In 1882 Professor Victor d'Hondt, of the University of Ghent in Belgium, proposed the system of party proportionality that bears his name, which is widely used in Europe today. ... D'Hondt proposed that one should allocate the seats to the parties one at a time. At each stage, a party $P_{i}$ with $v_{i}$ votes and (currently) $s_{i}$ seats is assigned the quotient $\Large\frac{v_i}{s_i+1}$, and the next seat is given to the party with the largest quotient. ... The Frenchman A Sainte-Laguë devised his arithmetic-mean system (but in the form 1, 3, 5, 7 ... ) in 1910, in order to correct the tendency of d'Hondt's rule to favour the large parties.

... at the theoretical level is probably the soundest of all the measures.

... while going to ensure the restoration of a telephone line himself, under a violent bombardment.

We will call a network a set of points or crossroads which will consist of vertices, joined together by lines or sides which will be the paths of the network. The shape of these paths is of no interest and the only thing that matters for two given points A and B is whether or not they are joined by one or more paths. Two networks will be said to be homeomorphic if one can establish between their vertices on the one hand, as well as between their paths on the other hand, a reciprocal and unambiguous correspondence. Two homeomorphic networks will be considered identical. It follows that the shape of the diagrams, planes or curves, by which it may be convenient to represent networks, has no theoretical importance. The location of the vertices can be arbitrary as well as the shape of the paths joining two given points. Care must be taken not to confuse the graphic crossing of two paths drawn on paper with a crossroads.

The study of networks can be pursued in many different ways and each of the definitions posed at the beginning makes it possible to initiate new research. We simply wanted to study, as best we could, two of the simplest cases one could think of. Simple as they are, they show, we believe, the complexity of the questions raised and the diversity of the methods which it is essential to employ. The subject, limited as it may seem at first glance, is in fact .. very vast and seems quite difficult. We have systematically left aside, so as not to lengthen the thesis, not only all the research that we have already started on spherical networks, but also all the practical applications of networks. Many questions of higher arithmetic, positional geometry, game theory, for example the research of Lucas, is immediately related to network theory. Other applications of more immediate use could also be considered, such as certain questions of graphic statics or especially of stereochemistry. We couldn't think of addressing them here.

The appearance in 1926 of 'Les Réseaux (ou Graphes)' was an important milestone in the historical development of graphs and their applications, from its first introduction by Euler (1735) with his famous problem on the bridges of Königsberg, to some early applications in chemical theory with the graphs of organic molecules. Most of the research in graph theory in the beginning of the last century still came from mathematical games and puzzles, but in his introduction, Sainte-Laguë seemed to be convinced of the great potential of applications of graph theory. Sainte-Laguë's book was the first textbook devoted to the study of graphs, containing most of what was known at his time, as for example, the four colour problem. In many aspects his book is very modern, by its subject, its presentation, and with many examples. It is interesting that many important notions had already been defined: trees, centres, chains, cycles, Eulerian cycles, Hamiltonian cycles, etc., although some of the notations are not the ones we use today.

His classes enjoyed considerable success, unequalled up to that time, and one of his lectures had around 2500 listeners, requiring him to give it three times in the large 900-seat Paul Painlevé amphitheatre at the Conservatoire National des Arts et Métiers. His warm, loud voice filled the lecture theatre, and his lectures were lively, fast, and clear. When teaching mathematics to practitioners, he insisted on the necessity of theoretical, numerical, and graphical exercises, and also on the need to distinguish between rigorous reasoning and that which is not rigorous, as well as the importance of using correct language. "We must not respond to the students' desire to know only recipes," he said. A forerunner in what may now be called 'new educational technologies', from 1928 onwards, he also used films for his geometry lessons.

... participate in the preparation of school youth, and to study and to bring about all the reforms concerning education.

We are not afraid to call the current crisis a crisis of our economic regime and consider participating in a study of ways to adapt the general economy to new conditions. We feel that the world is in the process of being renovated and that we can no longer, as immediately after the war, wait for others to think for us, intellectual workers. The new regime must be with our support, otherwise it will be against us.

Capitalism, considered here simply as an economic phenomenon and a financial system, seems to have had its day. It has fulfilled its role and it has done great things just as feudalism once did, but in more recent times it has not been able to foresee anything, or to organise anything.

In the 1937 brochure of the Section des Mathématiques, André Sainte-Laguë is listed as the secretary and organiser of the exhibition. The other committee members were Émile Borel (president), Paul Montel (vice-president), Raoul Bricard and Georges Darmois. In Salle 31 (Room 31), we have the following: "Three albums of curves by A Sainte-Laguë, present 50 curves each to the visitors: algebraic, transcendental, and various others."

For those visitors who are fascinated by the research carried out by engineers, and who rave at the wonders of modern industry, the organisers presented some of the properties of the strength of materials in the simple and easily assimilated form of a film. The film, 'De la similitude des longueurs et des vitesses' Ⓣ was written by André Sainte-Laguë.

Even more in times of war than in times of peace, 'trade unionism' must be synonymous with 'solidarity'.

He participated in the underground resistance in September 1940 and, known to be of a liberal mind, he was arrested by the Germans at his home in early October 1941 and imprisoned. But he knew how to remain discreet, and after many interrogations, the Germans, not finding evidence of his participation in clandestine activities, released him. When he resumed his class, he simply said to his pupils, "Gentlemen, I have been able to reflect for a long time, where I was, on the properties of unicursal curves ... ."

It was not until the Liberation that they learned that he had been a leader of the Organisation Civile et Militaire. He was decorated with the medal of the Resistance, and was appointed a member of the Provisional Consultative Assembly.

A cousin of my mother's, Guy Iliovici, a professor of mathematics in the Lycée Saint-Louis, also remained in Paris and wore a yellow star. Because he was Jewish, he lost his job, but his colleague and close friend Sainte-Laguë gave him half of his salary. He was deported with his wife Suzanne and his daughter Janine; they never returned.

At first prompted by what is done in aviation, I applied the laws of air resistance to insects, and I arrived with A Sainte-Laguë at this conclusion that their flight is impossible.

This myth stems from a well-known story of some engineers who proved that bumblebees shouldn't be able to fly because their wings are too small for the size of their bodies. In reality, bumblebees fly in quite a complicated way with their four wings, they don't just flap them up and down which probably would make it impossible for them to fly. In fact, they flap their wings front to back and simultaneously rotate them, like a figure-8, to create enough lift!

Dominique Sainte-Laguë, granddaughter of André Sainte-Laguë (1882-1950), professor of 'General Mathematics with a View to Applications' at the National Conservatory of Arts and Crafts from 1938 to 1950, has just donated to the central library of the Conservatoire National des Arts et Métiers (CNAM) a set documents related to her grandfather's activities. This gift, made up of printed matter, books and off-prints and manuscripts, as well as a set of photographs and glass plates that served as conference materials, provides a better understanding of the popularising and teaching activity of this pioneer of new educational technologies and graph theory.
...
This fund now enriches the collections of the CNAM, which did not keep all the publications of André Sainte-Laguë, and allows us to better understand his activity as a lecturer and writer, through numerous off-prints, as well as a set of articles published in the press and the manuscripts of his works such as that of 'La Machine humaine' Ⓣ, published by Fayard under the title 'De l'homme au robot' Ⓣ in 1953. The knowledge of the mathematician and the teacher, as well as that of his methods will no doubt benefit from the study of his manuscript notebooks.