Parallelism and intersection at ideal points under projective transformation

Question

This is rather a basic question in projective geometry but I have come across a line in section 2.7.2 (recovery of affine properties from images) from Multiple View Geometry (Hartley & Zisserman)

What is the significance of this statement? Does it suggest anything about the lines still being parallel? If 2 lines after projective transformation still intersect at a point at infinity on $l_{\infty}$, it seems to suggest that they are still parallel.

In an earlier section of 2.4.5 the authors gave an example to show a point at infinity is mapped to a finite point under projective transformation. Therefore as I understand parallelism is not preserved. I would like some help understanding the example given in the screenshot.

Thanks in advance.

Edit: https://medium.com/@unifyai/part-ii-projective-transformations-in-2d-2e99ac9c7e9f

Answer 1

You missed the word “imaged,” which abbreviates “image of.” A general projective transformation will certainly move the line at infinity to some other line.