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" Find the limiting value of xt~x3 jt*dx when x = oo . 4. A regular octahedron is inscribed in a cube, so that the corners of the octahedron are in the centres of the faces of the cube; prove that the volume of the cube is six times that of the octahedron.... "
The examinations for the degree of bachelor of arts, Jan., 1847 - Σελίδα 13
των Cambridge univ, exam. papers - 1847 - 80 σελίδες
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Spherical trigonometry

Isaac Todhunter - 1859 - 275 σελίδες
...of the intercepted portions of the parallelopiped will be equal in volume to one of the spheres. 12. A regular octahedron is inscribed in a cube so that...volume of the cube is six times that of the octahedron. 13. It is not possible to fill any given space with a number of regular polyhedrons of the same kind,...

Spherical Trigonometry: For the Use of Colleges and Schools

Isaac Todhunter - 1863 - 132 σελίδες
...of the intercepted portions of the parallelepiped will be equal in volume to one of the spheres. 12. A regular octahedron is inscribed in a cube so that the corners of the octahedron are at the centres of the faces of the cube; shew that the volume of the cube is six times that of the...

Spherical Trigonometry, for the Use of Colleges and Schools: With Numerous ...

Isaac Todhunter - 1879 - 158 σελίδες
...of the intercepted portions of the parallelepiped will be equal in volume to one of the spheres. 12. A regular octahedron is inscribed in a cube so that the corners of the octahedron are at the centres of the faces of the cube : shew that the volume of the cube is six times that of the...

Military examinations. Mathematical examination papers, set for entrance to ...

Woolwich roy. military acad, Walter Ferrier Austin - 1880
...chord AB, and on the tangents ТА, ТB respectively, PL is a mean proportional between PM and PN. 16. A regular octahedron is inscribed in a cube so that the corners of it are at the centres of the faces of the cube ; show that the volume of the cube is six times the...

Calendar

University of Sydney - 1903
...number of its edges, prove that S+F=Ef-2, and hence shew that there are only five regular polyhedra. A regular octahedron is inscribed in a cube so that the corners of the first are at the centres of the faces of the second. Compare the volumes of the solids. fi. Describe...

Mathematical And Physical Papers -- Vol. 5.

Sir George Gabriel Stokes - 1905
...its greatest area is ab(j2-rl). fx 3. Find the limiting value of xe~x<2 I e*2 dx when x = oo . J o 4. A regular octahedron is inscribed in a cube, so...to a weight by a string which passes over a fixed pulley ; supposing the water to revolve with a given angular velocity as the bucket is ascending or...

Mathematical and physical papers, Τόμος 5

George Gabriel Stokes - 1905
...that BDOP is a parallelogram, and that its greatest area is ab (72 - 1). /' trf dx when x = oo . j 4. A regular octahedron is inscribed in a cube, so...to a weight by a string which passes over a fixed pulley ; supposing the water to revolve with a given angular velocity as the bucket is ascending or...

Mathematical and Physical Papers, Τόμος 2

George Gabriel Stokes - 1883 - 366 σελίδες
...parallelogram, and that its greatest area is ab(J-2- I). 3. Find the limiting value of xt~x3 jt*dx when x = oo . 4. A regular octahedron is inscribed in a cube, so...to a weight by a string which passes over a fixed pulley ; supposing the water to revolve with a given angular velocity as the bucket is ascending or...
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