lines \(IX\) correspond to a single line \(IU\), then the numbers of lines \(IX\) which coincide with corresponding lines \(IU\) is \((\alpha+\beta)\). For Chasles the main values of this theorem were in its simplicity (it can be easily applied to infinity of questions), generality and uniformity (the reasoning in creating and proving theorems will be the same) and that the principle can therefore serve as an art of invention. Examples are given of Chasles’ solutions to (generalizations of) some of Poncelet’s theorems. These ideals had roots in French engineering schools (like the École Polytechnique) where the principle of generality was highly esteemed, only to be applied in subsequent applications when needed. The principle was rather popular for a quarter of the century and was a staple of mathematics education of many (European) universities. And its pervasiveness had to draw a backlash, notably first in Italian schools of mathematics, first by Giovanni Guccia in 1888 and then Corrado Segre who rebelled against this “automatic theorem proving” (to use a modern computer language); Segre related that one of his teachers used to call this kind of research tic-tac geometry. For Segre, modern mathematics was born out of “conversation, and generally to all those vectors of scientific sociability…that were set alongside institutional education and, allowing greater freedom of expression and debate between the interlocutors, proved particularly useful in the creative phase of research activity…”. This was a strong influence that seems to have limited influence and use of Chasles’ principle(s). Reviewer notes however that both of these aspects are useful and needed in mathematics – the “creative” and the automated aspects. At the development stage, mathematics is “creative”. Once the new creations are well understood, they become automated to the point that computers can do them. “Automated mathematics” can in turn lead back to “creative” mathematics. As always, the essence is the right proportion of the two.