Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page 33
... common , and the included angles ABC and FBC equal , because both are right angles : hence , the angles ACB and FCB are equal ( P. V. ) . But ACB is , by a hypothesis , a right angle : hence , FCB must also be a right angle , and ...
... common , and the included angles ABC and FBC equal , because both are right angles : hence , the angles ACB and FCB are equal ( P. V. ) . But ACB is , by a hypothesis , a right angle : hence , FCB must also be a right angle , and ...
Page 34
... common , and the included angles ABC and FBC equal , because both are right angles : hence , FC is equal to AC ( P. V. ) . But , AF is shorter than ACF ( A. 12 ) : hence , AB , the half of AF , is shorter than AC , the half of ACF ...
... common , and the included angles ABC and FBC equal , because both are right angles : hence , FC is equal to AC ( P. V. ) . But , AF is shorter than ACF ( A. 12 ) : hence , AB , the half of AF , is shorter than AC , the half of ACF ...
Page 39
... common part GBD , we have the angle GBE equal to the angle FAG . Again , the angles BGE and AGF are equal , because they are vertical an- gles ( P. II . ) : hence , the triangles GEB and GFA have two of their angles and the included ...
... common part GBD , we have the angle GBE equal to the angle FAG . Again , the angles BGE and AGF are equal , because they are vertical an- gles ( P. II . ) : hence , the triangles GEB and GFA have two of their angles and the included ...
Page 40
... equal to two right angles ; the sum of BGH and HGA is also equal to two right angles ( P. I. ) : hence , these sums are equal . are equal . Taking away the G / H B common part BGH , there remains the angle GHD equal 40 GEOMETRY .
... equal to two right angles ; the sum of BGH and HGA is also equal to two right angles ( P. I. ) : hence , these sums are equal . are equal . Taking away the G / H B common part BGH , there remains the angle GHD equal 40 GEOMETRY .
Page 41
... common part BGH , there remains the angle GHD equal to HGA . In like manner , it may be shown that BGH and GHC are equal . Cor . 3. If a straight line intersects two parallels , the opposite exterior and interior angles are equal . The ...
... common part BGH , there remains the angle GHD equal to HGA . In like manner , it may be shown that BGH and GHC are equal . Cor . 3. If a straight line intersects two parallels , the opposite exterior and interior angles are equal . The ...
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Common terms and phrases
AB² ABCD AC² adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence