## 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 4

... c . 3. A space , a surface , and a line , may be considered in two distinct ways . We may consider them in ...

... c . 3. A space , a surface , and a line , may be considered in two distinct ways . We may consider them in ...

**A .B**.**C**.D The position of a point in reference to any other point is determined by its direction and distance from ... Page 16

... figure ( T. III . ) , each to each . Thus the angles

... figure ( T. III . ) , each to each . Thus the angles

**a , b**,**c**, etc. , are respectively equal to the exterior F A**a B C**angles**A , B**,**C**, etc .; but the former angles are together equal to four right angles ( T. I. , C. III 16 GEOMETRY . Page 17

... B Let ABCDFG be a convex polygon . Conceive the sides to be produced all in the same direction , forming exterior angles , which we will denote by the capital letters

... B Let ABCDFG be a convex polygon . Conceive the sides to be produced all in the same direction , forming exterior angles , which we will denote by the capital letters

**A , B**,**C**, etc. , while their corresponding in- terior angles are ... Page 19

... C First . The straight line AB is the shortest distance between A and B ( A. XI . ) , and there- fore shorter than the broken line AC + CB . The same reasoning applies to each of the sides . Hence , we have AB < AC + CB ; AC < AB + CB ;

... C First . The straight line AB is the shortest distance between A and B ( A. XI . ) , and there- fore shorter than the broken line AC + CB . The same reasoning applies to each of the sides . Hence , we have AB < AC + CB ; AC < AB + CB ;

**BC**... Page 21

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**C**the figure CDE about DE as a hinge , until it returns into its primitive plane on the opposite side of AB , having the position FDE . Since each of the angles FDE and CDE is right , CDF is a straight line ( T. I. ,**C**. IV . ) . By the ...### 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