# C.; Hemery, C. Lebosse's Algèbre. Classe de Seconde C PDF

By C.; Hemery, C. Lebosse

Manuel scolaire de mathématiques, niveau seconde C, programmes de 1965. Algèbre. Cet ouvrage fait partie de l. a. assortment Lebossé-Hémery dont les manuels furent à l’enseignement des mathématiques ce que le Bled et le Bescherelle furent à celui du français.

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One who is prone to reason will attack this well known riddle in a different way. He will still do the pouring, but only mentally. He may fill, say, the three gallon keg and make a note of the fact that he has five gallons left in the big keg. This is registering the result of a physical operation performed only mentally, and this implies that the reasoner is in possession of the information, acquired previously, that if you take three gallons from eight gallons there remain five gallons. 14 The above description of the method of solving the riddle suggests that the reasoning involved consists of a series of physical operations performed in the imagination only, and that the performance of the operations mentally is made possible by the reasoner's knowledge, from previous experience, of the outcome of each individual operation.

Let us try the same scheme on another example. A block of wood in the form of a cube 3 x 3 x 3 inches is painted, say, blue. If the block were sawed up into one inch cubes, how many faces of each small cube would be blue? Here again the question may be answered experimentally by actually sawing up the big block and counting the number of painted faces of the individual small blocks. But the reasoner may arrive at the outcome of the sawing without having recourse to the actual operation, relying for his answer upon his knowledge, that is to say, his previous experience with the cube.

If two lines p and q are taken in F, their images in F' are two straight lines p' and q', but the angle p'q' is not equal to the angle pq, as a rule, and may be either smaller or larger than pq. In particular, the images of two parallel lines are not necessarily parallel, and the images of two perpendicular lines are not necessarily perpendicular. If we call figure F' the projection of figure F from the point S, we may say that projection preserves incidence and collinearity. The systematic study of projective geometry, or visual geometry, is the study of those properties of figures that remain unaltered by projection, just as it may be said of metrical geometry that it is the study of those properties of figures that remain unaltered in rigid motion.