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In this MathEducator StackExchange article, "Notation of points with coordinates", it's posed the question about what is the best notation for geometrical points and their coordinates: $P(3, 4)$ or $P = (3, 4)$?

Peharps History of Mathematics could help with this discussion: what is the first known written register of such association point <-> coordinates? Did $P(3, 4)$ come first, for instance?

Descartes' "La Géométrie" has no such explicit association.

Somehow, this question is related to the posts "When do we see for the first time the use of the Cartesian coordinates?" and "Cartesian coordinate system in Newton's work". But, in the references given, I've found no explicit association either.

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  • $\begingroup$ What came first hardly has any bearing on what is better, even assuming that it is not a purely subjective preference. Early notations were often clumsy. In this case, one can use both expressions for different purposes, first as a point's name labeled by its coordinates, and second as identifying a point with its tuple of coordinates. $\endgroup$
    – Conifold
    Commented Jun 19, 2020 at 13:52

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IMO, the notation $P(x,y)$ is "more correct".

See e.g. Felix Klein, Elementary Mathematics from an Advanced Standpoint: Geometry (1908), page 10.

As you have already noted, the usual representation of the coordinate plane is quite late: I suppose that we cannot find it in any 19th Century treatise regarding Analytic Geometry.

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