Download Space And Geometry In The Light Of Physiological, by Ernst Mach PDF
By Ernst Mach
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Extra info for Space And Geometry In The Light Of Physiological, Psychological And Physical Inquiry
Example text
The side of a square is equal to a and the products of the distances from the opposite vertices to a line l are equal to each other. Find the distance from the centre of the square to the line l if it is known that neither of the sides of the square is parallel to l. 197. One of the sides in a triangle ABC is twice the length of the other and LB = 2 LC. Find the angles of the triangle. 198. A circle touches the sides AB and AC of an isosceles triangle ABC. Let M be the point of tangency with the side AB and N the point of intersection of the circle and the base BC.
180. Given ina trapezoidABCD: lAB 1= I BC I = I CD I = a, I DA I = 2a. Taken respectively on the straight lines AB and AD are points E and F, other than the vertices of the trapezoid, so that the point of intersection of the altitudes of the triangle CEF coincides with the point of intersection of the diagonals of the trapezoid ABCD. Find the area of the triangle CEF. * • * 18t. The altitude of a right triangle ABC drawn to the hypotenuse AB is h, D being its foot; M and N are the midpoints of the line segments AD and DB, respectively.
Points P and Q are chosen on the lateral sides KL and M N of an equilateral trapezoid KLMN, respectively, such that the line segment PQ is parallel to the bases of the trapezoid. A circle can be inscribed in each of the trapezoids KPQN and PLMQ, the radii of these circles being equal to Rand r, respectively. Determine the bases I LM I and I KN I· 229. In a triangle ABC, the bisector of the angle A intersects the side BC at a point D. It is known that lAB I-IBD 1= a, I AC I I CD I = b. Find I AD I· 230.