By Smith, Charles, 1844-1916

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**Extra info for An elementary treatise on solid geometry**

**Sample text**

Then , , on the plane. between the line ... If the lines PP , and the plane. 31. The orthogonal projection of any plane area on any other plane is found by multiplying the area by the cosine of the angle between the planes. Divide the given area into a very great number of rectangles by two sets of lines parallel and perpendicular to the line of intersection of the given plane and the plane of Then, those lines which are parallel to the line projection. of intersection are unaltered by projection, and those which cos 6, where are perpendicular are diminished in the ratio 1 : 6 is the angle between the planes.

3oc - 4y f 7 + 13 = 0. plane 3os 4y + Iz = 0. Ex. 2. Find the equation of the plane through the origin and through the intersection of the two planes 5x - 3y -f 2* + 5 = and 3#/p: 5y - 2z - 7 = 0. Ex. 3. Shew that the three planes 2x + 5y + 3z=Q, x-y + 4z = 2, and - 5^ + 4 = intersect in a straight line. Ex. 4. Shew that the four planes 2x-Zy + 2z = 0,x + y-3z = 4, 3o;-y + z=2, and lx - 5y + &z = 1 meet in a point. 5. Shew that the four points (0, -1, -1) (4, 5, 1), (3, 9, 4) and - 4, 4, 4,) lie on a plane.

And (i) (ii) All parallel plane sections of a conicoid are similar similarly situated conies. Change the axes of co-ordinates one of the system plane of xy may be in such a way that the of parallel planes ; and let the equation of the surface be the general equation of the second degree. Let the equation of any one of the planes bo z = k.