Elements of Geometry and Trigonometry: With Notes |
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Page vii
... Cone , and the Sphere , NOTES ON THE ELEMENTS OF GEOMETRY , Note I. On some Names and Definitions , 192 219 II . On the Demonstration of Prop . 20 , Book I. and of some other fundamental Propositions in Geometry222 Addition to Note II ...
... Cone , and the Sphere , NOTES ON THE ELEMENTS OF GEOMETRY , Note I. On some Names and Definitions , 192 219 II . On the Demonstration of Prop . 20 , Book I. and of some other fundamental Propositions in Geometry222 Addition to Note II ...
Page 192
... cone is the solid produced by the revolution of a right - angled triangle SAB , conceived to turn about the im- moveable side SA . In this movement , the side AB describes a circular plane BDCE , named the base of the cone ; the ...
... cone is the solid produced by the revolution of a right - angled triangle SAB , conceived to turn about the im- moveable side SA . In this movement , the side AB describes a circular plane BDCE , named the base of the cone ; the ...
Page 193
With Notes Adrien Marie Legendre. III . If from the cone SCDB , the cone SFKH be cut off by a section parallel to the base , the remaining solid CBHF is called a truncated cone , or the frustum of a cone . We may conceive it to be ...
With Notes Adrien Marie Legendre. III . If from the cone SCDB , the cone SFKH be cut off by a section parallel to the base , the remaining solid CBHF is called a truncated cone , or the frustum of a cone . We may conceive it to be ...
Page 194
... cone and the cylinder . We may farther observe , that the name convex surface , is not limited to curve surfaces alone ; it in- cludes polyedral surfaces , or surfaces composed of several planes , and likewise surfaces partly curve and ...
... cone and the cylinder . We may farther observe , that the name convex surface , is not limited to curve surfaces alone ; it in- cludes polyedral surfaces , or surfaces composed of several planes , and likewise surfaces partly curve and ...
Page 199
... surface of a greater cylinder . Hence , finally , the convex surface of a cylinder is equal to the circumference of its base , multiplied by the altitude . PROPOSITION V. THEOREM . The solidity of a cone is BOOK VIII . 199.
... surface of a greater cylinder . Hence , finally , the convex surface of a cylinder is equal to the circumference of its base , multiplied by the altitude . PROPOSITION V. THEOREM . The solidity of a cone is BOOK VIII . 199.
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Elements of Geometry and Trigonometry from the Works of A. M. Legendre A. M. Legendre No preview available - 2017 |
Common terms and phrases
AC² adjacent adjacent angles altitude angle ACB angle BAC centre chord circ circle circular sector circumference circumscribed common cone consequently construction continued fraction convex surface cos² cosine cylinder demonstration determined diagonal diameter draw drawn equal angles equation equivalent faces figure formulas frustum greater homologous sides hypotenuse inclination inscribed intersection isosceles join less likewise manner measure multiplied number of sides opposite parallel parallelepipedon parallelogram perpendicular plane MN polyedron prism PROBLEM Prop PROPOSITION quadrilateral quantities radii radius ratio rectangle rectilineal triangle regular polygon right angles right-angled triangle SABC Scholium sector segment shew shewn side BC similar sin² sines solid angle sphere spherical polygon spherical triangle square straight line suppose tang tangent THEOREM third side three angles three plane angles triangle ABC triangular pyramids vertex vertices
Popular passages
Page 152 - AMB be a section, made by a plane, in the sphere, whose centre is C. From the...
Page 24 - THEOREM. In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and, conversely, equal chords subtend equal arcs.
Page 22 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Page 62 - Similar triangles are to each other as the squares of their homologous sides.
Page 211 - If two angles of one triangle are equal to two angles of another triangle, the third angles are equal, and the triangles are mutually equiangular.
Page 187 - Similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of their bases.
Page 140 - AT into equal parts .Ax, xy, yz, &c., each less than Aa, and let k be one of those parts : through the points of division pass planes parallel to the plane of the bases : the corresponding sections formed by these planes in the two pyramids will be respectively equivalent, namely, DEF to def, GHI to ghi, &c.
Page 150 - The radius of a sphere is a straight line, drawn from the centre to any point...
Page 168 - THEOREM. The surface of a spherical triangle is measured by the excess of the sum of its three angles above two right angles, multiplied by the tri-rectangular triangle.
Page 135 - XII.) ; in like manner, the two solids AQ, AK, having the same base, AOLE, are to each other as their altitudes AD, A M.