# How to say that a mathematical curve contains a point?

What would be the suitable Latin verb to express the idea that a curve (e.g. a circle, a parabola) contains/includes a point?

My first thought was

parabola punctum continet

but it seems that contineo and includo are closer to bound, restrain, etc. than to include as we use it in English.

Edit. la.wikipedia.org uses continet but the site is not know to be very good Latin.

• How you say this might depend on how much you care about the idea that a curve is a point-set. There are foundational approaches like smooth infinitesimal analysis (SIA) in which the opposite is true: one can prove that a curve can't consist of a set of points. A phrasing like the one in Draconis's answer can be used if you're willing to sidestep that issue. I believe the symbol ∈ comes from Greek epsilon, as an abbreviation for ἐστι (is), the idea being that if a is blue, then we can express this as a∈B, where B is the set of blue things.
– user3597
Oct 24, 2021 at 0:09
• I was thinking of the Euclidian definitions, a curve is basically an extended point
– user10176
Oct 24, 2021 at 8:33

Since you seemed to be open to Draconis' suggestions, I gather you are not wed to the set-theory idea of a line "containing" a point and are just looking for a way to say the point is on the line (i.e., it is either one of the line's end points or the line goes through it).

In that case, I would suggest: punctum in parabola situm est (situs, -a, -um = placed). Why? Because in such cases my go-to method is to Google what Euler has to say, and Euler has, for example, this to say:

Illustrissimus Auctor ostendit tria horum punctorum E, F et H semper in eadem linea recta fore sita

si tria puncta E, F, G forment triangulum EFG, tum quartum punctum H ita in recta EF producta [drawn out, extrapolated] erit situm, ut sit FH = 1/2 EF

Casus quo quatuor puncta in directum sunt sita

All examples taken from Solutio facilis problematum quorundam geometricorum difficillimorum.

(Sub quo titulo inconspicuo latet una e multis rebus ab Eulero nomen tenentibus, Recta Euleri.)

• I also looked for Euler's way to say it but didn't find this text, anyway this is a perfect answer! Thanks!
– user10176
Oct 24, 2021 at 18:24

It requires rearranging the sentence, but how about jaceō or sedeō with a preposition: "the point lies on the curve"?

• This could work, do you have any reference for it?
– user10176
Oct 23, 2021 at 19:28
• ...or simply sum. Oct 23, 2021 at 22:13