“Primary causes are unknown to us; but are subject to simple and constant laws, which may be discovered by observation, the study of them being the object of natural philosophy.
Heat, like gravity, penetrates every substance of the universe, its rays occupy all parts of space. The object of our work is to set forth the mathematical laws which this element obeys. The theory of heat will hereafter form one of the most important branches of general physics.”

— Joseph Fourier , book The Analytical Theory of Heat

Source: The Analytical Theory of Heat (1878), Ch. 1, p. 1

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Joseph Fourier 4

French mathematician and physicist 1768–1830

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“The one intelligible theory of the universe is that of objective idealism, that matter is effete mind, inveterate habits becoming physical laws. But before this can be accepted it must show itself capable of explaining the tridimensionality of space, the laws of motion, and the general characteristics of the universe, with mathematical clearness and precision; for no less should be demanded of every Philosophy.”

Charles Sanders Peirce (1839–1914) American philosopher, logician, mathematician, and scientist

The Architecture of Theories (1891)

“Geometry is that of mathematical science which is devoted to consideration of form and size, and may be said to be the best and surest guide to study of all sciences in which ideas of dimension or space are involved. Almost all the knowledge required by navigators, architects, surveyors, engineers, and opticians, in their respective occupations, is deduced from geometry and branches of mathematics. All works of art constructed according to the rules which geometry involves; and we find the same laws observed in the works of nature. The study of mathematics, generally, is also of great importance in cultivating habits of exact reasoning; and in this respect it forms a useful auxiliary to logic.”

Robert Chambers (publisher, born 1802) (1802–1871) Scottish publisher and writer

Robert Chambers, Chambers's Information for the People (1875) Vol. 2 https://books.google.com/books?id=vNpTAAAAYAAJ

“This consideration must alter the form of our proposed inquiry; for the question being thus at least partly decided, since it is ascertained that we have rays of heat which give no light, it can only become a subject of inquiry whether some of these heat-making rays may not have a power of rendering objects visible, superadded to their now already established power of heating bodies.”

William Herschel (1738–1822) German-born British astronomer, technical expert, and composer

This being the case, it is evident that the onus probandi [burden of proof] ought to lie with those who are willing to establish such an hypothesis, for it does not appear that Nature is in the habit of using one and the same mechanism with any two of our senses. Witness the vibration of air that makes sound, the effluvia that occasion smells, the particles that produce taste, the resistance or repulsive powers that affect the touch—all these are evidently suited to their respective organs of sense.
Source: Sir William Herschel: His Life and Works (1880), Ch.4 "Life and Works" on his discovery of the infrared.

“To conclude, if we call light, those rays which illuminate objects, and radiant heat, those which heat bodies, it may be inquired whether light be essentially different from radiant heat? In answer to which I would suggest that we are not allowed, by the rules of philosophizing, to admit two different causes to explain certain effects, if they may be accounted for by one. …If this be a true account of the solar heat, for the support of which I appeal to my experiments, it remains only for us to admit that such of the rays of the sun as have the refrangibility of those which are contained in the prismatic spectrum, by the construction of the organs of sight, are admitted under the appearance of light and colors, and that the rest, being stopped in the coats and humors of the eye, act on them, as they are known to do on all the other parts of our body, by occasioning a sensation of heat.”

William Herschel (1738–1822) German-born British astronomer, technical expert, and composer

Source: Sir William Herschel: His Life and Works (1880), Ch.4 "Life and Works" on his discovery of the infrared light.

“The laws of thought are natural laws with which we have no power to interfere, and which are of course not to be in any way confused with the artificial laws of a country, which are invented by men and can be altered by them. Every science is occupied in detecting and describing the natural laws which are inflexibly observed by the objects treated in the Science.”

William Stanley Jevons (1835–1882) English economist and logician

Introduction, Lesson I: Definition and Sphere of the Science.
Elementary Lessons on Logic (1870)

“Pure mathematics is, in its way, the poetry of logical ideas. One seeks the most general ideas of operation which will bring together in simple, logical and unified form the largest possible circle of formal relationships. In this effort toward logical beauty spiritual formulas are discovered necessary for the deeper penetration into the laws of nature.”

Albert Einstein (1879–1955) German-born physicist and founder of the theory of relativity

1930s, Obituary for Emmy Noether (1935)

“Science Of Energetics. Although the mechanical hypothesis just mentioned may be useful and interesting as a means of anticipating laws, and connecting the science of thermodynamics with that of ordinary mechanics, still it is to be remembered that the science of thermodynamics is by no means dependent for its certainty on that or any other hypothesis, having been now reduced, to a system of principles, or general facts, expressing strictly the results of experiment as to the relations between heat and motive power. In this point of view the laws of thermodynamics may be regarded as particular cases of more general laws, applicable to all such states of matter as constitute Energy, or the capacity to perform work, which more general laws form the basis of the science of energetics, — a science comprehending, as special branches, the theories of motion, heat, light, electricity, and all other physical phenomena.”

William John Macquorn Rankine (1820–1872) civil engineer

Source: A Manual of the Steam Engine and Other Prime Movers (1859), p. 31

“The general laws of Nature are not, for the most part, immediate objects of perception.”

George Boole (1815–1864) English mathematician, philosopher and logician

Source: 1850s, An Investigation of the Laws of Thought (1854), p. 4; Ch. 1. Nature And Design Of This Work
Context: The general laws of Nature are not, for the most part, immediate objects of perception. They are either inductive inferences from a large body of facts, the common truth in which they express, or, in their origin at least, physical hypotheses of a causal nature serving to explain phenomena with undeviating precision, and to enable us to predict new combinations of them. They are in all cases, and in the strictest sense of the term, probable conclusions, approaching, indeed, ever and ever nearer to certainty, as they receive more and more of the confirmation of experience. But of the character of probability, in the strict and proper sense of that term, they are never wholly divested. On the other hand, the knowledge of the laws of the mind does not require as its basis any extensive collection of observations. The general truth is seen in the particular instance, and it is not confirmed by the repetition of instances.

“Nature, in providing us with combustibles on all sides, has given us the power to produce, at all times and in all places, heat and the impelling power which is the result of it. To develop this power, to appropriate it to our uses, is the object of heat-engines.”

Nicolas Léonard Sadi Carnot (1796–1832) French physicist, the "father of thermodynamics" (1796–1832)

p, 125
Reflections on the Motive Power of Heat (1824)

“The phenomenon of the production of motion by heat has not been considered from a sufficiently general point of view. We have considered it only in machines… [for which] the phenomenon is… incomplete. It becomes difficult to recognize its principles and study its laws. …[T]he principle of the production of motion by heat… must be considered independently of any mechanism or… particular agent. It is necessary to establish principles applicable not only to steam-engines but to all imaginable heat-engines, whatever the working substance and whatever the method by which it is operated.”

Nicolas Léonard Sadi Carnot (1796–1832) French physicist, the "father of thermodynamics" (1796–1832)

Reflections on the Motive Power of Heat (1824)

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Joseph Fourier 4

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