Plane and solid geometry . ection EF a O ? In Fig. 2, isbase AB a O ? In Fig. 3, would a rt. section be a O ? 834. Note. The theorems and exercises on the cylinder that followwill be limited to cases in which the bases of the cylinders are the term cylinder is used, therefore, it must be understood to meana cylinder loith circular bases. See also § 846. Ex. 1369. Find the locus of all points at a distance of 6 inches froma straii;ht line 2 feet long. Ex. 1370. Find the locus of all points: (a) 2 inches from the lateralsurface of a right circular cylinder whose altitude is 12 inch
Plane and solid geometry . ection EF a O ? In Fig. 2, isbase AB a O ? In Fig. 3, would a rt. section be a O ? 834. Note. The theorems and exercises on the cylinder that followwill be limited to cases in which the bases of the cylinders are the term cylinder is used, therefore, it must be understood to meana cylinder loith circular bases. See also § 846. Ex. 1369. Find the locus of all points at a distance of 6 inches froma straii;ht line 2 feet long. Ex. 1370. Find the locus of all points: (a) 2 inches from the lateralsurface of a right circular cylinder whose altitude is 12 inches and theradius of whose base is 5 inches ; (b) 2 inches from the entire surface. Ex. 1371. A lo,2: is 20 feet long and 30 inches in diameter at thesmaller end. Find the dimensions of the largest piece of square timber,the same size at each end, that can be cut from the log. BOOK VIII 887 Proposition II. Theorem 835. Every section of a cylinder made by a plane pass-ing through an element is a parallelogram. (See § 834.). Given cylinder AB with base AK, and CDEF a section madeby a plane through element CF and some point, as D, not inCF, but in the circumference of the base. To prove CDEF a O, Argument 1. Through D draw a line in plane DF II CF. 2. Then the line so drawn is an element; , it lies in the cylindrical surface. 3. But this line lies also in plane BF. 4. ..it is the intersection of plane DF with the cylindrical surface, and coin-cides with DF. 5. .*. DE is a str. line and is II and = CF. 6. Also CD and EF are str. lines. 7. .-. CDEF is a O. 836. Cor. Evei^j section of a right circular cylindermade by a plane passing through an element is a ree-tangle. Ex. 1372. In the figure of Prop. II, the radius of the base is 4 inches,element CF is 12 inches, CD is 1 inch from the center of the base, and CFmakes with CD an angle of 60^ Find the area of section CDEF. Ex. 1373. Every section of a cylinder, parallel to an element, is aparallelogram. How is the base of thi
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometr, bookyear1912
