In defense of Euclid (was: Einstein's dream)

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In Defense of Euclid

A fellow called Euclid professed 
That geometry rightly assessed 
Would see equal inclines 
Of neighborly lines 
Make them slightly standoffish at best.

And so sensibly Euclid explained 
His art so pellucidly planed 
With crafty designs 
Full of parallel lines, 
He drove other logicians insane.

And so much of life it made clear! 
The Truths that we came to hold dear, 
Three wrongs make a right, 
A square knot is tight, 
An arrow flies straight through the air!

In the end, as you know, slow as light, 
Other axioms proved to have bite. 
Minkowski and Einstein 
Between them bent spacetime; 
Riemann had stayed up all night.

But for Beauty's sake Euclid held ground, 
And he measured his room all around. 
With its lengths so mismatched 
A black hole should have hatched, 
And not a right angle was found!

Previous version

Einstein's dream

As my fevered brain struggled to rest
Euclid's phantom appeared. He professed
That equal inclines 
Of neighborly lines 
Made them slightly standoffish at best.

And so sensibly Euclid explained 
His art so pellucidly planed 
With crafty designs 
Full of parallel lines
That my wilder theories were shamed.

For so much of life it made clear! 
The Truths that we came to hold dear, 
Three wrongs make a right, 
A square knot is tight, 
An arrow flies straight through the air!

I tried to explain the contortions
Of spacetime when bent by distortions
That slow down the flight
Of matter or light,
Quite kindly, in single-page portions.

But for Beauty the ghost held his ground, 
And he measured my room all around. 
With its lengths so mismatched 
A black hole should have hatched!
— On my nightstand this message I found:

"Even fools know that Beauty's a flower. 
Savor space and time, feel a cool shower. 
Stretch out youth's affine hopes 
Along curved grassy slopes; 
Climb wrinkled the ivory tower."

“In defence of Euclid” - what is the poet defending?
S1-3 say that the parallel lines postulate was thought so long to follow from Euclid’s axioms but it turned out it not to be so and logicians went insane trying to prove it till they found out they could not and so non Euclidean geometry was born in S4. 
So much so good. It’s a tale well told. 

I was in expecting the point in S5 to be that in leading maths astray for 2000 years Euclid did us a great service because he paradoxically laid the groundwork for non Euclidean geometry, as explained in S4. And so that would be the defence

But I don’t see S5 saying that. I’m not sure what it’s saying. The rhyme is tying up the poem in knots. The messaging is garbled.