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:



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