# Why is $s$ used for arc length?

Why is $s$ used for arc length? I looked around online, but I can't find a definite answer.

Thank you!

• I've always assumed $s$ to stand for "segment" (as in "line segment"). That said, I don't have any sources to back up my case. Feb 2, 2016 at 21:40
• @Omnomnomnom I looked up displacement and it's spatium in latin if that helps. It was just a thought.
– Karl
Feb 2, 2016 at 21:41
• Surprisingly, there's no answer in Cajori's History of Mathematical Notations. Feb 2, 2016 at 21:42
• Because using $d$ for displacement would just look stupid.$$\int dd$$ Feb 2, 2016 at 23:40
• I bet it comes from German Strecke or Latin spatium meaning distance. Feb 3, 2016 at 8:44

Propositio 4 [ page 13 ] Sit spatium $AM$, sive sit linea recta sive curva, $=s$, et celeritas, quam corpus habet in M sit $c$, quae erit functio quaedam ipsius $s$. Ab $M$ accipiatur elementum $Mm$, quod igitur motu aequabili idque celeritate $c$ percurri concipiendum est. Vocato elemento $Mm$, $ds$; erit tempus quo hoc elementum pe[r]curritur $=\frac{ds}{c}$. Integrando ergo habebitur tempus, quo totus arcus $AM$ absolvitur $=\int\frac{ds}{c}$.