Engineers From France

"Kepler (and Desargues) regarded the two "ends" of the ["straight"] line as meeting at "infinity" so that the line has the structure of a circle. In fact, Kepler actually thought of a line as a circle with its center at infinity."

"One of the first important steps to be taken in modern times... was due to Desargues. In a work published in 1639 Desargues set forth the foundation of the theory of four harmonic points, not as done today but based on the fact that the product of the distances of two conjugate points from the center is constant. He also treated the theory of poles and polars, although not using these terms."

"The discovery of a method for correct perspective is usually attributed to... Brunelleschi... The first published method appears in... On Painting [Della Pittura] by Alberti. ...Alberti's veil, used a piece of transparent cloth, stretched on a frame... viewing the scene with one eye... fixed... one could trace the scene directly onto the veil. ...The mathematical setting... is the family of lines ("light rays") through the point (the "eye"), together with the plane... (the "veil"). ...In this setting, the problems of perspective and were not very difficult, but the concepts were... a challenge to traditional geometric thought. Contrary to Euclid, one had... (i) Points at infinity ("vanishing points") where parallels met. (ii) Transformations that changed lengths and angles (projections). The first to construct a mathematical theory incorporating these ideas was Desargues,... although the idea of points at infinity had already been used by Kepler..."

"The book of Desargues (1639), Brouillon project d'une atteinte aux événemens des recontres du cône avec un plan (Schematic Sketch of What Happens When a Cone Meets a Plane), suffered an extreme case of delayed recognition, being completely lost for 200 years."

"The famous geometer Desargues worked on the lines of Kepler and is now commonly credited with the authorship of some of the ideas of his predecessor. ...the oneness of opposite infinities followed simply and logically from a first principle of Desargues, that every two straight lines, including parallels, have or are to be regarded as having one common point and one only. A writer of his insight must have come to this conclusion, even if the paradox had not been held by Kepler, Briggs, and we know not how many others, before Desargues wrote. ...Desargues must have learned directly or indirectly from the work in which Kepler propounded his new theory of these points, first called by him the Foci (foyers), including the modern doctrine of real points at infinity."

"... and more recently, Bernard Cache, have argued that Girard Desargues' mathematics provided a model for Leibniz's monad. ...Desargues was a founder of projective geometry, which offers a mathematical model for the intuitive notions of perspective and horizon by studying what remains invariable in projections. Outlining the concept of the "invariant," he gives his name to the "Desargues theorem," focusing on homological triangles. His disciple was the engraver, , author of a Treatise on Projections and Perspective (1665), who later taught linear perspective to stone cutters, carpenters, engravers, manufacturers of instruments and, less successfully, to painters. The perspective that Bosse teaches implicitly introduces the idea of infinity, in that he uses parallel lines with an infinitely extending vanishing point... Moreover, permeated by the knowledge of Desargues, Bosse develops a method for tracing shadows, which was inspired by his master."

"Girard Desargues... gave some courses of gratuitous lectures in Paris from 1626 to about 1630 which made a great impression upon his contemporaries. Both Descartes and Pascal had a high opionion of his work and abilities, and both made considerable use of the theorems he had enunciated."

"In 1636 Desargues issued a work on perspective; but most of his researches were embodied in his Brouillon project on conics, published in 1639, a copy of which was discovered by Chasles in 1845."

"Desrgues commences [in the Brouillon project] with a statement of the doctrine of continuity as laid down by Kepler: thus the points at the opposite ends of a straight line are regarded as coincident, parallel lines are treated as meeting at a point at infinity, and parallel planes on a line at infinity, while a straight line may be considered as a circle whose center is at infinity. The theory of involution of six points, with its special cases, is laid down, and the projective property of pencils in involution is established. The theory of polar lines is expounded and its analogue in space suggested. A tangent is defined as the limiting case of a secant, and an asymptote as a tangent at infinity. Desargues shows that the lines which join four points in a plane determine three pairs of lines in involution on any transversal, and from any conic through the four points another pair of lines can be obtained which are in involution with any two of the former. He proves that the points of intersection of the diagonals and the two pairs of opposite sides of any quadrilateral inscribed in a conic are a conjugate triad with respect to the conic, and when one of the three points is at infinity its polar is a diameter; but he fails to explain the case in which the quadrilateral is a parallelogran, although he had formed the conception of a straight line which was wholly at infinity. The book, therefore, may be fairly said to contain the fundamental theorems on involution, homology, poles and polars, and perspective."

"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."

"The researches of Kepler and Desargues will serve to remind us that as the geometry of the Greeks was not capable of much further extension, mathematicians were now beginning to seek for new methods of investigation, and were extending the conceptions of geometry. The invention of analytical geometry and of the infinitesimal calculus temporarily diverted attention from pure geometry, but at the beginning of the last century there was a revival of interest in it, and since then it has been a favourite subject of study with many mathematicians."

