Page:Calculus Made Easy.pdf/206

magnitude, so that $10\;dx$’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 ${\dfrac {dy}{dx}}=a$. What could we do? Still taking the little $d$’s as of finite size, we could draw $10$ of them, all with the same slope, and then put them together, end to end, like this:

Fig. 48.

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 ${\dfrac {dy}{dx}}=a$. And whether we take the $dy$’s and $dx$’s as finite or infinitely small, as they are all