Seems the various ways people are trying to proportionaly scale an image, up or down, could be more straight forward if one remembers ones algebra.

The formula is, y = mx, where m is the slope of the line. This is the ratio of y:x or m = y/x.

So if...

// max values for x and y
$y_max = 600;
$x_max = 800;

// image size
$y1 = 2000;
$x1 = 3000;

// use width for scaling
if ($x1 > $x_max)
{
    // find slope 
    $m = $y1/$x1;
    // set x side to max
    $x2 = $x_max;
    // set y side to a proportional size
    $y2 = $m * $x1;
}

The new image proportionally scaled will be x2 = 800, y2 = 533 (rounded).

To do it from the y side, simply reverse the x's and y's.