Elements of Geometry and Trigonometry |
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Page 171
... cone is equal to the circumference of its base , multiplied by half its side . G Let the circle ABCD be the base of a cone , S the vertex , SO the altitude , and SA the side then will its convex surface be equal to circ . OA × SA . For ...
... cone is equal to the circumference of its base , multiplied by half its side . G Let the circle ABCD be the base of a cone , S the vertex , SO the altitude , and SA the side then will its convex surface be equal to circ . OA × SA . For ...
Page 173
... 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 cone ; and also when the line AD is parallel to the axis , and thus forms ...
... 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 cone ; and also when the line AD is parallel to the axis , and thus forms ...
Page 174
... cone's base , H its altitude ; the solidity of the cone will be R2x H , or R2H . PROPOSITION VI . THEOREM The solidity of the frustum of a cone is equal to the sum of the solidities of three cones whose common altitude is the altitude ...
... cone's base , H its altitude ; the solidity of the cone will be R2x H , or R2H . PROPOSITION VI . THEOREM The solidity of the frustum of a cone is equal to the sum of the solidities of three cones whose common altitude is the altitude ...
Contents
Ratios and Proportions | 34 |
The Circle and the Measurement of Angles | 41 |
Problems relating to the First and Third Books | 57 |
14 other sections not shown
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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 consequently convex surface Cosine Cotang 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 M.
M. Sine number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM Prop proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant segment similar slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line Tang tangent THEOREM triangle ABC triangular prism vertex
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 |