 ... are 8 in. Find the surface and volume of the greatest possible cylinder, of the same axis, that can be cut from the prism. Ex. 1634. The base of a right pyramid is a regular hexagon whose sides are 20 in., and the lateral faces are inclined to the...  Vectors and Rotors: With Applications - Page 56by Olaus Henrici, George Charles Turner - 1903 - 204 pagesFull view - About this book
 | Henry Martyn Taylor - Euclid's Elements - 1895 - 708 pages
...parallel to AB. Wherefore, straight lines &c. EXERCISES. 1. The straight lines joining the middle points of opposite edges of a tetrahedron meet in a point, and bisect one another. 2. If two of the straight lines joining the middle points of two pairs of opposite edges... | |
 | Fletcher Durell - Geometry, Solid - 1904 - 232 pages
...opposite edges be joined, a parallelogram is formed. Ex. 25. Straight lines joining the midpoints of the opposite edges of a tetrahedron meet in a point and bisect each other. Ex. 26. The midpoints of the edges of a regular tetrahedron are the vertices of a regular octahedron.... | |
 | Henry Burchard Fine, Henry Dallas Thompson - Geometry, Analytic - 1909 - 346 pages
...yt, z2), (x¿, y3, z3) is i (X! + xi + *3), i (yi + У-2 + y.í), i (zi + z2 + z3). 16. Prove that the three lines joining the mid-points of opposite edges of a tetrahedron meet in a common point, whose coordinates are ^(x¡ + xí + rt + x4), i (yi + i/2 + y:i + yi), Нzi +z2 + z;)... | |
 | Henry Burchard Fine, Henry Dallas Thompson - Geometry, Analytic - 1909 - 344 pages
...(x2, y-2, z2), (xs, ys, za) is i (xi + Xz + z3), J (2/1 + 2/2 + 2/3), i(«i + za + 23). 15. Prove that the three lines joining the mid-points of opposite edges of a tetrahedron meet in a common point, whose coordinates are J(zi + z.2 + »'s + x4), J(2/i + 2/2 -1-2/3 + 2/4), i (zi + z2... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 490 pages
...in., and the lateral faces are inclined to the base at an angle of 60°. Find the volume. Ex. 1635. Lines joining the mid-points of opposite edges of...tetrahedron meet in a point and bisect each other. Ex. 1636. The altitude of a cone of revolution is 27 in., and its curved surface is 7 times the area... | |
 | Sophia Foster Richardson - Geometry, Solid - 1914 - 236 pages
...the midpoints of adjacent edges of a tetrahedron form a parallelogram. (Compare Ex. 8.) 121 a. The lines joining the midpoints of opposite edges of a tetrahedron meet in a point. Definition. The point of intersection of the lines joining the midpoints of opposite edges of a tetrahedron... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 pages
...in., and the lateral faces are inclined to the base at an angle of 60°. Find the volume. Ex. 1635. Lines joining the mid.points of opposite edges of...tetrahedron meet in a point and bisect each other. Ex. 1636. The altitude of a cone of revolution is 27 in., and its curved surface is 7 times the area... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 484 pages
...in., and the lateral faces are inclined to the base at an angle of 60°. Find the volume. Ex. 1635. Lines joining the mid-points of opposite edges of...tetrahedron meet in a point and bisect each other. Ex. 1636. The altitude of a cone of revolution is 27 in., and its curved surface is 7 times the area... | |
 | Walter Burton Ford, Charles Ammermann - Geometry, Modern - 1923 - 406 pages
...BC and GF is parallel to BC(?), etc.] 32. Prove that the three lines that join the mid-points of the opposite edges of a tetrahedron meet in a point and bisect each other. [HINT. Given LM, PQ, RS, three lines which, etc. To prove (?). Proof. Join PS, SQ, QR, PR. Then PS... | |
 | Walter Burton Ford, Charles Ammerman - Geometry, Plane - 1923 - 414 pages
...opposite edges is a parallelogram. 32. Prove that the three lines that join the raid-points of the opposite edges of a tetrahedron meet in a point and bisect each other. [HINT. Given LM, PQ, RS, three lines which, etc. To prove (?). Proof. Join PS, SQ, QR, PR. Then PS... | |
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