## Elements of Geometry and Trigonometry |

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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 circ.OA + circ.CD equal to AD x ( circ . circ.CD ) . 2 For , inscribe in the bases of the frustums two regular polygons of the same number of sides , and having their ... Page 173

having AO and DC for the radii of its bases , the vertex of the whole

having AO and DC for the radii of its bases , the vertex of the whole

**cone**being S. Hence this surface will be measured as we have said . This measure will always hold good , even when the point D falls on S , and thus forms a whole ... Page 174

The solidity of a

The solidity of a

**cone**is equivalent to the solidity of a pyramid having an equivalent base and the same altitude ( Book VII . Prop . XVII . ) . Scholium . Let R be the radius of a**cone's**base , H its altitude ; the solidity of the**cone**... Page 178

On the axis , let fall the perpen- F dicular AD : the

On the axis , let fall the perpen- F dicular AD : the

**cone**described by the triangle ABD is the third part of the cylinder described by the rectangle AFBD ( Prop . V. Cor . ) ; also the**cone**described by the triangle ADC is the third ... Page 179

If the perpendicular AD falls without r the triangle ; the solid described by ABC will , in that case , be the difference of the two

If the perpendicular AD falls without r the triangle ; the solid described by ABC will , in that case , be the difference of the two

**cones**described by ABD and ACD ; but at the same time , the cylinder described by BCEF will be the ...### What people are saying - Write a review

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### Common terms and phrases

ABCD adjacent altitude base become Book called centre chord circle circumference circumscribed common cone consequently contained Cosine Cotang cylinder described determine diameter difference distance divided draw drawn equal equations equivalent expressed extremities faces feet figure follows formed four frustum give given gles greater half hence homologous hypothenuse included inscribed intersection less let fall logarithm manner means measured meet middle multiplied number of sides opposite parallel parallelogram pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quadrant quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment sides similar Sine solid solid angle sphere spherical triangle square straight line suppose taken Tang tangent THEOREM third triangle triangle ABC unit vertex whole