Elements of Geometry and Trigonometry |
From inside the book
Results 6-10 of 16
Page 172
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 ...
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 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 ...
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 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 ...
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 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 ...
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 cones described by ABD and ACD ; but at the same time , the cylinder described by BCEF will be the ...
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
We haven't found any reviews in the usual places.
Other editions - View all
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
Bibliographic information
| Title | Elements of Geometry and Trigonometry DAVIES' COURSE OF MATHEMATICS |
| Author | Adrien Marie Legendre |
| Editor | Charles Davies |
| Translated by | David Brewster |
| Publisher | A.S. Barnes and Company, 1839 |
| Original from | Harvard University |
| Digitized | 14 Jan 2008 |
| Length | 359 pages |
| Export Citation | BiBTeX EndNote RefMan |