A Course of Mathematics: In Two Volumes. Composed for the Use of the Royal Military Academy, Volume 1Longman, Orme & Company, 1841 - Mathematics |
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Page 347
... angle they form be- tween them , is the angle contained by two lines , drawn from any point in the common section and at right angles to it , one of these lines in each plane . This is often called a dihedral angle . 5. ( 91a . ) If ...
... angle they form be- tween them , is the angle contained by two lines , drawn from any point in the common section and at right angles to it , one of these lines in each plane . This is often called a dihedral angle . 5. ( 91a . ) If ...
Page 359
... angle DEA = CEA . But the line joining AB bisects CG at right angles in E ; hence also the angle DEA is a right ... dihedral angle , and from any point in it perpendiculars be drawn to the planes which contain the dihedral angle , these ...
... angle DEA = CEA . But the line joining AB bisects CG at right angles in E ; hence also the angle DEA is a right ... dihedral angle , and from any point in it perpendiculars be drawn to the planes which contain the dihedral angle , these ...
Page 361
... angle at S be contained by the plane angles ASB , BSC , CSD , DSE , ESA : then the sum of these angles is always ... dihedral angle formed by DAC and EAC be equal to the dihedral angle formed by GBF and HBF . / C M In the lines CA and FB ...
... angle at S be contained by the plane angles ASB , BSC , CSD , DSE , ESA : then the sum of these angles is always ... dihedral angle formed by DAC and EAC be equal to the dihedral angle formed by GBF and HBF . / C M In the lines CA and FB ...
Page 362
... dihedral angles be shown to be equal . THEOREM XXV . ( 126. ) If two solid angles be contained , each by three plane ... angle at A be equal to the solid angle at B. E F EI Let the solid angle at A be applied to the solid angle at B , so ...
... dihedral angles be shown to be equal . THEOREM XXV . ( 126. ) If two solid angles be contained , each by three plane ... angle at A be equal to the solid angle at B. E F EI Let the solid angle at A be applied to the solid angle at B , so ...
Page 369
... dihedral angle of the planes of the great circles . 2. The square of the diagonal of any rectangular ... dihedral angles of a tetrahedron meet in one point ; and that point is the centre of a sphere inscribed in the tetrahedron . 5. If ...
... dihedral angle of the planes of the great circles . 2. The square of the diagonal of any rectangular ... dihedral angles of a tetrahedron meet in one point ; and that point is the centre of a sphere inscribed in the tetrahedron . 5. If ...
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Common terms and phrases
ABCD algebraic altitude arithmetical arithmetical progression base bisect breadth centre chord circle circumference coefficients common cone cosec cube root decimal denominator denoted diagonal diameter difference dihedral angle distance divided divisor draw drawn equal equation equiangular EXAMPLES expression figure fraction frustum geometrical given line greater hence inscribed integer intersection join length less lineation logarithms mantissa measure meeting method multiplied parallel parallel ruler parallelogram perpendicular plane polygon prism PROBLEM proportional quantity quotient radii radius ratio rectangle Reduce right angles rule Scholium segment sides sine solid angle solution square root straight line subtraction tangent THEOREM third trapezium triangle ABC u₁ vulgar fraction Whence