What message does the each of the ff quotations impart?

Question

"There is no royal way to Geometry." "That we are looking at the stars does not justify our falling into the gutter. "

Answer 1

Both of these responses are just guesses.

"There is no royal way to Geometry."  

I'm thinking a "royal way" is an easy, obvious route.  This implies a red carpet, which means it's hard to miss.  Further, it might imply that you are carried to your destination, using little of your own effort.  Think of a Roman emperor carried about on a platform, his servants doing the carrying and walking as he sits and enjoys the ride.  The answers in Geometry are not always obvious, and it requires your own thinking and effort to truly arrive at them.  

"That we are looking at the stars does not justify our falling into the gutter. "

My first reaction is that we spend a lot of time learning about celebrities (stars, athletes), many of whom turn out to be not such great people or role models.  So, wouldn't our time be better spent with other pursuits, other than paying attention to or following them?  But, that's just me applying a more current interpretation.  It sounds like the quote was written a while ago, though.  The general meaning, to me, suggests that it's all fine and good to gaze at stars or other beautiful things, but we still need to pay attention to what we are doing in or lives, whether it's knowing where we are walking or other daily tasks.  If we don't pay attention to what we really need to, we pay a price.  The "falling into the gutter" part implies a fall from grace or perusing "less Godly” things.  There's a religious connotation to the quote.  It almost sounds like it was spoken by a church official who distrusts science.  There is a historical struggle between Christianity (or its institutions) and astronomy.  The discoveries of astronomer Galileo challenged assumptions long held by the church.  So, the church of that time might have believed that Galileo was leading us away from God and "into the gutter."