magnitude, so that ${\displaystyle 10\;dx}$’s made up one inch, then there would be ten little triangles like

Now, suppose that we were ordered to reconstruct the “curve,” starting merely from the information that ${\displaystyle {\dfrac {dy}{dx}}=a}$. What could we do? Still taking the little ${\displaystyle d}$’s as of finite size, we could draw ${\displaystyle 10}$ of them, all with the same slope, and then put them together, end to end, like this:

And, as the slope is the same for all, they would join to make, as in Fig. 48, a sloping line sloping with the correct slope ${\displaystyle {\dfrac {dy}{dx}}=a}$. And whether we take the ${\displaystyle dy}$’s and ${\displaystyle dx}$’s as finite or infinitely small, as they are all