An elementary treatise on solid geometry by Smith, Charles, 1844-1916

By Smith, Charles, 1844-1916

This e-book was once initially released ahead of 1923, and represents a duplicate of a tremendous historic paintings, preserving an identical layout because the unique paintings. whereas a few publishers have opted to observe OCR (optical personality popularity) know-how to the method, we think this results in sub-optimal effects (frequent typographical error, unusual characters and complicated formatting) and doesn't effectively guard the ancient personality of the unique artifact. We think this paintings is culturally very important in its unique archival shape. whereas we try to accurately fresh and digitally increase the unique paintings, there are sometimes circumstances the place imperfections equivalent to blurred or lacking pages, negative photos or errant marks can have been brought because of both the standard of the unique paintings or the scanning technique itself. regardless of those occasional imperfections, we now have introduced it again into print as a part of our ongoing international e-book renovation dedication, offering buyers with entry to the absolute best ancient reprints. We savour your figuring out of those occasional imperfections, and essentially desire you take pleasure in seeing the ebook in a structure as shut as attainable to that meant via the unique writer.

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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.

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