Engineers From France

"Abstain from all pleasantry which could wound."

"What motives have influenced the writers who have rejected all religious systems? Is it the conviction that the ideas which they oppose are all injurious to society? Have they not rather included in the same proscription religion and the abuse of it?"

"Show neither passion nor weariness in discussion."

"When discussion degenerates into dispute, be silent; this is not to declare yourself beaten."

"Never direct an argument against any one. If you know some particulars against your adversary, you have a right to make him aware of it to keep him under control, but proceed with discretion, and do not wound him before others."

"The Collision of Bodies. ...[I]n the collision of bodies there is always expenditure of motive power. Perfectly elastic bodies only form an exception, and none such are found in nature."

"How much modesty adds to merit! A man of talent who conceals his knowledge is like a branch bending under a weight of fruit."

"Men desire nothing so much as to make themselves envied."

"Why try to be witty? I would rather be thought stupid and modest than witty and pretentious."

"[[Light|[L]ight]] is generally regarded as the result of a vibratory movement of the ethereal fluid. Light produces heat, or at least accompanies the radiating heat, and moves with the same velocity as heat. Radiating heat is then a vibratory movement. It would be ridiculous to suppose that it is an emission of matter while the light which accompanies it could be only a movement."

"I do not know why these two expressions, good sense and common sense, are confounded. There is nothing less common than good sense."

"It must be that all honest people are in the galleys; only knaves are to be met with elsewhere."

"The strain of suffering causes the mind to decay."

"We say that man is an egotist, and nevertheless his sweetest pleasures come to him through others. He only tastes them on condition of sharing them."

"I rejoice for all the misfortunes which might have happened to me, and which I have escaped."

"Hope being the greatest of all blessings, it is necessary, in order to be happy, to sacrifice the present to the future."

"Life is a short enough passage. I am half the journey. I will complete the remainder as I can."

"In the nineteenth century Sadi Carnot combined the old idea that perpetual-motion machines are impossible (an early and incomplete version of the first law) with the (heat is a substance) to prove that in a heat engine a discharge of heat to the cold surroundings was inevitable. From this starting point, he and others deduced some remarkable conclusions about the efficiency of heat engines and about the properties of matter..."

"The more nearly an object approaches perfection, the more we notice its slightest defects."

"Recherché pleasures cause simple pleasures to lose all their attractions."

"To neglect the opportunity of an innocent pleasure is a loss to ourselves."

"One could... safely declare that 'Physics... can be defined as that subject which treats of the transformation of energy.' The philosophical version of Herakleitos and Empedokles... a continual cycle of changes and exchanges, had... crystallized into a quantitative physical theory. But this... picture... was... incomplete. For... there was a second, equally general and fundamental element in Nature—a directional one. This had first been formulated in the 1820s by the Mozart of modern physics, Sadi Carnot. ...Carnot started with the question: What proportion of the heat in any system is 'available' as a means of producing mechanical energy? ...Carnot demonstrated ...a one-hundred-per-cent-efficient engine could exploit only a fraction of the heat supplied to it... A 'super-efficient' machine which could exploit all the heat supplied, would be (as Carnot's mathematics proved) a machine... one could get out of it more energy than was supplied... In an ... physical changes could at most be perfectly reversible; [but] in normal cases they would result in the progressive... 'degradation' of mechanical energy by the production of unavailable heat. To characterize this... Clausius coined the word ... [T]he directional principle of Carnot and Clausias (which gave precise expression to Newton's insight that 'motion is more easily lost than got, and is continually upon the decrease') became the Second Law of Thermodynamics."

"It may sometimes be necessary to yield the right, but how is one to recover it when wanted?"

"Do nothing that all the world may not know."

"Love is almost the only passion that the good man may avow. It is the only one which accords with delicacy."

"In the present state of science... no operation is known by which heat can be absorbed into a body, without either elevating its temperature or becoming latent, and producing some alteration in its physical condition; and the fundamental axiom adopted by Carnot may be considered as still the most probable basis for an investigation of the motive power of heat; although this, and with it every other branch of the theory of heat, may ultimately require to be reconstructed on another foundation, when our experimental data are more complete. On this understanding the author of the present paper refers to Carnot's fundamental principle, as if its truth were thoroughly established."

