Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry and Mensuration. Accompanied with All the Necessary Logarithmic and Trigonometric Tables |
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Page vi
... Theorems 137 138 SIXTH BOOK . Definitions . 152 Theorems 154 SEVENTH BOOK . Definitions Theorems Definitions Theorems EIGHTH BOOK . ............... Regular polyedrons . Application of Algebra to the solution of Geometrical Problems ...
... Theorems 137 138 SIXTH BOOK . Definitions . 152 Theorems 154 SEVENTH BOOK . Definitions Theorems Definitions Theorems EIGHTH BOOK . ............... Regular polyedrons . Application of Algebra to the solution of Geometrical Problems ...
Page 12
... theorem is a proposition which requires a demonstra- tion . VI . A corollary is an immediate consequence of one or more propositions . If any new course of reasoning is required to establish it , this reasoning is so simple that it may ...
... theorem is a proposition which requires a demonstra- tion . VI . A corollary is an immediate consequence of one or more propositions . If any new course of reasoning is required to establish it , this reasoning is so simple that it may ...
Page 14
... THEOREM I. When a straight line meets or crosses another , the adjacent angles are supplements ; and the opposite angles are equal . A G C B F For , drawing FG perpendicular to AB ... Theorem . side . 14 GEOMETRY . THEOREMS Of angles.
... THEOREM I. When a straight line meets or crosses another , the adjacent angles are supplements ; and the opposite angles are equal . A G C B F For , drawing FG perpendicular to AB ... Theorem . side . 14 GEOMETRY . THEOREMS Of angles.
Page 18
... THEOREM VI . The exterior angle , formed by producing one of the sides of a triangle , is equal to the sum of the two interior and opposite angles of the triangle . In the triangle ABC , if the side AB be pro- duced to D , the exterior ...
... THEOREM VI . The exterior angle , formed by producing one of the sides of a triangle , is equal to the sum of the two interior and opposite angles of the triangle . In the triangle ABC , if the side AB be pro- duced to D , the exterior ...
Page 19
... THEOREM VII . Either side of any triangle is less than the sum of the other two sides , and greater than their difference . First . The straight line AB is the shortest distance between A and B ( A. XI . ) , and there- fore shorter than ...
... THEOREM VII . Either side of any triangle is less than the sum of the other two sides , and greater than their difference . First . The straight line AB is the shortest distance between A and B ( A. XI . ) , and there- fore shorter than ...
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Common terms and phrases
ABē ABCD altitude angles equal apothem base bisecting centre chord circle circumference circumscribed circle circumscribed polygon cone consequently corresponding cosec Cosine Cotang cubic cylinder decimal denote diameter dicular distance divided draw drawn equally distant equation exterior angles feet figure frustum GEOMETRY given angle given line gives greater half hence homologous hypotenuse inches included angle intersection logarithm measure middle point multiplied number of sides opposite parallel parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedral angle polyedron prism PROBLEM proportion pyramid quadrant quadrilateral radii radius ratio rectangle regular polygon respectively equal right angles right-angled triangle Scholium secant similar similar triangles Sine slant height solid sphere spherical triangle square straight line subtract suppose surface Tang Tangent THEOREM three sides triangle ABC volume