By Lebossé C., Hémery C.

Desk des matières :

Livre I. — Calcul algébrique

Première leçon. — Nombres algébriques
    Addition des nombres algébriques
    Sommes algébriques
    Propriétés des rapports
Deuxième leçon. — Puissances. Racines d’un nombre arithmétique. Racines d’un nombre algébrique
Troisième leçon. — Égalités. Rapports égaux. Proportions. Inégalités
Quatrième leçon. — Vecteurs. Relation de Chasles
Cinquième leçon. — Expressions algébriques. Monômes. Polynômes
Sixième leçon. — Multiplication des monômes et des polynômes. Identités remarquables
Septième leçon. — department des monômes et des polynômes. Identités remarquables
Huitième leçon. — Fractions rationnelles. Expressions irrationnelles

Livre II. — Le most advantageous degré

Neuvième leçon. — Équation du optimal degré à une inconnue
Dixième leçon. — Équations se ramenant au ideal degré. *Équations irrationnelles
Onzième leçon. — Inéquation du leading degré à une inconnue
Douzième leçon. — Signe du binôme du best degré. *Applications aux inéquations
Treizième lecon. — Systèmes d’équations du prime degré à deux inconnues
    I. Élimination par substitution
    II. Élimination par addition
Quatorzième leçon. — *Systèmes d’équations du most advantageous degré (suite)
Quinzième leçon. — Systèmes d’équations à plusieurs inconnues
    Systèmes particuliers
Seizième leçon. — Problèmes du most effective degré

Livre III. — Les fonctions

Dix-septième leçon. — Généralités sur les fonctions. Coordonnées et graphiques
Dix-huitième leçon. — Étude de los angeles fonction : y = ax
Dix-neuvième leçon. — Étude de l. a. fonction : y = ax + b
Vingtième leçon. — functions de l. a. fonction linéaire
Vingt et unième leçon. — Étude de los angeles fonction : y = ax²
Vingt-deuxième leçon. — Étude de l. a. fonction : y = 1/x
Vingt-troisième leçon. — Étude de l. a. fonction : y = a/x

Livre IV. — Le moment degré

Vingt-quatrième lecon. — Équation du moment degré
Vingt-cinquième leçon. — *Relations entre les coefficients et les racines
Vingt-sixième leçon. — *Signe des racines
Vingt-septième leçon. — *Équations et systèmes se ramenant au moment degré
Vingt-huitième leçon. — *Trinôme du moment degré
Vingt-neuvième leçon. — *Inéquations du moment degré. Applications
Trentième leçon. — Problèmes du moment degré

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Extra resources for Algèbre : Classe de Seconde des Lycées et Collèges. Programme 1947

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I realise this. However, you might like to use these two new arrivals to show that 1 7 41 239 577 99 17 3 < < < < 2< < < < 1 5 29 169 408 70 12 2 A further homing in on where 2 lives. It’s very impressive how much can be said with just simple mathematics. True, but it does help to have good observations to work on. A lesson I’ve learned from all of this in relation to the search for a fraction exactly matching 2 is that it could be an awfully long search. Why? Well, we have just shown that the leading six fractions of the sequence 1 3 7 17 41 99 239 577 .

An oft quoted statement of his is, “Beauty is the first test. ” Sounds nice, but is this true? Whether it is or not, he seemed proud of the fact that none of the mathematics he created ever found an application. This seems to me like a strange thing to say. One that raised hackles. ” Ouch! Consequences of the Irrationality of 2 Earlier, you said the ancients used to say that the side and diagonal of a square are incommensurable. Would you spell out what they meant by this? They meant that the side of a square and its diagonal cannot both be measured exactly with the same ruler, no matter how fine its markings.

One for all. Very sophisticated. Let me suppose that I lay exactly m tiles along the long side of length 2, and exactly n tiles along the short side of length 1. The plan would look something like this: IRRATIONALITY AND ITS CONSEQUENCES n tiles 1 m tiles with no gaps between the square tiles. I see. Since there are no gaps, and each tile side has length s, it must be that 2 = ms while 1 = ns Is this not so? Seems logical to me since m tiles, each of length s, measure exactly ms units, with n such tiles measuring ns units.

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