Elements

The three irreducible elements of geometry are Point, Line and Plane.

They are unary qualities.

“Unary”, here, signifies that geometric elements have exactly one quale each.
These quales differ, each from every other.
Each can stand alone.
Elements of a kind are identical, but not unique.

• A Point is just a place—without size of any value (such as, say, zero) whatsoever
• A Line is just extension—without ends, or place, or sides, or thickness of any value (such as zero) whatsoever, or length of any value at all (such as ∞)
• A Plane is just spread—without edges, or thickness of any value (such as zero), or area of any value (such as ∞²)

In regard to a line's quality,

• Extension is synonymous with straight: that is, straightness is extension's (and so a line's) specific, invariant, stand-alone quality. By complete contrast,
• Curvature is variable, and arbitrarily specified, so is not a unary quality, and thus not a geometric element.

One often reads that a straight line has zero curvature.
This is mistaken. Lines are not curved—to any degree (such as zero, or ∞) whatsoever.
Lines are not curves, and,
Curves are not lines.

In regard to a plane's quality,

• Spread is synonomous with flat: that is, flatness is spread's (and so a plane's) specific, invariant, stand-alone quality. By complete contrast,
• Surface Curvature is variable, and arbitrarily specified, so is not a unary quality, and thus not a geometric element.

A plane is not a surface, “of zero curvature.”
Planes are not curved—to any degree (such as zero, or ∞) whatsoever.

None of the elements is quantifiable.
A point cannot be made more - or less - of a place than it is;
a line cannot be made more - or less - of a line than it is;
a plane cannot be made more - or less - of a plane than it is.

Each of the elements is a single, whole, unbroken thing,
Projective Geometry is for this reason sometimes called, “Synthetic” Geometry,
to bring out the (stark) contrast with so-called, “Analytic” Geometry,
which (because to “analyse” is to “break into bits”) is very much concerned with broken elements,
and with counting the bits.

Thus, also, the common intuition that lines and planes are composed of points is mistaken,
since it implies that some elements are sums of other elements.
However, while sums are quantities,
elements are not.
It is simply that there is nothing available to sum.

Accordingly, neither measurement, nor its concomitant, metrication, is native to geometry.

Because units have starts and endings, and geometric elements do not, there are no units.

This means that Projective Geometry cannot specify absolute sizes—of anything.