Elements of Geometry and Trigonometry: With Notes |
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Page 110
... inclination of two planes is the quantity , greater or less , by which they are separated from each other ; this quantity is measured ( 7. IV . ) by the angle contained between two perpendiculars drawn in these planes , at the same ...
... inclination of two planes is the quantity , greater or less , by which they are separated from each other ; this quantity is measured ( 7. IV . ) by the angle contained between two perpendiculars drawn in these planes , at the same ...
Page 113
... inclination of the oblique line AB to the plane MN ; which inclination is evident- ly equal with respect to all such lines AB , AC , AD , as are equally distant from the perpendicular ; for all the triangles ABP , ACP , ADP , & c . are ...
... inclination of the oblique line AB to the plane MN ; which inclination is evident- ly equal with respect to all such lines AB , AC , AD , as are equally distant from the perpendicular ; for all the triangles ABP , ACP , ADP , & c . are ...
Page 123
... inclination of the planes ASC , ASB , be equal to that of the planes DTF , DTE . Having taken SB at pleasure , draw BŎ perpendicular to the plane ASC ; from the point O , D at which that perpendicular meets the plane , draw OA 7 BOOK V.
... inclination of the planes ASC , ASB , be equal to that of the planes DTF , DTE . Having taken SB at pleasure , draw BŎ perpendicular to the plane ASC ; from the point O , D at which that perpendicular meets the plane , draw OA 7 BOOK V.
Page 124
... inclination of the two planes ASB , ASC ; the angle PDE is that of the two planes DTE , DTF ; hence those two inclinations are equal to each other . It must , however , be observed , that the angle A of the right- angled triangle OAB is ...
... inclination of the two planes ASB , ASC ; the angle PDE is that of the two planes DTE , DTF ; hence those two inclinations are equal to each other . It must , however , be observed , that the angle A of the right- angled triangle OAB is ...
Page 126
... inclination of the two planes ASC , ASB in the solid angle . All we have to prove is , that the triangle AOb of the plane figure is equal to the triangle AOB of the solid figure . Now the two triangles B'SA , BSA are right - angled at A ...
... inclination of the two planes ASC , ASB in the solid angle . All we have to prove is , that the triangle AOb of the plane figure is equal to the triangle AOB of the solid figure . Now the two triangles B'SA , BSA are right - angled at A ...
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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
ACē adjacent adjacent angles altitude angle ACB angle BAC centre chord circ circle circular sector circumference circumscribed common cone consequently construction continued fraction convex surface cosē 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 sinē 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.