Jacques Ozanam quotes
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.
Jacques Ozanam
Mathematicks therefore is a Science which teaches or contemplates whatever is capable of Measure or Number as such. When it relates to Number, it is called Arithmetick; but when to measure, as Length, Breadth, Depth, Degrees of Velocity in Motion, Intenseness or Remissness of Sounds, Augmentation or Diminution of Quality, 6tc. it is called Geometry.
Jacques Ozanam
The sun, as we have already said, is placed in the middle of our system, as a source of light and heat, to illuminate and vivify all the planets subordinate to it. Without his benign influence the earth would be a mere block, which in hardness would surpass marble and the most compact substances with which we are acquainted; no vegetation, no motion would be possible: in a word, it would be the abode of darkness, inactivity and death. The first rank therefore among inanimate beings cannot be refused to the sun; and if the error of addressing to a created object that adoration which is due to the Creator atone could admit of excuse, we might be tempted to excuse the homage paid to the sun by the ancient Persians, as is still the ease among the Guebres, their successors, and some savage tribes in America.
Jacques Ozanam
The Usefulness of the Mathematicks in General, and of some Parts of them in Particular, in the common Affairs of Humane Life, has rendered some competent Knowledge of them very necessary to a great Part of Mankind, and very convenient to all the Rest that are any way conversant beyond the Limits of their own particular callings.
Jacques Ozanam
The Essential Parts of the Simple or Pure Mathematicks are Arithmetick and Geometry, which mutually assist one another, and are independent on any other Sciences, except perhaps on Artificial Logick: But doubtless Natural Logick may be sufficient to a Man of Sense. The other parts are chiefly Physical Subjects explained by the Principles of Arithmetics or Geometry.
Jacques Ozanam
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.
Jacques Ozanam