The Essential Parts of the Simple or Pure Mathematicks are Arithmetick and Geometry, which mutually assist one another, and are independent on any ot… - Jacques Ozanam

There are two general Methods made use of in the Mathematicks, viz. Synthesis and Analysis, which we shall explain, after having acquainted the Reader, that the Method we make use of to resolve a Mathematical Problem, is called Zetetick; and that that Method which determines when, and by what way, and how many different ways a Problem may be resolved, is called Poristick. But in treating of Methods, we will first premise, that in general, a Method is the Art of disposing a Train of Arguments or Consequences in a right Order, either to discover the Truth of a Theorem, which we would find out, or to demonstrate it to others, when found.

Arithmetic and geometry, according to Plato, are the two wings of the mathematician. The object indeed of all mathematical questions, is to determine the ratios of numbers, or of magnitudes ; and it may even be said, to continue the comparison of the ancient philosopher, that arithmetic is the mathematician's right wing; for it is an incontestable truth, that geometrical determinations would, for the most part, present nothing satisfactory to the mind, if the ratios thus determined could not be reduced to numerical ratios. This justifies the common practice, which we shall here follow, of beginning with arithmetic.

To be perfectly ignorant in all the Terms of them is only tolerable in those, who think their Tongues of as little Use to them, as generally their Understandings are. Those whom Necessity has obliged to get their Bread by Manual Industry, where some Degree of Art is required to go along with it, and who have had some Insight into these Studies, have very often found Advantages from them sufficient to reward the Pains they were at in acquiring them. And whatever may have been imputed (how justly I'm not now to determine) to some other Studies, under the Notion of Insignificancy and Loss of Time ; yet these, I believe, never caused Repentance in any, except it was for their Remissness in the Prosecution of them. And though Plato's Censure, that those who did not understand the 117 Prop. of the 10th Element, ought not to be ranked among Rational Creatures, wax unreasonable and unjust: Yet to give a Man the Character of Universal Learning that is destitute of a competent Knowledge in the Mathematics, is no less so.