## Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry and Mensuration. Accompanied with All the Necessary Logarithmic and Trigonometric Tables |

### From inside the book

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**bisecting**it . 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 For , drawing FG perpendicular to AB , we see that the angle AFC ... Page 23

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**bisects**this line . Cor . II . If a straight line have any two of its points equi- distant from the extremities of a second line , it will be perpen- dicular to the second line and**bisect**it . THEOREM XIV . If a line be drawn**bisecting**... Page 29

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**bisect**- ing the angle ACG ( Post . VI . ) , and meet- ing AB at L , draw GL . The two triangles ACL , GCL , are equal ( T. XX . ) , and LG = LA . Therefore , AB = AL + LB = LG + B D Α C L D F E B E LB , which is greater than BG ( T. VII ... Page 30

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**bisects**the vertical angle of an isosce- les triangle ,**bisects**the base perpendicularly , and divides the triangle itself into two equal parts . Cor . II . An equilateral triangle is equi - angular , that is , has all its angles equal ... Page 35

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**bisect**each other , that is , they divide each other into halves . A D B C In the two triangles EAB and ECD , we have the angle EAB of the first equal to ECD of the second , being alternate an- gles in reference to the parallels AB and ...### 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