Scientific Schools: France. The Polytechnic school at Paris ..., Part 1

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1862 - 130 pages
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Page 30 - The . shortest path from one point to another, on the surface of the sphere, is the arc of a great circle which joins the two given points. The sum of the sides of a spherical triangle, or of any spherical polygon, is less than the circumference of a great circle. Poles of an arc of a great or small circle.— They serve to trace arcs of circles on the sphere. Every plane perpendicular to the extremity of a radius is tangent to the sphere. Measure of the angle of two arcs of great circles. Properties...
Page 29 - The volume of any prism is equal to the product of its base by its altitude. Let V denote the volume, B the base, and H the altitude of the prism DA'.
Page 28 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Page 40 - Having given two sides and an angle opposite to one of them, or two angles and a side opposite to one of them.
Page 28 - The areas of similar polygons are to each other as the squares of the homologous sides of the polygons. Notions on surveying for content (arpentage').
Page 61 - ... indeed not merely the only great school, but, until the Institute was founded, the only scientific body in France. Working on its first idea of high professorial lectures, practically applied and explained by repetiteurs, its success in its own purely scientific line was, and has continued to be, astonishing. Out of its sixteen earliest professors, ten still retain an European name. Lagrange, Monge, Fourcroy, La Place, Guyton de Morveau were connected with it. Malus, Hauy, Biot, Poisson, and...
Page 27 - In a right-angled triangle, the square of the number which expresses the length of the hypothenuse is equal to the sum of the squares of the numbers which express the lengths of the other two sides. The three sides of any triangle being expressed in numbers, if from the extremity of one of the sides...
Page 62 - ... reproduced in the letters of war ministers, of artillery and engineer officers commanding the school of application at Metz, or of committees from the similar schools for the mines and the roads and bridges. The last of these occasions illustrates the present position of the school. On the 5th of June 1850, the legislative assembly appointed a mixed commission of military men and civilians, who were charged to revise all the programs of instruction, and to recommend all needful changes in the...
Page 43 - Asvmptotes of the hyperbola. — The asymptotes coincide with the diagonals of the parallelogram formed on any two conjugate diameters. — The portions of a secant comprised between the hyperbola and its asymptotes are equal. — Application to the tangent and to its construction. The rectangle of the parts of a secant, comprised between a point of the curve and the asymptotes, is equal to the square of half of the diameter to which the secant is parallel. Form of the equation of tho hyperbola referred...

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