## 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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**Theorems**137 138 SIXTH BOOK . Definitions ..**Theorems**.. 152 154 SEVENTH BOOK . Definitions ...**Theorems**.. EIGHTH BOOK . 174 177 ... Definitions 191**Theorems**192 Regular polyedrons .. 208 Application of Algebra to the solution of ... Page 12

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**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

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**THEOREM**I. When a straight line meets or crosses another , the adjacent angles are supplements ; and the opposite ...**Theorem**. Cor . III . And as all the angles that 14 GEOMETRY .**THEOREMS**Of angles. Page 15

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**THEOREM**II . If through the vertex of any angle , lines are drawn perpen- dicular respectively to its sides , they will form a new angle , either equal to the first , or supplementary to it . Let BAC be the given angle , DE perpendic ... Page 18

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**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 ...### Other editions - View all

### Common terms and phrases

a+b+c ACē altitude angles equal apothem bisect centre chord circ circumference cone consequently corresponding cosec Cosine Cotang cylinder decimal denote described diameter dicular distance divided draw drawn equation equivalent exterior angles feet figure formed frustum give given line greater half hence homologous sides hypotenuse inscribed circle intersection logarithm measure middle point multiplied number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedral angle polyedron prism PROBLEM proportion pyramid quadrant radii radius ratio rectangle regular inscribed regular polygon respectively equal right angles right-angled triangle Scholium secant sector similar similar triangles Sine slant height solid sphere spherical triangle square straight line subtract suppose surface Tang tangent THEOREM three sides triangle ABC triangular prism vertex volume