of which is ${\displaystyle dx}$, is similar to the original triangle; and it is obvious that the value of the ratio ${\displaystyle {\frac {dy}{dx}}}$ is the same as that of the ratio ${\displaystyle {\frac {y}{x}}}$. As the angle is ${\displaystyle 30^{\circ }}$ it will be seen that here

(2) Let ${\displaystyle x}$ represent, in Fig. 5, the horizontal distance, from a wall, of the bottom end of a ladder,

${\displaystyle AB}$, of fixed length; and let ${\displaystyle y}$ be the height it reaches up the wall. Now ${\displaystyle y}$ clearly depends on ${\displaystyle x}$. It is easy to see that, if we pull the bottom end ${\displaystyle A}$ a bit further from the wall, the top end ${\displaystyle B}$ will come down a little lower. Let us state this in scientific language. If we increase ${\displaystyle x}$ to ${\displaystyle x+dx}$, then ${\displaystyle y}$ will become ${\displaystyle y-dy}$; that is, when ${\displaystyle x}$ receives a positive