(1) d... merely means "a little bit of." Thus dx means a little bit of — Calculus Made Easy

"If, for the purpose of time, 1/60 be called a small fraction, then 1/60 of 1/60 (being a small fraction of a small fraction) may be regarded as a small quantity of the second order of smallness."

"Some calculus-tricks are quite easy. Some are enormously difficult. The fools who write the textbooks of advanced mathematics—and they are mostly clever fools—seldom take the trouble to show you how easy the easy calculations are. On the contrary, they seem to desire to impress you with their tremendous cleverness by going about it in the most difficult way."

"The witty Dean Swift once wrote: "So Natralists observe, a Flea "Hath smaller Fleas that on him prey. "And these have smaller Fleas to bite em, "And so proceed ad infimitum. An ox might worry about a flea of ordinary size—a small creature of the first order of smallness. But he would probably not trouble himself about a fleas flea, being of the second order of smallness, it would be negligible. Even a gross of fleas fleas would not be of much account to the ox."

"(2) \int which is merely a long S... may be called, if you like, "the sum of." Thus \int dx means the sum of all the little bits of x or \int dt means the sum of all the little bits of t. Ordinary mathematicians call this symbol "the integral of."

"Now any fool can see that if x is considered as made up of a lot of little bits, each of which is called dx, if you add them all up together you get the sum of all the dxs (which is the same thing as the whole of x). The word "integral" simply means "the whole."

"We shall have... to learn under what circumstances we may consider small quantities to be so minute that we may omit them from consideration. Everything depends upon relative minuteness."