...MB, NB; the angle COD is the supplement of the inclination of the faces MB, NB. PROP. XLIV. THEOR. If a solid angle be contained by three plane angles, any two of them are together greater than the third. Let the solid angle at A (fig. 49) be contained by the three plane...

...greater ratio ? Do the definitions and theorems of Book v. include incommensurable magnitudes ? 3. If a solid angle be contained by three plane angles, any two are together greater than the third. Define the inclination of a plane to a plane, and shew that it...

...to a third plane ; their common section shall be perpendicular to the same plane. PROP. XX. THEOREM. If a solid angle be contained by three plane angles, any two of them are greater than the third. PROP. XXJ. THEOREM. Every solid angle is contained by plane angles, which together are less than four...

...parallelograms about the diameter of any parallelogram are similar to the whole and to one another. 3. If a solid angle be contained by three plane angles, any two of them are greater than the third. 4. Find the cube root of 20/ — 94 ^b and the greatest common measure of 2; — 2 x$ z\ + 4 (xyzfi...

...parallelograms about the diameter of any parallelogram are similar to the whole and to one another. 3. If a solid angle be contained by three plane angles, any two of them are greater than the third. 4. Find the cube root of 20? — 94 \?1) and the greatest common measure of x — 2 xi i\ + 4 (:cyz)J...

...MATHEMATICS.— PROFESSOR WILSON. GEOMETRY AND TRIGONOMETRY. 1. Define a solid angle, and show that if a solid angle be contained by three plane angles, any two of them are together greater than the third. ^Euclid b. xi., p. 20. 2. Show that similar polygons inscribed in...

...prove that the rectangle contained by AB, A'B1 is four times as great as that contained by BC', B'C. 6. If a solid angle be contained by three plane angles, any two of them are greater than the third. Within the area of a given triangle is described a triangle, the sides of which are parallel to those...

...prove that the rectangle contained by AB, A'B' is four times as great as that contained by B C',BC. 6. If a solid angle be contained by three plane angles, any two of them are greater than the third. Within the area of a given triangle is described a triangle, the sides of which are parallel to those...

...off by long narrow planes, find the number of plane and of solid angles in the resulting solid. 9. If a solid angle be contained by three plane angles, any two of these angles are together greater than the third angle. CONIC SECTIONS. 1. A parabola being traced...

...right angles to a plane, the other also shall be at right angles to the same plane. 12. PROP. XX. — If a solid angle be contained by three plane angles, any two of them are greater than the third. 13. Two planes being perpendicular to each other, draw a third perpendicular to both. ALGEBRA. Uted...