“Hitherto, the science of Man has been limited to researches… respecting some of its laws, to results deduced from single or insulated observations, and to theories often based on mere glimpses; and these constitute pretty nearly all the materials it possesses.”

Introductory
A Treatise on Man and the Development of His Faculties (1842)

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Adolphe Quetelet 52
Belgian astronomer, mathematician, statistician and sociolo… 1796–1874

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“A physical theory, like an abstract science, consists of definitions and axioms as first principles, and of propositions, their consequences; but with these differences:—first, That in an abstract science, a definition assigns a name to a class of notions derived originally from observation, but not necessarily corresponding to any existing objects of real phenomena, and an axiom states a mutual relation amongst such notions, or the names denoting them; while in a physical science, a definition states properties common to a class of existing objects, or real phenomena, and a physical axiom states a general law as to the relations of phenomena; and, secondly,—That in an abstract science, the propositions first discovered are the most simple; whilst in a physical theory, the propositions first discovered are in general numerous and complex, being formal laws, the immediate results of observation and experiment, from which the definitions and axioms are subsequently arrived at by a process of reasoning differing from that whereby one proposition is deduced from another in an abstract science, partly in being more complex and difficult, and partly in being to a certain extent tentative, that is to say, involving the trial of conjectural principles, and their acceptance or rejection according as their consequences are found to agree or disagree with the formal laws deduced immediately from observation and experiment.”

William John Macquorn Rankine (1820–1872) civil engineer

Source: "Outlines of the Science of Energetics," (1855), p. 121; Second paragraph

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“The results of a scrutiny of the materials of chemical science from a mathematical standpoint are pronounced in two directions. In the first we observe crude, qualitative notions”

J. R. Partington (1886–1965) British chemist

Introduction
Higher Mathematics for Chemical Students (1911)
Context: The results of a scrutiny of the materials of chemical science from a mathematical standpoint are pronounced in two directions. In the first we observe crude, qualitative notions, such as fire-stuff, or phlogiston, destroyed; and at the same time we perceive definite measurable quantities such as fixed air, or oxygen, taking their place. In the second direction we notice the establishment of generalizations, laws, or theories, in which a mass of quantitative data is reduced to order and made intelligible. Such are the law of conservation of matter, the laws of chemical combination, and the atomic theory.

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