Indeed. It's such a beautiful book.

I love Playfair's too.

I used to have a lot of trouble with Euclid's (translated) definition of a straight line, ... What the heck is "lies evenly". Playfair's made it click.

Another point is those Euclidean definitions aren't really formal definitions, but familiarisations. Then it makes more sense.

After Playfairs my understanding of an Euclidean straight line is that it's a function from a pair of points to a set of points (that forms the line) such that if you invoke the same function on any pair of points in its range you get back the same exact set of points (the range of the function). This made it click why a "straight line" in hyperbolic geometry or spherical geometry is still a "straight line".

On a different note, David Berlinski's Tour of Calculus is possibly the most atrocious, verbal diarrheaic book I have ever read. The formula of the book seems to be that every confusing sentence can be righted if every noun is accompanied by 20 florid adjectives and verbs by 59 muddled adverbs and no one will notice that the sentence is nonsense.

For some reason it gets a lot of love among some HN readers. Very few books generate as much revulsion in me than that one.