Elements of Plane and Solid GeometryGinn, Heath, & Company, 1885 - 398 σελίδες |
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Σελίδα viii
... SPHERE . SECTIONS AND TANGENTS 349 • DISTANCES ON THE SURFACE OF THE SPHERE 356 SPHERICAL ANGLES . 363 SPHERICAL POLYGONS AND PYRAMIDS . 365 COMPARISON AND MEASUREMENT OF SPHERICAL SURFACES 383 VOLUME OF THE SPHERE -396 ELEMENTS OF ...
... SPHERE . SECTIONS AND TANGENTS 349 • DISTANCES ON THE SURFACE OF THE SPHERE 356 SPHERICAL ANGLES . 363 SPHERICAL POLYGONS AND PYRAMIDS . 365 COMPARISON AND MEASUREMENT OF SPHERICAL SURFACES 383 VOLUME OF THE SPHERE -396 ELEMENTS OF ...
Σελίδα 348
... a cone of revo- lution , and R and r be the radii of its bases , we have B and b π r2 , = and √ BX b = TRr . . ' . V = } π II ( R2 + r2 + R r ) . = T R2 , BOOK VIII . THE SPHERE . ON SECTIONS AND TANGENTS 348 GEOMETRY.- BOOK VII .
... a cone of revo- lution , and R and r be the radii of its bases , we have B and b π r2 , = and √ BX b = TRr . . ' . V = } π II ( R2 + r2 + R r ) . = T R2 , BOOK VIII . THE SPHERE . ON SECTIONS AND TANGENTS 348 GEOMETRY.- BOOK VII .
Σελίδα 349
... Sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre . A sphere may be generated by the revolution of a semicircle about its ... sphere THE SPHERE SECTIONS AND TANGENTS •
... Sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre . A sphere may be generated by the revolution of a semicircle about its ... sphere THE SPHERE SECTIONS AND TANGENTS •
Σελίδα 350
George Albert Wentworth. PROPOSITION I. THEOREM . 678. Every section of a sphere made by a plane is a circle . C Let the section ABC be a plane section of a sphere whose centre is 0 . We are to prove section ABC a circle . From the ...
George Albert Wentworth. PROPOSITION I. THEOREM . 678. Every section of a sphere made by a plane is a circle . C Let the section ABC be a plane section of a sphere whose centre is 0 . We are to prove section ABC a circle . From the ...
Σελίδα 353
... sphere . For , if we bisect the sphere through P and B , and in the section draw the diameter P P ' and chord BP ' , the Abpp ' , when applied to △ BP P ' , will coincide with it . Q. E. F. PROPOSITION IV . THEOREM . 694. Through any ...
... sphere . For , if we bisect the sphere through P and B , and in the section draw the diameter P P ' and chord BP ' , the Abpp ' , when applied to △ BP P ' , will coincide with it . Q. E. F. PROPOSITION IV . THEOREM . 694. Through any ...
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AABC ABCD altitude apothem arc A B axis base and altitude centre centre of symmetry chord circumference circumscribed coincide cone of revolution conical surface COROLLARY cylinder denote diagonals diameter dihedral angle distance divided draw equal respectively equally distant equilateral equivalent frustum given point Hence homologous sides hypotenuse intersection isosceles lateral area lateral edges lateral faces Let A B Let ABC line A B measured by arc middle point number of sides opposite parallel lines parallelogram parallelopiped pass perimeter perpendicular plane MN polyhedral angle prove Q. E. D. PROPOSITION radii ratio rect rectangles regular inscribed regular polygon right angles right section S-ABC SCHOLIUM similar polygons slant height sphere spherical angle spherical polygon spherical triangle straight line drawn surface tangent tetrahedron THEOREM trihedral upper base vertex vertices volume