## Elements of Geometry and Trigonometry |

### From inside the book

Results 6-10 of 12

Page 171

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**circ**. OA SA . For , inscribe in the base of A the cone any regular polygon ABCD , and on this polygon as a base conceive a pyramid to be constructed having S for its vertex : this pyramid will be a G B regular pyramid , and will be ... Page 172

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**circ**. Kl = 1 (**circ**. OA +**circ**. CD ) ; therefore , the convex surface of a frustum of a cone is equal to its side multi- plied by the circumference of a section at equal distances from the two bases . Scholium . If a line AD , lying ... Page 176

... of the inscribed circle ( Book V. Prop . II . ) . Now , the sur- face described in the revolution by any one side of the regular polygon , as DE , has D C N F E B K M HNL O P 04 A been shown to be equal to DEx

... of the inscribed circle ( Book V. Prop . II . ) . Now , the sur- face described in the revolution by any one side of the regular polygon , as DE , has D C N F E B K M HNL O P 04 A been shown to be equal to DEx

**circ**. NM 176 GEOMETRY . Page 177

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**circ**. ON :**circ**. NM ; hence EDx**circ**. NM = HI ×**circ**. ON ; and since the same may be shown for each of the other sides , it is plain that the surface described by the entire perimeter is equal to ( FH + HI + IP + PQ + QA ) ×**circ**ON = ... Page 178

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**circ**. OF ( Prop . IX . Cor . ) . But when the number of sides of the polygon is indefinitely increased , BC + CD , becomes the arc BCD , OF becomes equal to OA , and the surface described by BC + CD , becomes the surface of the zone D ...### Other editions - View all

### Common terms and phrases

adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface Cosine cylinder diagonal diameter dicular distance divided draw drawn equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar Sine Cotang slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex