## Elements of Geometry |

### From inside the book

Results 1-5 of 15

Page vii

...

...

**cone**, and the cylinder . The measure of the surfaces and solidities of these bodies is deter- mined by a method analogous to that of Archimedes , and found- ed , as to surfaces , upon the same principles , which we have endeavoured to ... Page 177

...

...

**cone**, and the hypothenuse SB de- scribes the convex surface of the**cone**. The point S is called the vertex of the**cone**, SA the axis or altitude , and SB the side . Every section HKFI , made perpendicularly to the axis , is a circle ... Page 178

Adrien Marie Legendre. 510. Two cylinders or two

Adrien Marie Legendre. 510. Two cylinders or two

**cones**are similar , when their axes are to each other as the ...**cone**and the sphere are the three round bodies , which are treated of in the elements . Preliminary Lemmas upon ... Page 179

...

...

**cone**and cylin- der . It should be observed , moreover , that the denomination of convex surface is not confined to curved surfaces ; it compre- hends polyedral faces , or surfaces composed of several planes , also surfaces that are in ... Page 183

... surface of a greater cylinder . We conclude , then , that the convex surface of a cylinder is equal to the circumference of the base multiplied by its altitude . THEOREM . 524. The solidity of a

... surface of a greater cylinder . We conclude , then , that the convex surface of a cylinder is equal to the circumference of the base multiplied by its altitude . THEOREM . 524. The solidity of a

**cone**is equal Of the Three Round Bodies .### Other editions - View all

### Common terms and phrases

ABC fig adjacent angles altitude angle ACB angle BAC base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal angles equiangular equilateral equivalent figure formed four right angles frustum GEOM given point gles greater hence homologous sides hypothenuse inclination intersection isosceles triangle JOHN CRERAR LIBRARY join less Let ABC let fall line AC mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced proposition pyramid S-ABC radii radius ratio rectangle regular polygon right angles Scholium sector segment semicircle semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three angles triangle ABC triangular prism triangular pyramids vertex vertices whence