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I wonder what would be a good/early reference for the fact:

rational points on the unit sphere (centered at the origin) are dense.

Stereographic projection (from a rational point in the sphere) provides a bijection between rational points on the sphere and rational points in euclidean space, where the rationals are dense. (This is a special case of a rational line intersecting a quadric in two rational points)

In many places in the literature the above statement is made, but no reference is given. I am looking for (early) references that provide this fact, perhaps only for the circle or the 2-sphere first.

While related, this question does not quite answer my question; I am looking for early references.

I wonder what would be a good/early reference for the fact:

rational points on the unit sphere (centered at the origin) are dense.

Stereographic projection (from a rational point in the sphere) provides a bijection between rational points on the sphere and rational points in euclidean space, where the rationals are dense. (This is a special case of a rational line intersecting a quadric in two rational points)

In many places in the literature the above statement is made, but no reference is given. I am looking for (early) references that provide this fact, perhaps only for the circle or the 2-sphere first.

While related, this question does not quite answer my question; I am looking for early references.

I wonder what would be a good reference for the fact:

rational points on the unit sphere (centered at the origin) are dense.

Stereographic projection (from a rational point in the sphere) provides a bijection between rational points on the sphere and rational points in euclidean space, where the rationals are dense. (This is a special case of a rational line intersecting a quadric in two rational points)

In many places in the literature the above statement is made, but no reference is given. I am looking for (early) references that provide this fact, perhaps only for the circle or the 2-sphere first.

I wonder what would be a good/early reference for the fact:

rational points on the unit sphere (centered at the origin) are dense.

Stereographic projection (from a rational point in the sphere) provides a bijection between rational points on the sphere and rational points in euclidean space, where the rationals are dense. (This is a special case of a rational line intersecting a quadric in two rational points)

In many places in the literature the above statement is made, but no reference is given. I am looking for (early) references that provide this fact, perhaps only for the circle or the 2-sphere first.

While related, this question does not quite answer my question; I am looking for early references.