An Elementary Treatise on Geometry: Simplified for Beginners Not Versed in Algebra. Part II, Containing Solid Geometry, with Its Application to the Solution of Problems |
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Page 86
... diameter of the sphere , e . g . the diameter AB . * Questions on Definitions . 1 How is that solid bounded , which is called a cylinder ? 2. What do you call the convex surface of a cylinder ? 3. What the bases of a cylinder ? 4. What ...
... diameter of the sphere , e . g . the diameter AB . * Questions on Definitions . 1 How is that solid bounded , which is called a cylinder ? 2. What do you call the convex surface of a cylinder ? 3. What the bases of a cylinder ? 4. What ...
Page 88
... diameter ? The teacher ought now to vary these ques- tions , and illustrate them by an apparatus . * * * OF CYLINDERS . QUERY I. D If a cylinder ABCD , be cut by a plane parallel to its base , what remark can you make with regard to the ...
... diameter ? The teacher ought now to vary these ques- tions , and illustrate them by an apparatus . * * * OF CYLINDERS . QUERY I. D If a cylinder ABCD , be cut by a plane parallel to its base , what remark can you make with regard to the ...
Page 94
... each other ? Ans . They are to each other , in solidity , as the cubes constructed upon the radii , or upon the diameters of their bases . Q. How can you prove this ? A. Let figure I and II represent two simi- lar 94 SOLID GEOMETRY .
... each other ? Ans . They are to each other , in solidity , as the cubes constructed upon the radii , or upon the diameters of their bases . Q. How can you prove this ? A. Let figure I and II represent two simi- lar 94 SOLID GEOMETRY .
Page 96
... diameters , it follows , that the cubes of the radii are also in the same ratio as the cubes of the diameters ; consequently , if the two cylinders are in pro- portion to the cubes of the radii of their bases , they are also in ...
... diameters , it follows , that the cubes of the radii are also in the same ratio as the cubes of the diameters ; consequently , if the two cylinders are in pro- portion to the cubes of the radii of their bases , they are also in ...
Page 114
... diameter . 2d . That all radii as well as all diameters of the same sphere , are equal to one another . 3d . That when the diameter or radius of a sphere is known , the whole sphere is determined . QUERY I. If you cut a sphere by a ...
... diameter . 2d . That all radii as well as all diameters of the same sphere , are equal to one another . 3d . That when the diameter or radius of a sphere is known , the whole sphere is determined . QUERY I. If you cut a sphere by a ...
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Common terms and phrases
ABCDEF arcs axis basis ABC basis and height bodies calculate called CAVSAS centre cone ABC consequently convex surface corresponding sides cube root cubic contents cubic feet cubic inches diameter distance divided DOCERE draw equal and parallel equal bases equal heights find the solidity foot found by multiplying frustrum GEORGIA LIBRARIES inferences logarithms lower basis manner mean proportional multiplying its basis oblique parallelopiped paral parallel circles parallel planes perpendicular plane angles Plane Geometry plane MN plane parallel polygon PROBLEM prove pyra pyramid ABCD pyramids of equal QUERY radii radius ramid ratio Remark RERVM right angles right cone right cylinder right parallelopiped right prism similar solid angle Solid Geometry SOLUTION spherical spherical angle square feet straight line third three pyramids tiplying triangle AGC triangular prism triangular pyramid truncated prism ungula UNIVERSITY OF GEORGIA upper basis vertex vertices whole pyramid zone