The reader will find no figures in this work. The methods which I set forth do not require either constructions or geometrical or mechanical reasonings: but only algebraic operations, subject to a regular and uniform rule of procedure.

Newton was the greatest genius that ever existed, and the most fortunate, for we cannot find more than once a system of the world to establish.

It has cost them but a moment to cut off that head; but a hundred years will not be sufficient to produce another like it.

The ordinary operations of algebra suffice to resolve problems in the theory of curves.

It took the mob only a moment to remove his head; a century will not suffice to reproduce it.

The reader will find no figures in this work. The methods which I set forth do not require either constructions or geometrical or mechanical reasonings: but only algebraic operations, subject to a regular and uniform rule of procedure.

As long as algebra and geometry have been separated, their progress have been slow and their uses limited; but when these two sciences have been united, they have lent each mutual forces, and have marched together towards perfection.