"Hardly less interesting than the new ideas of Descartes and Cavalieri are those of their contemporary Desargues... who made important researches in geometry. But for the still more brilliant geometrical achievements of Descartes, these might have led to the immediate development of projective geometry, the elements of which are contained in Desargues's work."

"In general this geometry instead of dealing with definite triangles, polygons, circles, etc., in the Euclidean manner, is based on a consideration of all points of a straight line, of all lines through a common point and of the possible effects of setting up an orderly one-to-one correspondence between them. In particular, Desargues makes a comparative study of the different plane sections of a given cone, deducing from known properties of the circle analogous results for the other conic sections."

"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."

"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 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."

"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."

"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."

"In the following work, I have endeavoured to exhibit the full extent of the Military and Naval Forces which the government of Great Britain can bring into the field, or launch upon the ocean. I have likewise described the connection of these forces with the government of the country, and also the discipline usually exercised in order to produce a hardihood in battle, invulnerable to fear and unassailable by cowardice. My observations on these subjects were derived from a residence of five years in England; during which time I was constantly employed in visiting and viewing every object and institution worthy of notice relative to the British Army and Navy."

"For 12 years I have had the honor of teaching geometry and mechanics applied to the arts, in favor of the industrial class... on the most important questions to the well-being, education, and morality of the workers, to the progress of national industry, to the development of all means of prosperity that work can produce for the splendor and happiness of our country."

"It is to the director of workshops and factories that it is suitable to make, by means of geometry and applied mechanics, a special study of all the ways to economize the efforts of workers... For a man to be a director of others, manual work has only a secondary importance; it is his intellectual ability (force intellectuelle) that must put him in the top position, and it is in instruction such as that of the Conservatory of the Arts and Professions, that he must develop it."

"I found myself obliged, through perhaps unique circumstances, to devote myself to my mathematical research, almost without help, advice or even books... Endlessly occupied by a thousand different matters and constrained my state duties, it is the work of an engineer that I herewith present and not the fruit of the meditations of a savant."

"Charles Dupin's Discourse on the Condition of the Workers (1873) introduced such concepts as time study and balanced ."

"In the 19th century, the French geometer Charles Pierre Dupin discovered a nonspherical surface with circular lines of curvature. He called it a cyclide in his book, Applications de Geometrie published in 1822. Recently, cyclides have been revived for use as surface patches in computer aided geometric design (CAGD). Other applications of eyelides in CAGD are possible (e.g., variable radius blending) and require a deep understanding of the geometry of the cyclide."

"The first appears to have been made by Baron Charles Dupin in 1826 to illustrate an address to the Conservatoire des Arts et Metiers in Paris. The map shows the number of persons per male child in school for each department and is the first moral ."

"Of the early management pioneers, history has provided us with the best records for four men: Robert Owen, Charles Babbage, Andrew Ure, and Charles Dupin... Ure knew the French engineer and management writer Charles Dupin, and when Dupin visited Great Britain in 1816–1818, Ure escorted him around the Glasgow factories. Dupin commented that many of the managers of these factories were Ure’s own students."

"The total extent to which steam power is applied in Great Britain was estimated by Baron Dupin, 1825, to be equivalent to the power of 320,000 horses in constant action; and since that period it has prodigiously increased, independently of our rapidly extending railways. To this immense command of power our country owes much of its commercial prosperity, besides a vast addition to the comforts and conveniences of life."

"Amongst the important results of the recent attempts to extend Science to the labouring classes, maybe ranked the elementary treatises published by Baron Dupin. Possessing an extraordinary fund of scientific information, as well as of practical knowledge collected during a period of twenty years, in the workshops and manufacturing establishments of the most enlightened nations of Europe, combined with a singular degree of clearness, elegance, and ingenuity, in mathematical and physical expositions, this distinguished individual might have continued to delight and instruct inquirers of the highest description, by works classical and profound, but without having witnessed the occurrences alluded to, he might never have directed his attention and his efforts to this most interesting object, the improvement of humble and neglected intellect."

"If ever, in the British Islands, the useful citizen should lose these virtues, we may be sure, that for England as well as for any other country, notwithstanding the protection of the most formidable navy, notwithstanding the foresight and activity of diplomacy the most extended, and of political science the most profound, the vessels of a degenerate commerce, repulsed from every shore would speedily disappear from those seas whose surface they now cover with the treasures of the universe, bartered for the treasures of the industry of the three kingdoms."

"The successes obtained in the government of the arts, are similar to the successes obtained in the government of men. We may succeed for a time, by fraud, by surprise, by violence: we can succeed permanently only by means directly opposite. It is not alone the courage, the intelligence, the activity of the manufacturer and the merchant which maintain the superiority of the productions and the commerce of their country; it is far more their wisdom, their economy, above all their probity."

"This is what it behoves us to know: as Frenchmen, for the advantage of France; as friends of all humanity, by that just and generous sentiment which makes us feel interest in the dignity, the peace, the independence, the happiness of all nations, on whatever spot of the globe nature may have placed their country."

