Elements of Geometry and Trigonometry |
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Page 166
A cone is the solid generated by the revolution of a right- angled triangle SAB , conceived to turn about the immoveable side.SA. In this movement , the side AB describes a circle BDCE , named the buse of the ...
A cone is the solid generated by the revolution of a right- angled triangle SAB , conceived to turn about the immoveable side.SA. In this movement , the side AB describes a circle BDCE , named the buse of the ...
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 171
The convex surface of a cone is equal to the circumference of its base , multiplied by half its side . Let the circle ABCD be the base of a cone , S the vertex , SO the altitude , and SA the side : then will its convex sur- face be ...
The convex surface of a cone is equal to the circumference of its base , multiplied by half its side . Let the circle ABCD be the base of a cone , S the vertex , SO the altitude , and SA the side : then will its convex sur- face be ...
Page 172
Let BIA - DE be a frustum of a cone : then will its convex surface be equal to AD x circ.OA + circ.CD - s ( circ . 2 circ.CD ) . L E G K For , inscribe in the bases of the frustums two regular polygons of the same number of sides ...
Let BIA - DE be a frustum of a cone : then will its convex surface be equal to AD x circ.OA + circ.CD - s ( circ . 2 circ.CD ) . L E G K For , inscribe in the bases of the frustums two regular polygons of the same number of sides ...
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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 |