Spherical Trigonometry ...Macmillian and Company, limited, 1859 - 275 páginas |
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Página 99
... volume of a regular polyhedron . The area of one face of the polyhedron is ma2 π cot and -- " m therefore the surface of the polyhedron is mFa2 π cot • 4 m Also the volume of the pyramid which has one face H 2 POLYHEDRONS . 99 cae is ...
... volume of a regular polyhedron . The area of one face of the polyhedron is ma2 π cot and -- " m therefore the surface of the polyhedron is mFa2 π cot • 4 m Also the volume of the pyramid which has one face H 2 POLYHEDRONS . 99 cae is ...
Página 100
Isaac Todhunter. Also the volume of the pyramid which has one face of the polyhedron for base and O for vertex is therefore the volume of the polyhedron is r ma2 π cot and 3 4 · mFra2 Π 12 cot m m 139. To find the volume of a ...
Isaac Todhunter. Also the volume of the pyramid which has one face of the polyhedron for base and O for vertex is therefore the volume of the polyhedron is r ma2 π cot and 3 4 · mFra2 Π 12 cot m m 139. To find the volume of a ...
Página 101
... volume of a tetrahedron . A tetrahedron is one - sixth of a parallelopiped which has the same altitude and its base double that of the tetrahedron ; thus if the edges and their inclinations are given we can take POLYHEDRONS . 101 B ...
... volume of a tetrahedron . A tetrahedron is one - sixth of a parallelopiped which has the same altitude and its base double that of the tetrahedron ; thus if the edges and their inclinations are given we can take POLYHEDRONS . 101 B ...
Página 102
... volume in Art . 139. The volume of a tetrahedron may also be expressed in terms of its six edges ; for in the figure of Art . 139 let BC = a ' , CA = b ' ′ , AB = c ; then . COS α = b2 + c2 2bc - a cos B = = c2 + a2 - b's 2 ca cos y ...
... volume in Art . 139. The volume of a tetrahedron may also be expressed in terms of its six edges ; for in the figure of Art . 139 let BC = a ' , CA = b ' ′ , AB = c ; then . COS α = b2 + c2 2bc - a cos B = = c2 + a2 - b's 2 ca cos y ...
Página 103
... volume to one of the spheres . 12. A regular octahedron is inscribed in a cube so that the corners of the octahedron are in the centres of the faces of the cube ; prove that the volume of the cube is six times that of the octahedron ...
... volume to one of the spheres . 12. A regular octahedron is inscribed in a cube so that the corners of the octahedron are in the centres of the faces of the cube ; prove that the volume of the cube is six times that of the octahedron ...
Otras ediciones - Ver todas
Spherical Trigonometry: For the Use of Colleges and Schools Isaac Todhunter Vista de fragmentos - 1949 |
Spherical Trigonometry: For the Use of Colleges and Schools Isaac Todhunter Vista de fragmentos - 1929 |
Términos y frases comunes
A+B+C ambiguity angular points approximately bisecting Cambridge centre circular measure cloth cos b cos cos² cos³ cosine Crown 8vo deduce denote drawn equal angles equilateral example expressed Fcap formulæ formulæ of Art greater Hence hypothenuse inscribed Legendre's Theorem less Let ABC lune meet middle point Napier's analogies Napier's Rules obtained octahedron opposite angle opposite sides parallelopiped perpendicular plane angles plane triangle Plane Trigonometry polar triangle pole polygon preceding article primitive triangle prove quadrant R₁ r₂ radius regular polyhedron respectively right angle right-angled triangles Second Edition shew shewn sides and angles Similarly sin b cos sin b sin sin² sin³ sine solid angle sphere spherical excess spherical triangle Spherical Trigonometry subtended Suppose surface tangent tetrahedron Treatise triangle ABC Trigono Trinity College values π π
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