On Arithmetic (1300 - 1699)

"Music submits itself to principles which it derives from arithmetic." (St. Thomas d'Aquin," Summa theologica", 1485)

"[...] if the worth of the arts were measured by the matter with which they deal, this art - which some call astronomy, others astrology, and many of the ancients the consummation of mathematics - would be by far the most outstanding. This art which is as it were the head of all the liberal arts and the one most worthy of a free man leans upon nearly all the other branches of mathematics. Arithmetic, geometry, optics, geodesy, mechanics, and whatever others, all offer themselves in its service." (Nicolaus Copernicus, "On the Revolutions of the Heavenly Spheres", 1543)

"The sciences are taught in following order: morality, arithmetic, accounts, agriculture, geometry, longimetry, astronomy, geomancy, economics, the art of government, physic, logic, natural philosophy, abstract mathematics, divinity, and history." (AbulFazl ibn Mubarak, "Ain-i-Akbery", cca.1590)

"It is true that not every geometric construction is elegant, for each particular problem has its own refinements. It is also true that [that construction] is preferred to any other that makes clear not the structure of a work from an equation but the equation from the structure; thus the structure demonstrates itself. So a skillful geometer, although thoroughly versed in analysis, conceals the fact and, while thinking about the accomplishment of his work, sheds light on and explains his problem Then, as an aid to the arithmeticians, he sets out and demonstrates his theorem with the equation or proportion he sees in it." (François Viète, "On the Meaning and Components of Analysis and on Matters Useful to Zetetics", 1591)

"Thus the analysis of angular sections involves geometric and arithmetic secrets which hitherto have been penetrated by no one." (François Viète, cca 1615)

"Mathematic is either Pure or Mixed: To Pure Mathematic belong those sciences which handle Quantity entirely severed from matter and from axioms of natural philosophy. These are two, Geometry and Arithmetic; the one handling quantity continued, the other dissevered. [...] Mixed Mathematic has for its subject some axioms and parts of natural philosophy, and considers quantity in so far as it assists to explain, demonstrate and actuate these." (Francis Bacon, "De Augmentis", 1623)

"And having thus passed the principles of arithmetic, geometry, astronomy, and geography, with a general compact of physics, they may descend in mathematics to the instrumental science of trigonometry, and from thence to fortification, architecture, engineering, or navigation. And in natural philosophy they may proceed leisurely from the history of meteors, minerals, plants, and living creatures, as far as anatomy. Then also in course might be read to them out of some not tedious writer the institution of physic. […] To set forward all these proceedings in nature and mathematics, what hinders but that they may procure, as oft as shall be needful, the helpful experiences of hunters, fowlers, fishermen, shepherds, gardeners, apothecaries; and in other sciences, architects, engineers, mariners, anatomists." (John Milton, "On Education", 1644)

"For, Mathematical Demonstrations being built upon the impregnable Foundations of Geometry and Arithmetick, are the only Truths, that can sink into the Mind of Man, void of all Uncertainty; and all other Discourses participate more or less of Truth, according as their Subjects are more or less capable of Mathematical Demonstration." (Christopher Wren, [lecture at Gresham College] 1657)

"Indeed, many geometric things can be discovered or elucidated by algebraic principles, and yet it does not follow that algebra is geometrical, or even that it is based on geometric principles (as some would seem to think). This close affinity of arithmetic and geometry comes about, rather, because geometry is, as it were, subordinate to arithmetic, and applies universal principles of arithmetic to its special objects." (John Wallis, "Mathesis Universalis", 1657)

"The method I take to do this is not yet very usual; for instead of using only comparative and superlative Words, and intellectual Arguments, I have taken the course (as a Specimen of the Political Arithmetic I have long aimed at) to express myself in Terms of Number, Weight, or Measure; to use only Arguments of Sense, and to consider only such Causes, as have visible Foundations in Nature." (William Petty, "Essays in Political Arithmetic", 1679)