## Elements of Geometry and Trigonometry |

### From inside the book

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Page 166

A

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

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

... 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

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

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 ...### What people are saying - Write a review

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Elements of Geometry and Trigonometry from the Works of A. M. Legendre A. M. Legendre No preview available - 2017 |

### 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