way. The enlarged square is made up of the original square ${\displaystyle x^{2}}$, the two rectangles at the top and on the right, each of which is of area ${\displaystyle x\cdot dx}$ (or together ${\displaystyle 2x\cdot dx}$), and the little square at the top right-hand corner which is ${\displaystyle (dx)^{2}}$. In Fig. 2 we have taken ${\displaystyle dx}$ as

Fig. 2.	Fig. 3.

quite a big fraction of ${\displaystyle x}$—about ${\displaystyle {\tfrac {1}{5}}}$. But suppose we had taken it only ${\displaystyle {\tfrac {1}{100}}}$—about the thickness of an inked line drawn with a fine pen. Then the little corner square will have an area of only ${\displaystyle {\tfrac {1}{10,000}}}$ of ${\displaystyle x^{2}}$, and be practically invisible. Clearly ${\displaystyle (dx)^{2}}$ is negligible if only we consider the increment ${\displaystyle dx}$ to be itself small enough.

Let us consider a simile.

Suppose a millionaire were to say to his secretary: next week I will give you a small fraction of any money that comes in to me. Suppose that the secretary were to say to his boy: I will give you a small fraction of what I get. Suppose the fraction in each case to be ${\displaystyle {\tfrac {1}{100}}}$ part. Now if Mr. Millionaire received during the next week £${\displaystyle 1000}$, the secretary