"What happens... in a steam-engine... ? The caloric developed in the furnace by the effect of the combustion traverses the walls of the boiler, produces steam, and in some way incorporates itself with it. The latter carrying it away, takes it first into the cylinder, where it performs some function, and from thence into the condenser, where it is liquefied by contact with the cold water... [T]he cold water of the condenser takes possession of the caloric... It is heated by the intervention of the steam as if it had been placed directly over the furnace. The steam is here only a means of transporting the caloric."

"Clapeyron, in 1834, recalled attention to Carnot's reasoning, and usefully applied the principle of Watt's diagram of energy to the geometrical exhibition of the different quantities involved in the cycle of operations by which work is derived from heat by the temporary changes it produces in the volume or molecular state of bodies. He also first gave a representation of Carnot's processes in an analytical form. But for nearly twenty years after the appearance of Carnot's treatise little appears to have been done with reference to the theory of heat."

"Carnot's reasoning... to show that in the ascent of the piston in the cylinder, more work is done against external forces than is required to be done by them to produce the descent and restore the piston to its first position. And in order that Carnot's axiom may be applied with strictness, and yet with simplicity, it is better to consider a hypothetical, than the actual engine."

"According to the doctrine of the church, God resembles a proposing enigmas, and devouring those who cannot guess them."

"If we carefully examine the... cycle of operations we easily see that they are reversible, i.e., that the transference of the given amount of caloric back again... by performing the same operations in the opposite order, requires that we expend on the piston, on the whole, as much work as was gained during the direct operations. This most important idea is due to Carnot, and from it he deduces his test of a perfect engine, or one which yields from the transference of a given quantity of caloric from one body to another (each being at a given temperature) the greatest possible amount of work. And the test is simply that the cycle of operations must be reversible."

"The science of Thermodynamics, founded by the labors of these three illustrious men, has led to the most important developments in all departments of physical science. It has pointed out relations among the properties of bodies which could scarcely have been anticipated in any other way; it has laid the foundation for the Science of Chemical Physics; and, taken in connection with the kinetic theory of gases, as developed by Maxwell and Boltzmann, it has furnished a general view of the operations of the universe which is far in advance of any that could have been reached by purely dynamical reasoning."

"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."

"For a considerable portion of the present century, Davy's discoveries about heat were neglected, or only casually mentioned; but this was of comparatively little consequence, as their early reception might have kept back for a time the grand developments which must next be mentioned—immense strides in the theoretical and mathematical treatment of the subject, and to a considerable extent independent of the nature of heat. These are due to Fourier and Sadi Carnot, and it may well be said that it is in great part attributable to their remarkable works that the true theory of heat... received so rapidly its present enormous development. ...Very different in form and object from the systematic treatise of Fourier, is the profound and valuable essay of Sadi Carnot, Reflexions sur la Puissance Motrice du Feu, published in 1824. The author endeavours to determine how it is that heat produces mechanical effect..."

"An interesting theorem bearing his name and typical of projective geometry is as follows:—If two triangles ABC and A'B'C' are so related that lines joining corresponding vertices meet in a point O, then the intersections of corresponding sides will lie in a straight line A"B"C". It remained for Monge, the inventor of descriptive geometry... and others more than a century later to carry this development forward. Desargues's work was indeed practically lost until Poncelet in 1822 proclaimed him the Monge of his century."

"We owe to Desargues the theory of involution and of transversals; also the beautiful conception that the two extremities of a straight line may be considered as meeting at infinity, and that parallels differ from other pairs of lines only in having their points of intersection at infinity. He re-invented the and showed its application to the construction of gear teeth, a subject elaborated more fully later by La Hire."

"Perceiving that the practitioners of these arts ["...among others, the cutting of stones in architecture, that of sun-dials, that of perspective in particular"] had to burden themselves with the laborious acquisition of many special facts in geometry, he sought to relieve them by developing more general methods and printing notes for distribution among his friends."

"Desargues contented himself with enunciating general principles remarking:—"He who shall wish to disentangle this proposition will easily be able to compose a volume.""

