Elements of Geometry and Trigonometry: With Notes |
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Page 48
... altitude of a parallelogram is the perpendicular EF which measures the dis- tance of two opposite sides AB , CD , taken as bases . V. The altitude of a triangle is the perpendicular AD let fall from the vertex of an angle A , on the ...
... altitude of a parallelogram is the perpendicular EF which measures the dis- tance of two opposite sides AB , CD , taken as bases . V. The altitude of a triangle is the perpendicular AD let fall from the vertex of an angle A , on the ...
Page 50
... altitude , their up- bases DC , FE will be situated per both in one straight line parallel to AB . Now , from the ... altitude , are equivalent . Cor . Every parallelogram is equivalent to the rectangle which has the same base and the ...
... altitude , their up- bases DC , FE will be situated per both in one straight line parallel to AB . Now , from the ... altitude , are equivalent . Cor . Every parallelogram is equivalent to the rectangle which has the same base and the ...
Page 51
... altitude are to each other as their bases . Let ABCD , AEFD be two rect- angles having the common altitude AD : they are to each other as their bases AB , AE . Suppose , first , that the bases are commensurable , and are to each other ...
... altitude are to each other as their bases . Let ABCD , AEFD be two rect- angles having the common altitude AD : they are to each other as their bases AB , AE . Suppose , first , that the bases are commensurable , and are to each other ...
Page 52
... altitude , are to each other as their bases AB , AE in like manner the two rect- angles AEHD , AEGF , having the same altitude AE , are to each other as their bases AD , AF : thus we have the two pro- portions , ABCD : AEHD :: AB : AE ...
... altitude , are to each other as their bases AB , AE in like manner the two rect- angles AEHD , AEGF , having the same altitude AE , are to each other as their bases AD , AF : thus we have the two pro- portions , ABCD : AEHD :: AB : AE ...
Page 53
... altitude seven , this second rectangle will be represented by the number 12 × 7 = 84 ; and we shall hence be ... altitude . For the parallelogram ABCD is equivalent FD ( 1. III . Cor . ) to the rectangle ABEF , which has the same base AB ...
... altitude seven , this second rectangle will be represented by the number 12 × 7 = 84 ; and we shall hence be ... altitude . For the parallelogram ABCD is equivalent FD ( 1. III . Cor . ) to the rectangle ABEF , which has the same base AB ...
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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
AC² adjacent adjacent angles altitude angle ACB angle BAC centre chord circ circle circular sector circumference circumscribed common cone consequently construction continued fraction convex surface cos² 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 sin² 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.