"Its [mathematical analysis] chief attribute is clearness; it has no means for expressing confused ideas. It compares the most diverse phenomena and discovers the secret analogies which unite them. If matter escapes us, as that of air and light because of its extreme tenuity, if bodies are placed far from us in the immensity of space, if man wishes to know the aspect of the heavens at successive periods separated by many centuries, if gravity and heat act in the interior of the solid earth at depths which will forever be inaccessible, mathematical analysis is still able to trace the laws of these phenomena. It renders them present and measurable, and appears to be the faculty of the human mind destined to supplement the brevity of life and the imperfection of the senses, and what is even more remarkable, it follows the same course in the study of all phenomena; it explains them in the same language, as if in witness to the unity and simplicity of the plan of the universe, and to make more manifest the unchangeable order which presides over all natural causes." (Baron Jean-Baptiste-Joseph Fourier, "Théorie Analytique de la Chaleur", 1822)
"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." (Jean-Baptiste-Joseph Fourier, "The Analytical Theory of Heat", 1822)
"The aim of every science is foresight. For the laws of established observation of phenomena are generally employed to foresee their succession. All men, however little advanced make true predictions, which are always based on the same principle, the knowledge of the future from the past." (Auguste Compte, "Plan des travaux scientifiques nécessaires pour réorganiser la société", 1822)
"The effects of heat are subject to constant laws which cannot be discovered without the aid of mathematical analysis. The object of the theory is to demonstrate these laws; it reduces all physical researches on the propagation of heat, to problems of the integral calculus, whose elements are given by experiment. No subject has more extensive relations with the progress of industry and the natural sciences; for the action of heat is always present, it influences the processes of the arts, and occurs in all the phenomena of the universe." (Jean-Baptiste-Joseph Fourier, "The Analytical Theory of Heat", 1822)
"Machines which do not receive their motion from heat [...] can be studied even to their smallest details by the mechanical theory. [...] A similar theory is evidently needed for heat-engines. We shall have it only when the laws of Physics shall be extended enough, generalized enough, to make known beforehand all of the effects of heat acting in a determined manner on any body." (N Lazare S Carnot, "Reflections on the Motive Power of Heat and on Machines Fitted to Develop Power", 1824)
"Machines which do not receive their motion from heat [...] can be studied even to their smallest details by the mechanical theory. [...] A similar theory is evidently needed for heat-engines. We shall have it only when the laws of Physics shall be extended enough, generalized enough, to make known beforehand all of the effects of heat acting in a determined manner on any body." (Nicolas L S Carnot, "Reflections on the Motive Power of Heat and on Machines Fitted to Develop Power", 1824)
"There are no rules or models; that is, there are no rules except general laws of nature which hover over art and special laws which apply to specific subjects." (Victor M Hugo, "Cromwell", 1827)
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