Elements of Geometry and Trigonometry |
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Page 166
A cylinder is the solid generated by the revolution of a rectangle ABCD , conceived to turn about the immoveable side AB . In this movement , the sides AD , BC , con- tinuing always perpendicular to AB , describe equal circles DHP ...
A cylinder is the solid generated by the revolution of a rectangle ABCD , conceived to turn about the immoveable side AB . In this movement , the sides AD , BC , con- tinuing always perpendicular to AB , describe equal circles DHP ...
Page 167
Two cylinders , or two cones , are similar , when their axes are to each other as the diameters of their bases . 5. If in the circle ACD , which forms the base of a cylinder , a polygon ABCDE be inscribed , a right prism , constructed ...
Two cylinders , or two cones , are similar , when their axes are to each other as the diameters of their bases . 5. If in the circle ACD , which forms the base of a cylinder , a polygon ABCDE be inscribed , a right prism , constructed ...
Page 168
... which form the bases of the zone or segment . Note . The Cylinder , the Cone , and the Sphere , are the three round bodies treated of in the Elements of Geometry.hie 1 PROPOSITION . I. THEOREM . The convex surface of. 168 GEOMETRY .
... which form the bases of the zone or segment . Note . The Cylinder , the Cone , and the Sphere , are the three round bodies treated of in the Elements of Geometry.hie 1 PROPOSITION . I. THEOREM . The convex surface of. 168 GEOMETRY .
Page 169
The convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude . Let CA be the radius of the van do au given cylinder's base , and H its sopho altitude : the circumference whose radius is CA being ...
The convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude . Let CA be the radius of the van do au given cylinder's base , and H its sopho altitude : the circumference whose radius is CA being ...
Page 170
Let CA be the radius of the base of the cylinder , and H the altitude . Let the circle G whose radius is CA be repre- sented by area CA , it is to be proved that the solidity of the cylinder is equal to area CAX H. Inscribe in the ...
Let CA be the radius of the base of the cylinder , and H the altitude . Let the circle G whose radius is CA be repre- sented by area CA , it is to be proved that the solidity of the cylinder is equal to area CAX H. Inscribe in the ...
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Common terms and phrases
ABCD adjacent altitude base become Book called centre chord circle circumference circumscribed common cone consequently construction contained corresponding cosine Cotang cylinder described diameter difference distance divided draw drawn equal equation equivalent evident expressed extremities fall figure follows formed formulas four frustum give given gles greater half hence homologous included inscribed intersection less likewise logarithm manner means measured meet middle multiplied opposite parallel parallelogram parallelopipedon pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment shown sides similar sine solid solid angle sphere spherical triangle square straight line Suppose surface taken tang tangent THEOREM third triangle triangle ABC vertex whole
Bibliographic information
| Title | Elements of Geometry and Trigonometry |
| Author | Adrien Marie Legendre |
| Editor | Charles Davies |
| Translated by | David Brewster |
| Edition | 4 |
| Publisher | A.S. Barnes and Company, 1834 |
| Original from | the University of California |
| Digitized | 14 Oct 2010 |
| Length | 359 pages |
| Export Citation | BiBTeX EndNote RefMan |