On Numbers (1700-1724)

"To understand the theory of chance thoroughly, requires a great knowledge of numbers, and a pretty competent one of Algebra." (John Arbuthnot, "An Essay on the Usefulness of Mathematical Learning", 1701)

"Imaginary numbers are a fine and wonderful refuge of the divine spirit almost an amphibian between being and non-being." (Gottfried Leibniz, 1702)

"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, etc. it is called Geometry." (Jacques Ozanam, "A Mathematical Dictionary: Or; A Compendious Explication of All Mathematical Terms", 1702)

"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 et al, "Recreations in Mathematics and Natural Philosophy", 1703)

"Further, it cannot escape anyone that for judging in this way about any event at all, it is not enough to use one or two trials, but rather a great number of trials is required. And sometimes the stupidest man|by some instinct of nature per se and by no previous instruction" (this is truly amazing)| knows for sure that the more observations of this sort that are taken, the less the danger will be of straying from the mark." (Jacob Bernoulli, "Ars Conjectandi" ["The Art of Conjecturing"], 1713

"It seems that to make a correct conjecture about any event whatever, it is necessary to calculate exactly the number of possible cases and then to determine how much more likely it is that one case will occur than another." (Jacob Bernoulli, "Ars Conjectandi" ["The Art of Conjecturing"], 1713))

"The probability of an Event is greater, or less, according to the number of Chances by which it may Happen, compar’d with the number of all the Chances, by which it may either Happen or Fail. […] Therefore, if the Probability of Happening and Failing are added together, the Sum will always be equal to Unit." (Abraham De Moivre, "The Doctrine of Chances", 1718)