By Smith, Charles, 1844-1916
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Additional info for An elementary treatise on solid geometry
Is ~ - . olmn Find the surface generated by a straight line which and meets two given straight lines. is parallel to a fixed plane A 14. straight line meets two given straight lines and makes the same angle with both of them; find the surface which it generates. Any two by a straight 15. ratio finite straight lines line ; same which it are divided in the find the equation of the surface generates. A 16. straight line always parallel to the plane of yz passes 2 2 2 2 through the curves x + y = a 2 = 0, and x = az, 2/ = 0; prove that the equation of the surface generated is , Three straight lines mutually at right angles meet in a 17.
33 any one of its possible positions be a^, y v z l and x y, z ) the co-ordinates of the middle point of the line. ( be the length of the line, we have extremities of the line in x Then, y< >2> 22 allcl lct l>o > if 21 But, since y 1 = mx l and 21 ^=c, and #2 = -wo;2 2 = 0, A Z 2 = -c, we have is the ellipse whose equations are = moves so as always line z2 -z 2 = 2c, and Hence the locus of the middle point (2) , to intersect three which are not all parallel to the same surface generated by the straight line.
I , and and which -=-==- n I r ni 0. that the straight lines ft y aa bfi / cy in n J will lie in one plane, if a V< a) y ( a Two systems of rectangular axes have the same origin ; if a plane cut them at distances a, &, c, and a, 6 , c from the origin, A t>- then 111111 EXAMPLES ON CHAPTER 7. 35 II Determine the locus of a point which moves from two given straight lines. so as always to be equally distant Through two straight lines given in space two planes are at right angles to one another ; find the locus of their line of intersection.
An elementary treatise on solid geometry by Smith, Charles, 1844-1916