Elements of Geometry and Trigonometry: With Notes |
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Page 2
... perpendicular to CD . XI . Every angle BAC , less than D right angle , is an acute angle ; every angle DEF , greater than a right angle , is an obtuse angle . E XII . Two lines are said to be parallel , when , being situated in the same ...
... perpendicular to CD . XI . Every angle BAC , less than D right angle , is an acute angle ; every angle DEF , greater than a right angle , is an obtuse angle . E XII . Two lines are said to be parallel , when , being situated in the same ...
Page 5
... perpendicular to AB , and GH to EF ; the angles ACD and EGH will be equal to each other . D H G F B Take the four distances CA , CB , GE , GF all equal ; the distance AB will be equal to the distance EF , and the line EF being placed on ...
... perpendicular to AB , and GH to EF ; the angles ACD and EGH will be equal to each other . D H G F B Take the four distances CA , CB , GE , GF all equal ; the distance AB will be equal to the distance EF , and the line EF being placed on ...
Page 6
... perpendicular to AB , in like manner AB will be perpendicular to DE . For , since DE is perpendicular to AB , the angle ACD must be equal to its adjacent one DCB , and both of them must be right . But since ACD is a right angle , its ...
... perpendicular to AB , in like manner AB will be perpendicular to DE . For , since DE is perpendicular to AB , the angle ACD must be equal to its adjacent one DCB , and both of them must be right . But since ACD is a right angle , its ...
Page 12
... perpendicular to that base , and divides the angle at the vertex into two equal parts . In a triangle which is not isosceles , any side may be assumed indifferently as the base ; and the vertex is , in that case , the vertex of the ...
... perpendicular to that base , and divides the angle at the vertex into two equal parts . In a triangle which is not isosceles , any side may be assumed indifferently as the base ; and the vertex is , in that case , the vertex of the ...
Page 14
... perpendicular AB will be shorter than any oblique line . Secondly , The two oblique lines , AC , AE drawn on different sides of the perpendicular , at equal distances BC , BE , will be equal . Thirdly , Of two oblique lines , AC , AD ...
... perpendicular AB will be shorter than any oblique line . Secondly , The two oblique lines , AC , AE drawn on different sides of the perpendicular , at equal distances BC , BE , will be equal . Thirdly , Of two oblique lines , AC , AD ...
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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.