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By Smith, Charles, 1844-1916

This ebook used to be initially released ahead of 1923, and represents a duplicate of a tremendous historic paintings, preserving an identical structure because the unique paintings. whereas a few publishers have opted to observe OCR (optical personality reputation) know-how to the method, we think this ends up in sub-optimal effects (frequent typographical blunders, unusual characters and complicated formatting) and doesn't safely defend the historic personality of the unique artifact. We think this paintings is culturally very important in its unique archival shape. whereas we attempt to appropriately fresh and digitally increase the unique paintings, there are sometimes cases the place imperfections reminiscent of blurred or lacking pages, terrible photos or errant marks can have been brought as a result of both the standard of the unique paintings or the scanning strategy itself. regardless of those occasional imperfections, now we have introduced it again into print as a part of our ongoing international publication upkeep dedication, delivering buyers with entry to the absolute best historic reprints. We enjoy your realizing of those occasional imperfections, and in actual fact wish you get pleasure from seeing the ebook in a layout as shut as attainable to that meant via the unique writer.

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Extra resources for An elementary treatise on solid geometry

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1. Find the perpendicular distance of an angular point of a cube from a diagonal which does not pass through that angular point. Ex. 2. a^\. line of intersection of Ex. 3. Shew that the two lines x - 2 = 2y - 6 = 3z, 4x - 11 = 4y - 13 = 3z meet in a point, and that the equation of the plane on which they lie is Ex. 4. H Of *b fi trough the point ^w& z ~ "x througli the line whose equations are a. y Ans. (a , /3 , 7% and P _ ~~ y a - 1 I Ex. 5. The shortest distances between the diagonal and the edges which it does not meet are of a rectangular parallelepiped be where a, 6, c are Ex.

The equation of the 11 plane through three given points. / 2 , , ^2 ), (xs ys ^3 ). , , The general equation Ax -f By 4- Cz + D = 0. If the three given points are on this plane, + By\ + Cfc + Ax^ t Ax + By^ + Gz + D and 9 we have = 0, Z> 0. s D from these four equations, we Eliminating A, B, 0, have for the required equation x , y , x. / , -0. i and 8 = be the equations of two planes, be the general equation of a plane through their intersection. For, since S and S are both of the first and hence S \8 = represents degree, so also is If 8=0 S X S = will 17.

Mm + nn 0. N are M, proportional to the direction-cosines of a line, the actual direction-cosines will be ___ M L N Hence the angle between two lines whose direction-cosines and L N respectively is M, N are proportional to L, * r>r\o 1 y( The condition 7 , LL + MM + NN + ^ + ^ *j (L* + M* + N*y 1 2 M } . 2 a ) of perpendicularity is as before LL + MM + NN = 0. Ex. 1. Ex. 2. Shew Shew that the 3x= -y= Ex. that the lines ~ line = = * | and ^ 4z=3t/= -Z = is - are -^ 1 at right angles. perpendicular to the line -4z.

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