Algèbre, Arithmétique et Géométrie. Classe de Troisième by C.; Hemery, C. Lebosse

By C.; Hemery, C. Lebosse

Cours conforme au programme du 23 juin 1962.

Table des matières :

Algèbre et Arithmétique

Leçon 1 — Rapports
Leçon 2 — Proportions
Leçon three — Racine carrée entière d’un nombre entier
Leçon four — Racine carré approchée. — Racine carrée exacte
Leçon five — Radicaux arithmétiques. — Racines d’un nombre relatif
Leçon 6 — Expressions algébriques. — Monômes
Leçon 7 — Polynômes
Leçon eight — Multiplication des monômes et des polynômes
Leçon nine — Identités remarquables
Leçon 10 ­— department des monômes et des polynômes. — Décomposition en facteurs
Leçon eleven — Fractions rationnelles
Leçon 12 — Équation du premiere degré à une inconnue
Leçon thirteen — Équations qui se ramènent au most suitable degré. — Équations littérales
Leçon 14 — Systèmes d’équations du most advantageous degré
    Élimination par substitution
    Élimination par addition
    Généralisations
Leçon 15 — Inéquation du ultimate degré à une inconnue
Leçon sixteen — Les problèmes d’algèbre
Leçon 17 — Fonctions et graphiques
Leçon 18 — Étude de l. a. fonction : y = ax
Leçon 19 — Étude de l. a. fonction : y = ax + b
Leçon 20 — functions de l. a. fonction : y = ax + b

Géométrie

I. Géométrie plane

Leçon 1 — Rapport de deux segments. — issues divisant un section dans un rapport donné
Leçon 2 — Théorème de Thalès
Leçon three — purposes du théorème de Thalès
    Propriété des bissectrices d’un triangle
    Constructions
Leçon four — Triangles semblables
    Premières applications
Leçon five — Cas de similitude des triangles
Leçon 6 — functions de l. a. similitude
Leçon 7 — kinfolk métriques dans le triangle rectangle
Leçon eight — Rapports trigonométriques
Leçon nine — family trigonométriques dans le triangle rectangle
Leçon 10 — kinfolk métriques dans le cercle
Leçon eleven — buildings géométriques
Leçon 12 — Polygones réguliers. — Périmètre du cercle
Leçon thirteen — Mesure des aires

II. Géométrie dans l’espace

Leçon 14 — Généralités sur le plan
Leçon 15 — Droites parallèles. — perspective de deux droites
Leçon sixteen — Droite et plan parallèles
Leçon 17 — Plans parallèles
Leçon 18 — Droite et plan perpendiculaires
Leçon 19 — Droites orthogonales. — Perpendiculaires et obliques
Leçon 20 — Angles dièdres
Leçon 21 — Plans perpendiculaires
Leçon 22 — Projections orthogonales. — Vecteurs

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Practically no other sources of funds, which in the past had sponsored most scientific research, seem to be able to afford the expenses required by large-scale research, although in an affluent country private sponsorship would not seem impossible, if, say, a number of institutions contributed toward a common fund. Whoever sponsors research on a large scale must be convinced that it is needed, that it is useful, that it advances humanity. Generally, the arguments for scientific effort, listed in order of increasing range of importance and time, are that ( 1 ) , far from being wasted, the funds granted for research enable people of many professions to be employed and trained in advanced thought and skill; ( 2 ) immediate applications, or technological fallout, result since many of the techniques and instruments developed for research are also useful for other purposes; ( 3 ) scientific knowledge gained in one field is applicable in many other fields, particularly knowledge about physical forces that are ultimately responsible for any phenomenon of nature has very wide applications; ( 4 ) knowledge is a part of our heritage and civilization which must be advanced and passed on to future generations, and scientifically objective procedure is an important part of education and should promote the improvement in human attitudes that is very much needed if substantial gains are to be accomplished by mankind in the future; ( 5 ) the greatest achievement may lie ahead when, with the help of science, man might begin to understand himself, his purpose, and his destiny.

To this end science contributes objectivity of thought, an essential part of any kind of advancement. Exploration of nuclear forces has led to "high-energy" or "particle" physics. The theory of quantum mechanics had to be conceived to explain atomic phenomena. A picture involving waves in association with particles had to be invoked. A dualism, that waves and particles are equivalent, was established, as energy is equivalent to mass. This is the way nature operates. It seems mysterious to us according to familiar experience with larger objects.

They are exploring nature because nature is here to be explored and they seemed quite justified in their attitude since successful research effort often does not tolerate any distractions, but if a research effort were slowed down because no one is inclined to develop the arguments necessary to obtain funds for vigorous pursuit of a science, then a change in approach would be needed. Science is too valuable an effort to be retarded by lack of convincing arguments which so obviously exist but need proper formulation.

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