Elements of Plane and Solid GeometryGinn, Heath, & Company, 1885 - 398 σελίδες |
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Σελίδα viii
... 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 GEOMETRY . BOOK I. RECTILINEAR FIGURES . INTRODUCTORY viii CONTENTS .
... 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 GEOMETRY . BOOK I. RECTILINEAR FIGURES . INTRODUCTORY viii CONTENTS .
Σελίδα 286
... volume . 504. DEF . Equal polyhedrons are polyhedrons which have the same form and volume . ON PRISMS . 505. DEF . A Prism is a polyhedron two of whose faces are equal and parallel polygons , and the other faces are parallelo- grams ...
... volume . 504. DEF . Equal polyhedrons are polyhedrons which have the same form and volume . ON PRISMS . 505. DEF . A Prism is a polyhedron two of whose faces are equal and parallel polygons , and the other faces are parallelo- grams ...
Σελίδα 297
... one dimension in common are to each other as the products of their other two dimensions ) . Multiply these equalities together ; then P ρι = a X b x c Q. E. D. PROPOSITION X. THEOREM . 538. The volume of a rectangular PRISMS . 297.
... one dimension in common are to each other as the products of their other two dimensions ) . Multiply these equalities together ; then P ρι = a X b x c Q. E. D. PROPOSITION X. THEOREM . 538. The volume of a rectangular PRISMS . 297.
Σελίδα 298
... volume . We are to prove But P Ū P = Ū a X b x c volume of P = a xbx c . § 537 § 500 1X1X1 is the volume of P ; .. the volume of P = a Xb xc . Q. E. D. 539. COROLLARY I. Since a cube is a rectangular parallelo- piped having its three ...
... volume . We are to prove But P Ū P = Ū a X b x c volume of P = a xbx c . § 537 § 500 1X1X1 is the volume of P ; .. the volume of P = a Xb xc . Q. E. D. 539. COROLLARY I. Since a cube is a rectangular parallelo- piped having its three ...
Σελίδα 299
George Albert Wentworth. PROPOSITION XI . THEOREM . 542. The volume of any parallelopiped is equal to the product of its base by its altitude . G Ri H N E A K B Let ABCD - F be a parallelopiped having all its faces oblique , and HR its ...
George Albert Wentworth. PROPOSITION XI . THEOREM . 542. The volume of any parallelopiped is equal to the product of its base by its altitude . G Ri H N E A K B Let ABCD - F be a parallelopiped having all its faces oblique , and HR its ...
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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