On Mechanics (-1799)

"[...] 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)

"I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses; for whatever is not deduced from the phenomena is to be called a hypothesis, and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy." (Sir Isaac Newton, "Philosophiæ Naturalis Principia Mathematica" ["The Mathematical Principles of Natural Philosophy"], 1687)

"Moreover, it must be confessed that perception and that which depends upon it are inexplicable on mechanical grounds, that is to say, by means of figures and motions. And supposing there were a machine, so constructed as to think, feel, and have perception, it might be conceived as increased in size, while keeping the same proportions, so that one might go into it as into a mill. That being so, we should, on examining its interior, find only parts which work one upon another, and never anything by which to explain a perception. Thus it is in a simple substance, and not in a compound or in a machine, that perception must be sought for." (Gottfried W Leibniz, "Monadology", 1714)

"[...] the ideas which these sciences [Geometry, Theoretical Arithmetic and Algebra] involve extend to all objects and changes which we observe in the external world; and hence the consideration of mathematical relations forms a large portion of many of the sciences which treat of the phenomena and laws of external nature, as Astronomy, Optics, and Mechanics. Such sciences are hence often termed Mixed Mathematics, the relations of space and number being, in these branches of knowledge, combined with principles collected from special observation; while Geometry, Algebra, and the like subjects, which involve no result of experience, are called Pure Mathematics." (William Whewell, "The Philosophy of the Inductive Sciences Founded Upon Their History" Vol. 1, 1747)

"There must be a double method for solving mechanical problems: one is the direct method founded on the laws of equilibrium or of motion; but the other one is by knowing which formula must provide a maximum or a minimum. The former way proceeds by efficient causes: both ways lead to the same solution, and it is such a harmony which convinces us of the truth of the solution, even if each method has to be separately founded on indubitable principles. But is often very difficult to discover the formula which must be a maximum or minimum, and by which the quantity of action is represented." (Leonhard Euler, "Specimen de usu observationum in mathesi pura", Novi Commentarii academiae scientiarum Petropolitanae 6, 1756/57)

"Statics is the science of the equilibrium of forces. In general, force or power is the cause, whatever it may be, which induces or tends to impart motion to the body to which it is applied. The force or power must be measured by the quantity of motion produced or to be produced. In the state of equilibrium, the force has no apparent action. It produces only a tendency for motion in the body it is applied to. But it must be measured by the effect it would produce if it were not impeded. By taking any force or its effect as unity, the relation of every other force is only a ratio, a mathematical quantity, which can be represented by some numbers or lines. It is in this fashion that forces must be treated in mechanics." (Joseph-Louis de Lagrange, "Mechanique Analytique", 1788)

"The reader will find no figures in this work. The methods which I set forth do not require either constructions or geometrical or mechanical reasonings: but only algebraic operations, subject to a regular and uniform rule of procedure." (Joseph-Louis de Lagrange, "Mechanique Analytique", 1788)

"Natural processes should be judged different from mechanical ones because they are self-organizing." (Immanuel Kant, "Critique of Judgment", 1790)

"The knowledge of mechanics is one of those things that contribute to distinguish civilized nations from barbarians. From it the works of art derive much of their beauty and value; without it we can make very little progress in the knowledge of the works of nature. By this science we are enabled to improve every power and force in nature, and render the motions of the elements water, air, and fi re, subservient to the purposes of life." (George Adams, "Lectures on Natural and Experimental Philosophy" Vol. 3, 1794)