"He gives the theory of involution of six points, but his definition of "involution" is not quite the same as the modern definition, first found in Fermat, but really introduced into geometry by Chasles. On a line take the point A as origin (souche), take also the three pairs of points B and H, C and G, D and F; then, says Desargues, if AB \cdot AH = AC \cdot AG = AD \cdot AF, the six points are in "involution." If a point falls on the origin, then its partner must be at an infinite distance from the origin. If from any point P lines be drawn through the six points, these lines cut any transversal MN in six other points, which are also in involution; that is, involution is a projective relation."

"Blaise Pascal... was one of the very few contemporaries who appreciated the worth of Desargues. He says in his Essais pour les coniques, "I wish to acknowledge that I owe the little that I have discovered on this subject to his writings.""

"In his chief work Desargues enunciates the propositions:— 1. A straight line can be considered as produced to infinity and then the two opposite extremities are united. 2. Parallel lines are lines meeting at infinity and conversely. 3. A straight line and a circle are two varieties of the same species. On these he bases a general theory of the plane sections of a cone."

"He met Descartes while employed by Cardinal Richelieu at the , and they with others met regularly in Paris for the discussion of the new Copernican theory and other scientific problems."

"Pascal made grateful acknowlegement to Desargues for his skill in projective geometry."

"After his own fashion, Desargues discussed cross ratio; poles and polars; Kepler's principle (1604) of continuity, in which a straight line is closed at infinity and parallels meet there; involutons; assymptotes at tangents at infinity; his famous theorem on triangles in perspective; and some of the projective properties of quadrilaterals inscribed in conics. Descartes greatly admired Desargue's invention, but happily for the future of geometry did not hesitate on that account to advocate for his own."

"Desargues also gives the theory of polar lines. What is called "" in elementary works is as follows: If the vertices of two triangles, situated either in space or in a plane, lie on three lines meeting in a point, then their sides meet in three points lying on a line, and conversely. This theorem has been used since by Brianchon, Sturm, Gergonne, and others. Poncelet made it the basis of his beautiful theory of homological figures."

"The beginning of the seventeenth century witnessed also a revival of . ...it remained for Girard Desargues... and for Pascal to leave the beaten track and cut out fresh paths. They introduced the important method of Perspective. All conics on a cone with circular base appear circular to an eye at the apex. Hence Desargues and Pascal conceived the treatment of the conic sections as projections of circles. Two important and beautiful theorems were given by Desargues: The one is on the "involution of the six points," in which a transversal meets a conic and an inscribed quadrangle; the other is that, if the vertices of two triangles, situated either in space or in a plane, lie on three lines meeting in a point, then their sides meet in three points lying on a line; and conversely. This last theorem has been employed in recent times by Brianchon, C. Sturm; Gergonne, and Poncelet. Poncelet made it the basis of his beautiful theory of homological figures."

"The influence exerted by the lectures of Desargues on Descartes, Pascal and the French geometricians of the seventeenth century was considerable; but the subject of projective geometry soon fell into oblivion, chiefly because the analytical geometry of Descartes was so much more powerful as a method of proof or discovery."

"Pascal greatly admired Desargues' results... Pascal's and Desargues writings contained some of the fundamental ideas of modern synthetic geometry."

"More than two hundred years before Poncelet, the important concept of a occurred independently to... Johann Kepler... and the French architect Girard Desargues... Kepler (in his Paralipomena in Vitellionem, 1604) declared that a parabola has two foci, one of which is infinitely distant in two opposite directions, and that any point on the curve is joined to this "blind focus" by a line parallel to the axis. Desargues (in his Brouillion project..., 1639) declared that parallel lines have a common end point at an infinite distance. ...And again ...When no point of a line is at a finite distance, the line itself is at an infinite distance... The groundwork was thus laid for Poncelet to derive projective space from ordinary space by postulating a common "line at infinity" for all the planes parallel to a given plane."

"Desargues the architect was doubtless influenced by what in his day was surrealism. In any event, he composed more like an artist than a geometer, inventing the most outrageous technical jargon in mathematics for the enlightenment of himself and the mystification of his disciples. Fortunately Desarguesian has long been a dead language."