"The French botanist and chemist Henri-Louis Duhamel de Monceau (1700–1782) identified a fungal disease on the bulbs of saffron crocus (now named Helicobasidium purpureum) and illustrated its sclerotia on the bulbs. His report was read to the Academie royale des Sciences in April 1728; it was “wellconceived, thorough, and conclusive, and led to his election as adjoint chimiste in the same year” (Eklund 1971:223). Duhamel discovered that this fungus spreads underground from one bulb to another. In his Éléments d’agriculture (two volumes, 1762; English edition, 1764), he also accepted insects as a cause of some plant diseases."

"This Duhamel has invented an infinity of machines which serve no purpose, has written and translated a multitude of books on agriculture, of which it is not known if they have any useful result, that is still awaited."

"Though he loved many innovations in science and devoted his life to introduce useful ones in the arts, he didn't like them in politics and even less in the statutes of the academies"

"New “agronomy,” [was] an experimental science of agriculture founded around midcentury by the chemist and botanist Henri-Louis Duhamel du Monceau"

"There is nobody who is not surprised of the small price of pins; but we shall be even more surprised, when we know how many different operations, most of them very delicate, are mandatory to make a good pin. We are going to go through these operations in a few words to stimulate the curiosity to know their detail; this enumeration will supply as many articles which will make the division of this work... The first operation is to have brass go through the drawing plate to calibrate it."

"To manage is to forecast and plan, to organize, to command, to coordinate and to control. To foresee and plan means examining the future and drawing up the plan of action. To organize means building up the dual structure, material and human, of the undertaking. To command means binding together, unifying and harmonizing all activity and effort. To control means seeing that everything occurs in conformity with established rule and expressed demand."

"Every employee in an undertaking — workman, foreman, shop manager, head of division, head of department, manager, and if it is a state enterprise the series extends to the minister or head of a state department — takes a larger or smaller share in the work of administration, and has, therefore, to use and display his administrative faculties. By administrative knowledge we mean planning, organization, command, coordination, and control: it can be elementary for the workman, but must be very wide in the case of employees of high rank, especially managers of big concerns. Everyone has some need of administrative knowledge."

"# satisfying shareholders and employees; labor and management."

"# coordination of all efforts towards the overall goal;"

"# ensuring good relations between the various departments and with the outside world;"

"# recruiting, organizing and directing the workforce;"

"# ensuring that unity of action, discipline, anticipation, activity, order, etc., exist in all parts of the enterprise;"

"One could define the administrative department by saying that it includes everything that is not part of the other departments, but one can define it in a more positive manner by saying that it is specifically responsible for;"

"According to the dictionary, to administer is to govern, or to manage a public or private business. It means, therefore, to seek to make the best possible use of the resources available in achieving the goal of the enterprise. Administration includes, therefore, all the operations of the enterprise. But as a result of the usual way of organizing things to facilitate the running of the business, a certain number of activities constitute the special departments; the technical department, the commercial department, the financial department, etc., and the scope of the administrative department is found to be reduced accordingly."

"In my opinion, it is the industry concerned which should have the chief say in the question of the amount of theoretical training required. It is the industry which uses the products of the schools, and, like every consumer, it has the right to make its wishes known."

"Administration, which calls for the application of wide knowledge and many personal qualities, is above all the art of handling men, and in this art, as in many others, it is practice that makes perfect. This is one of the reasons why we should release our future engineers for practical work as early as possible; there are many drawbacks to staying too long at school."

"Industry, which needs young men who are healthy, tractable, unpretentious and, I would even say, full of illusions, often receives engineers who are tired out, weak in body, and less ready than one could wish to take modest jobs and work so hard that everything seems easy to them. I am convinced that they could begin practical work much earlier and just as well prepared, by leaving things which are not used in practice out of their school education."

"Would you like to know, for instance, to what extent higher mathematics is used in our two great industries? Well, it is never used at all. Having found this to be the case in my own experience, after quite a long career, I wondered whether I was not an exception; so I made enquiries, and I found that it was a general rule that neither engineers nor managers used higher mathematics in carrying out their duties. We must, of course, learn mathematics that goes without saying but the question is how much must we learn? Up to the present this point has nearly always been decided simply by professors, but it seems to me to be a question in which professors do not count very much, and in which they count less as they become more learned and more devoted to their work. They would like to pass on all their scientific knowledge and they find that their pupils always leave them too soon."

"Every employee in an undertaking, then, takes a larger or smaller share in the work of administration, and has, therefore, to use and display his administrative faculties. This is why we often see men, who are specially gifted, gradually rise from the lowest to the highest level of the industrial hierarchy, although they have only had an elementary education. But young men, who begin practical work as engineers soon after leaving industrial schools, are in a particularly good position both for learning administration and for showing their ability in this direction, for in administration, as in all other branches of industrial activity, a man’s work is judged by its results."